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Business Math: A Step-by-Step Handbook

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Jean-Paul Olivier

Copyright Year: 2017

Last Update: 2021

Publisher: Lyryx

Language: English

Formats Available

Conditions of use.

Attribution-NonCommercial-ShareAlike

Table of Contents

PART 1: Mathematic Fundamentals for Business

  • Chapter 1: How To Use This Textbook
  • Chapter 2: Back to the Basics
  • Chapter 3: General Business Management Applications

PART 2: Applications in Human Resources, Economics, Marketing, and Accounting

  • Chapter 4: Human Resource & Economic Applications
  • Chapter 5: Marketing and Accounting Fundamentals
  • Chapter 6: Marketing Applications
  • Chapter 7: Accounting Applications

PART 3: Applications in Finance, Banking, and Investing: Working With Single Payments

  • Chapter 8: Simple Interest: Working With Single Payment & Applications
  • Chapter 9: Compound Interest: Working With Single Payments
  • Chapter 10: Compound Interest: Applications Involving Single Payments

PART 4: Applications in FInance, Banking, and Investing: Working With A Continuous Series of Payments (Annuities)

  • Chapter 11: Compound Interest: Annuities
  • Chapter 12: Compound Interest: Special Applications of Annuities

PART 5: Applications in Finance, Banking, and Investing: Amortization and Special Concepts

  • Chapter 13: Understanding Amortization & Its Applications
  • Chapter 14: Bonds and Sinking Funds
  • Chapter 15: Making Good Decisions

Ancillary Material

About the book.

Business Mathematics was written to meet the needs of a twenty-first century student. It takes a systematic approach to helping students learn how to think and centers on a structured process termed the PUPP Model (Plan, Understand, Perform, and Present). This process is found throughout the text and in every guided example to help students develop a step-by-step problem-solving approach.

This textbook simplifies and integrates annuity types and variable calculations, utilizes relevant algebraic symbols, and is integrated with the Texas Instruments BAII+ calculator. It also contains structured exercises, annotated and detailed formulas, and relevant personal and professional applications in discussion, guided examples, case studies, and even homework questions.

About the Contributors

Jean-Paul Olivier has been teaching Business and Financial Mathematics, as well as Business Statistics and Quantitative Methods for the past 21 years. He is a dedicated instructor interested in helping his students succeed through multi-media teaching involving PowerPoints, videos, whiteboards, in-class discussions, readings, online software, and homework practice. He regularly facilitates these quantitative courses and leads a team of instructors. You may have met Jean-Paul at various mathematical and statistical symposiums held throughout Canada (and the world). He has contributed to various mathematical publications for the major publishers with respect to reviews, PowerPoint development, online algorithmic authoring, technical checks, and co-authoring of textbooks. This text represents Jean-Paul’s first venture into solo authoring

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Business Mathematics

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Business Mathematics consists of Mathematical concepts related to business. It comprises mainly profit, loss and interest. Maths is the base of any business. Business Mathematics financial formulas, measurements which helps to calculate profit and loss , the interest rates, tax calculations, salary calculations, which helps to finish the business tasks effectively and efficiently.

Table of contents:

  • Related Topics
  • Important Terms
  • Problems and Solutions

Business Mathematics is highly related to the Statistics concepts which give solutions to business problems. In business, we deal with the exchange of money or products, which have a monetary value. Each business leads to some profit and some loss. To identify these factors, we have to study the primary topics of Maths such as formulas to find a profit, loss, their percentages, discount, etc. Even Though, the requirement of this subject does not contain pure Maths, it needs Mathematical thinking and some Maths formulas . Here, we will discuss what is Business Mathematics, terminologies, and important formulas with problems and solutions.

What is Business Mathematics?

Business Math always deals with profit or loss. The cost of a product is fixed by taking into consideration it’s profit, margin, cash discount, trade discount, etc. Business mathematics is used by commercial companies to record and manage business works. Commercial businesses use maths in departments of accounting, inventory management, marketing, sales forecasting and financial analysis.

Business Mathematics Topics

The most important topics covered in Business Mathematics are:

  • Profit and Loss
  • Simple and Compound Interest
  • Interest Rates
  • Markups and markdowns
  • Taxes and Tax Laws
  • Discount Factor
  • Depreciation
  • Future and Present Values
  • Financial Statements

Business Mathematics Basic Terms

  • Selling Price: The market price is taken to sell a product.
  • Cost Price: The original price of the product is the cost price.
  • Profit: If the selling price is more than the cost price, the difference in the prices is the profit.
  • Loss: If the selling price is less than the cost price, the difference in the prices is the loss.
  • Discount: The reduced amount in the selling price of a product.
  • Simple Interest: Simple interest is that interest which is counted against the capital amount or the portion of the main amount that remains unpaid.
  • Compound Interest: Compound interest is the investment rate that increases exponentially.

Business Mathematics Formulas

Here, the 9 basic Business Mathematics formulas that we cannot ignore. They are:

Net Income Formula:

Net Income = Revenue – Expense

Accounting Equation:

Assets = Liabilities + Equity

Equity = Assets – Liabilities

Cost of Goods Sold Formula:

COGS = Beginning inventory + Purchase during the period – Ending inventory

Break-Even point Formula:

Break-Even Point = Fixed cost / (Sales Price per unit – variable cost per unit)

Current Ratio Formula:

Current Ratio = Current Assets / Current Liabilities

Profit Margin Formula:

Profit Margin = (Net Income/ Revenue) × 100

Return of Investment (ROI) Formula:

ROI = [(Invest gain – Cost of Investment)/ Cost of Investment] × 100

Markup Formula:

Markup Percentage = [(Revenue- COGS)/COGS] × 100

Selling Price using Markup = (COGS × markup percentage) + COGS

COGS = Cost of goods sold

Inventory Shrinkage Formula:

Inventory Shrinkage = [(Recorded Inventory – Actual Inventory)/ Recorded Inventory] × 100

Business Mathematics Example

While doing business, one can earn a good profit or face loss. The price of a product is fixed, taking into consideration it’s cost price, profit, margin, trade discount, cash discount, etc. The price marked on the commodity is called marked price or catalogue price. For trading purposes, the manufacturer proposes a discount on the MRP to the buyer. This is called a trade discount. In addition to the trade discount, if the buyer pays cash against goods, he gets another cut called cash discount. The price of the object after subtracting the trade discount and cash discount is called the selling price. Thus, we have, Selling price = Cost price – Dis counts.  Let us discuss the most important concept called “Profit and Loss” here.

Profit and Loss:

A profit is the earned amount received by a business on selling a product whereas loss is the amount which is less than the actual price of the product. The formula for profit and loss is given based on the selling price and cost price of a commodity.

Both these measures have their percentage value also and they are given by;

Business Mathematics Problems and Solutions

Question 1: A music system was bought for Rs.10,500 and sold at Rs.9,500. Find the amount of profit or loss.

Solution: Given,

Cost Price of the music system = Rs.10,500

Selling Price of the music system = Rs. 9,500

We can see here, C.P. is greater than S.P. Therefore, there is a loss in this business.

Hence, we need to calculate the loss amount.

Loss = C.P. – S.P.

Loss = 10,500 – 9,500 = Rs.1,000/-.

Question 2: A pair of shoes is bought at Rs 200 and sold at a profit of 10%. Find the selling price of the shoes.

Profit = 10% of Rs.200

P = (10/100) × 200 = Rs. 20

S.P. = C.P. + Profit

S.P. = 200 + 20 = Rs.220/-

Question 3: If the cost price of an article including 20% for taxes is Rs. 186, then find the original cost of the article excluding taxes.

Let x be the original price of an article.

Tax = 20% of x = (20/100) × x = 0.2x

According to the given statement,

Original cost + tax = New cost price

x + 0.2x = Rs. 186

1.2x = Rs. 186

x = Rs. 186/1.2

x = Rs. 155

Therefore, the cost of the article without taxes = Rs. 155

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What to Know About Business Math

  • Math Tutorials
  • Pre Algebra & Algebra
  • Exponential Decay
  • Worksheets By Grade

No matter what your career, business math will give you indispensable real-world knowledge to help you take control of your finances. Take the first step in making better choices with your money by getting familiar with business mathematics.

What Is Business Math?

Business math is a type of mathematics course that is meant to teach people about money and provide them with the tools they need to make informed financial decisions. Business math not only teaches about the specifics of finances related to owning and operating a business but also offers helpful advice and information related to personal finance. These classes prepare any consumer to manage their finances responsibly and profitably by explaining everything they need to know about accounting, economics, marketing, financial analysis, and more. Business math will help to make the ins and outs of money and commerce make sense, even to the most math-averse individuals, using relevant and authentic applications.

Why Take Business Math?

Business math is not just for business owners, contrary to what its name might suggest. A number of different professionals utilize business math-related skills every day.

Bankers, accountants, and tax consultants all need to become well-acquainted with every aspect of corporate and personal finance in order to deliver appropriate advice and problem solve with customers. Real estate and property professionals also employ business mathematics often when calculating their commission, navigating the mortgage process, and managing taxes and fees upon closing a deal.

When it comes to professions that deal more with capital allocation, such as investment consulting and stockbroking, understanding investment growths and losses and making long-term financial predictions is a fundamental part of the daily job. Without business math, none of these jobs could function.

For those that do own a business, business math is even more important. Business math can help these individuals to be successful by providing them with a solid understanding of how to manage goods and services to make a profit. It teaches them how to juggle discounts, markups, overhead, profits, inventory management, payroll, revenue, and all of the other complexities of running a business so that their career and finances can flourish.

Topics Covered in Business Math

Economics, accounting, and other consumer math subjects likely to be taught in a business mathematics course include:

  • Depreciation
  • Discount Factor
  • Financial Statements (personal or business)
  • Future and Present Values
  • Interest rates
  • Investment and Wealth Management
  • Markups and Markdowns
  • Mortgage Finance and Amortization
  • Product inventory
  • Taxes and Tax Laws
  • Simple and Compound Interest

Mathematical Skills That Will Prepare You for Business Math

If you decide that a business math course will help further your career or if you would just like to be more financially savvy, a strong understanding of the following mathematical concepts will help to prepare you for this course.

  • Be comfortable reading, writing, and making estimates for whole numbers up to 1,000,000.
  • Be able to add, subtract, multiply, and divide any integers (using a calculator if needed).

Fractions, Decimals, and Percentages

  • Be able to add, subtract, multiply, and divide fractions, simplifying as needed.
  • Be able to calculate percentages.
  • Be able to convert between fractions, decimals, and percentages.

Basic Algebra

  • Be able to solve equations with one or more variables.
  • Be able to calculate proportions .
  • Be able to solve multi-operational equations.
  • Be able to correctly apply values and variables to any given formula (e.g. when given the formula for calculating simple interest, I=Prt, be able to input the correct values for P=principal, r=interest rate, and t=time in years to solve for I=interest). These formulas do not need to be memorized.
  • Be able to solve for the mean, median and mode of a data set
  • Be able to interpret and understand the significance of the mean, median, and mode.
  • Be able to interpret different types of graphs and charts such as bar and line graphs, scatter plots, and pie charts to understand the relationships between different variables.
  • Popular Math Terms and Definitions
  • Definition of a Percentile in Statistics and How to Calculate It
  • 7th Grade Math Course of Study
  • MBA Math Skills Every Business Student Needs
  • The Typical 10th Grade Math Curriculum
  • Eighth Grade Math Concepts
  • What Is Profit Sharing? Pros and Cons
  • Business Majors: Finance
  • Lesson Plan: Adding and Multiplying Decimals
  • Compound Interest Worksheets
  • Two-Digit Multiplication Worksheets to Practice With
  • What Is Disposable Income? Definition and Examples
  • The Horse Problem: A Math Challenge
  • What Can I Do With a Degree in Business?
  • Exponents and Bases

essay about business math

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Business Mathematics: Course, Topics, Importance

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  • Updated on  
  • Mar 20, 2023

essay about business math

Business Mathematics is a specialized field of mathematics that deals with the application of mathematical concepts and techniques in business settings. It involves the use of mathematical tools and models to analyze business data, solve problems, and make informed decisions. A Business Mathematics Course is designed to equip students with the necessary skills and knowledge to handle complex business situations using mathematical concepts.

Ug- Bachelors CoursePg- Masters Course 
Ug- 3 Year Pg- 4 Year 
Ug- 10+2 with at least  50%Pg- Graduate with at least  50%

This Blog Includes:

What is business mathematics, why study business mathematics , top universities offering business mathematics courses, topics covered in business mathematics course, importance of business mathematics, admission process, english proficiency requirements , documents required, job and salary .

This course is an educational program that focuses on the application of mathematical concepts and techniques to solve real-world business problems. The course covers various topics, including financial mathematics, probability , statistics, linear programming, and game theory, among others. Business Mathematics is an interdisciplinary field that combines mathematical concepts with business principles and practices. It helps students develop strong analytical and problem-solving skills that are essential for making informed decisions and managing complex business scenarios.

There are several reasons why studying a Business Mathematics Course can be beneficial. Here are some of the key reasons:

  • This course can help you advance your career by providing you with specialized knowledge and skills that are in demand in the job market.
  • It can give you a competitive edge over other candidates and open up opportunities for higher-paying and more rewarding positions.
  • This course helps you develop strong analytical skills that are essential for analyzing complex business problems and making informed decisions. You learn how to approach problems systematically, break them down into smaller components, and solve them using mathematical models and techniques.
  • This course is directly applicable to real-world business scenarios, providing you with practical skills that can be immediately applied in the workplace. You learn how to use mathematical models and techniques to analyze data, manage risks, plan finances, and optimize operations.
  • Business Mathematics provides you with tools to make informed decisions based on data analysis and modelling, which can lead to improved business outcomes.

Also, Read- Top Management Courses

There are several universities that provide Business Mathematics courses, below are some of them 

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A Business Mathematics Course covers a broad range of topics. Some of the essential topics covered in this Course include

This topic covers the concepts of simple and compound interest, annuities, amortization, and the time value of money.
ProbabilityThis topic involves the study of random events and their likelihood of occurrence. It includes the study of probability distributions, expected values, and variance.
This topic consists of the collection, analysis, and interpretation of data. It consists of the study of descriptive statistics, inferential statistics, hypothesis testing, and regression analysis
This topic involves using mathematical models to optimise business operations. It includes the study of linear equations, inequalities, and optimization techniques.
Game TheoryThis topic consists of the study of strategic decision-making in competitive situations. It consists of the study of Nash equilibrium, dominant strategies, and the prisoner’s dilemma.

Business Mathematics is a critical aspect of any business operation. Here are some reasons why this course is essential:

  • Data Analysis: Business Mathematics provides tools and techniques to analyze business data, which is crucial for making informed decisions.
  • Risk Management: This course helps businesses to manage risks by identifying potential risks and developing strategies to mitigate them.
  • Financial Planning: Business Mathematics helps businesses to plan and manage their finances effectively. It involves the use of mathematical models to forecast future revenues and expenses.
  • Optimisation: This course helps businesses to optimize their operations, improve efficiency, and reduce costs.

If you want to pursue a Business Mathematics course our expert at leverage edu help you to make your admission process easy 

  • First, you have to enrol with us on the Leverage edu app, and then we will assign you, a country expert,
  • With the help of AI course finder , your expert will provide you with the best courses along with the universities that you can easily target based on your academic performance 
  • Essays, letters of recommendation , and statements of purpose also take care of by us, we have a dedicated editorial team that will share and help you with the format 
  • Once you are done with documentation verification, we will put your application in universities for further process
  • For more guidance, you can call us immediately on 1800 57 2000, we will be ready to guide and help you out with the entire process.

Also Read- Scope of MBA in Finance

For the abroad study process, students need to full fill the requirement of English Proficiency tests like IELTS, TOEFL, PTE , Duolingo etc.

  • Scores can differ from university to university but this is the eligible score from in a given range Students can easily target good university 
  • Below given table includes the eligibility score, for the English test 
IELTS Overall band 6.5
Above 91  
PTEAbove 57
Above 110

These are the mandatory document required for the admission process 

  • Academic Transcripts  
  • English Proficiency Test scorecard

Career Scope

The career scope of the Business Mathematics courses provides you lots of job options, the person knowing this subject can find their career in the following fields. 

  • Data Analyst
  • Data Scientist
  • Business Intelligence Analyst
  • Operation Manager 
  • Financial Manage
  • Financial Analyst

Business Mathematics Courses can lead to various job opportunities with competitive salaries in different industries. The salary ranges mentioned above are based on averages and may vary depending on factors such as experience, location, and industry.

$65,000 to $100,000 per year,53,20,315 to 81,91,650 INR
$50,000 to $80,000 per year40,92,550 to 65,52,512 INR
Business Intelligence Analyst$70,000 to $100,000 per year57,33,448 to 81,91,650 INR
$80,000 to $120,000 per year65,52,512 to 98,29,980 INR
Operations Manager$70,000 to $100,000 per year57,33,448 to 81,91,650 INR
$50,000 to $80,000 per year40,92,550 to 65,52,512 INR

Also Read- Vedic Maths

A: Anyone interested in learning how to apply mathematical concepts to business settings can take a Business Mathematics Course.

A: A Business Mathematics Course can prepare you for various jobs, including financial analyst, data analysis, operations management, and market research.

A: The duration of a Business Mathematics Course depends on the institution and program. Typically, it can range from a few weeks to a year or more.

Well, we hope that this blog provided you with the essential details about Business Mathematics. If you are planning to study a degree in mathematics, take the help of Leverage Edu ’s AI-based tool narrows down a customised list of courses and universities that match your interests and preferences thus guiding you in making an informed decision towards your dream career!

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  • Business Mathematics

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Mathematics

Mathematics is considered to be the study of numbers, shapes & patterns and when this discipline is applied in a business, it becomes Business Maths. For a business, it is a vital subject that a student has to deal with. It acts as a tool that helps in solving and controlling various business problems. The basic objective to learn this subject is to adapt the knowledge of various mathematical tools and techniques and models which helps in dealing with real-life business situations. It is also referred to as "commercial mathematics". In this article, we will talk about this particular subject ie. Business Mathematics. What does it mean, what are the various topics included in this, the importance of learning mathematics for business along with its scope? 

What is Business Mathematics?

This is the discipline that consists of mathematical concepts related to the business and it is not only limited to cost, profit/loss, and interest. It is beyond these basic concepts and includes other mathematical concepts as well. The operations or financial activities are controlled by business mathematics such as control on the cash flows, payroll, revenue, financial analysis, risk analysis, etc. The mathematical formulas help in almost every field of business such as in wage or salary calculation, employee performance management, profit & loss analysis, etc. Mathematical models help in analysing the business problems and finding out the appropriate solutions so that those problems do not arise in the future. It also helps in evaluating the problems and taking appropriate decisions in this regard to simplifying the business processes.

Topics covered in Business Maths

The fundamental topics covered in business maths subject are mentioned below which can be covered from any business maths book:

Ratios and Proportions

Simple and Compound interest including the application of Annuity

Bill Discounting & Average Due Date

Mathematical reasoning (basic application)

Set Theory &  application of Venn Diagram

Variation, Indices, Logarithms

Permutation and Combinations

Linear Simultaneous Equations

Quadratic Equations

Determinants and Matrices

Constant and variables, Functions, Limit & Continuity

Differentiability & Differentiation, Partial Differentiation

Derivatives 

Maxima & Minima

Indefinite Integrals

Definite Integrals

Statistical Representation of Data

Measures of Central Tendency and Dispersion

Correlation and Regression

Index Numbers

Time Series Analysis

Probability

Theoretical Distribution

Importance of Commercial Mathematics

Business is all about management. Management of each and every aspect related to the business helps it to grow and in this management commercial mathematics plays a huge role.

Business maths plays a vital role in creating the base of the business. In a business, it is very important to analyse the costs associated with the production of goods and services such as cost of raw materials, plant & machinery, rent, wages, marketing, administrative expenses, warehousing, interest as well as repayment of loans, etc. Only after analysing all the costs, estimation of profits can be done and in this whole process, commercial maths plays a prominent role.  

This particular subject helps in pricing the products and services after analysing all the costs and then in calculating the gross or net profit. This helps in analysing if the business is enough to run all the operations and if they are getting profits from the business or not.

This discipline helps in maintaining the good health of the company. It helps in calculating all the business taxes which is also a vital part of the company. Mathematics helps in maintaining this and helps in calculating the actual business profit after deduction of all the taxes & other deductions.

Business Maths helps in assessing the financial performance of the business. It helps in estimating the incomes & expenditures along with the risk analysis. It also helps in the assessment of the rivals and their key areas along with their business strategies.

This very discipline helps in taking and improving decision making about different aspects of business such as costs, raw materials, marketing, advertising, strategies for the short and long term, etc. It helps in analysing unforeseen situations and making decisions in favour of the company.

Scope 

Commercial Maths is one of the important disciplines for the commerce stream. It is being taught to the students from school level to college level in different mathematical finance courses or business maths courses or any other courses related to the commerce field. A person needs other skills as well along with knowledge of mathematics such as economics, business studies, accountancy along with good communication skills. The persons knowing this subject can found their career in the following fields:

Securities analyst

Equity analyst

Expenditure analysts

Budget Analyst

Market Research Analyst

Policy underwriters

Risk analyst

Financial analysts

Investment analysts

What is the definition of Business Mathematics?

Profit and loss are constantly present in business maths. A product's cost is determined by taking into account its profit, margin, cash discount, trade discount, and other factors. Commercial businesses utilise business mathematics to track and manage their operations. To make a few like Accounts, inventory managers, marketing, sales tally, and financial analysis are all areas where maths is used in commercial organisations.

Topics in Business Mathematics

The following are some of the most essential subjects studied in Business Mathematics:

Profit and Loss Statements

Easy and combined interests are mainly the two types of  interests.

Rates of Interest

Markups and markdowns are two different types of markups and markdowns.

Taxes and Tax Legislation

Factor of Discount

Depreciation

Values of the Future and Present

Statements of Financial Position

The value of fundamental maths in the business

More knowledge than product manufacturing or service distribution is required to learn a business. When The firm is established, it should take care of its finances as well as make adequate plans for its survival.

Understanding corporate mathematics is essential for maintaining efficient operations and accurate record keeping. Pricing items or services is required from the beginning to the finish, when we must determine whether the aim was met. Let's look at some examples of how maths is used in business.

Problems and Solutions in Business Mathematics

Example 1: A music system cost Rs.10,500 and was sold for Rs.9,500. Calculate the loss or profits.

Solution:  As stated,

Cost Price or the CP of a music system is = Rs.10,500

Selling Price or the SP of system is = Rs. 9,500

We can conclude here that C.P. is greater than S.P. Hence, it's a loss in business.

Therefore, we need to tally the loss amount.

Loss = C.P. – S.P.

Loss = 10,500 – 9,500 = Rs.1,000/-.

Example 2: A pair of shoes is purchased for Rs 200 and sold at a 10% profit. Determine the shoe's retail price.

Solution:  Given,

Profit = 10% of Rs.200

P = (10/100) × 200 = Rs. 20

S.P. = C.P. + Profit

S.P. = 200 + 20 = Rs.220/-

To wrap up the discussion of Business maths, we have learned about its meaning, topics, importance as well as scope of this subject. Basically, it includes all the mathematical concepts that can be applied to business and management so that it can run successfully. The basic purpose of Mathematics for economics and business is to analyse the business problems and find out the solutions of those problems and control the issues in such a way that it does not occur again in the future and if occurs damages should be minimum . It helps in almost every part of the business such as income & expenditure, sales and purchases, profit & loss, risk management, financial management, payroll management, etc. Besides this, this subject offers various career fields as well.

Mathematical concepts relating to business make up business mathematics. Profit, loss, and interest make up the majority of it. All startups are built on the platform of mathematics sciences. To name a few like Loss and profit, interest rates, tax calculators, and wage calculations are all computed using financial formulae, measurements, and calculations in business mathematics, all of which contribute in performing corporate activities successfully and efficiently.

Business Mathematics is closely linked to statistical principles that provide answers to business challenges. Every business generates a profit and a loss. To discover these aspects, we must study basic maths topics such as profit and loss formulas, percentages, discounts, and so on. Even while this subject does not require pure maths, it does involve mathematical reasoning and some maths formulas. We'll go through what Business Mathematics is, terminology, and key formulas, as well as problems and solutions.

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FAQs on Business Mathematics

1.What Are The Topics In Business Mathematics?

Ratio and proportion, profit and loss, interest, determinants, matrices, averages, probability, set theory, reasoning, correlation, regression, measures of Central Tendency, dispersion, time analysis, index numbers, and other topics are covered in this subject.

2.How Can Business Mathematics Help You Make Better Decisions?

It aids in the analysis of the many elements of the business after analysing the current and previous structure as well as the company's performance. Going over the income and expense accounts, for example, can assist in making judgments about business operations so that income can be enhanced and expenses can be minimised. It aids in the decision-making process for marketing and advertising, as well as during any problem that arises after conducting market research. 

3.What's the Difference Between Mathematics and Business Mathematics?

Business mathematics is a commercial subject that is applied to business, whereas mathematics is an important discipline that works with numbers, patterns, and varied shapes. The former is a broader subject because it encompasses everything, including arithmetic, algebra, topology, geometry, and so on, but the later is a subset of mathematics that only deals with principles that are useful for business.Common mathematics is based on arithmetic principles whereas business mathematics is business related and does not involve complex equations. 

4.How Mathematical Models are Used in Business?

Mathematical models aid in the easy representation of real-life business scenarios and challenges. Probability aids in the analysis of any risk or event's possibilities, whereas regression entails the examination of both independent and dependent variables. It aids in the making of judgments such as investment decisions and market and business performance predictions. It aids in the simplification of business procedures. The process of model learning can be difficult for some people and hence they are required to go through the concepts properly. 

Mathematics and Business Relationship Research Paper

  • To find inspiration for your paper and overcome writer’s block
  • As a source of information (ensure proper referencing)
  • As a template for you assignment

Introduction

Critical path method (cpm), project evaluation and review technique (pert), project planning and management: cpm/pert, graphical modeling of project activities, limitations of cpm/pert methods.

Mathematics is a field of study which has been very useful in various sorts of analysis leading to business decision making. In this paper, the focus is on applying mathematical tools and techniques to business decision-making. The paper starts with a discussion of PERT and CPM Techniques. Then the use of this technique in project planning is elaborated. Finally, both thee techniques are combined as an application and a business decision is made. Relevant examples are discussed to illustrate the link of PERT/CPM to business decision-making. Graphical modeling of a sample project is done.

This method is used to identify the shortest path available. In business, various processes are identified for doing a particular job and the shortest way to finish the job is identified using CPM.

Critical Path Method (CPM) charts are similar to PERT charts and are sometimes known as PERT/CPM. In a CPM chart, the critical path is indicated. A critical path has a set of dependent tasks (each dependent on the preceding one) which together take the longest time to complete. Although it is not normally done, a CPM chart can define multiple, equally critical paths. Tasks that fall on the critical path should be noted in some way, so that they may be given special attention. One way is to draw critical path tasks with a double line instead of a single line.

Tasks that fall on the critical path should receive special attention from both the project manager and the personnel assigned to them. The critical path for any given method may shift as the project progresses; this can happen when tasks are completed either behind or ahead of schedule, causing other tasks which may still be on schedule to fall on the new critical path.

Program evaluation and review technique (PERT) charts depict task, duration, and dependency information. Each chart starts with an initiation node from which the first task, or tasks, originates. If multiple tasks begin at the same time, they are all started from the node or branch, or fork out from the starting point. Each task is represented by a line which states its name or another identifier, its duration, the number of people assigned to it, and in some cases the initials of the personnel assigned. The other end of the task line is terminated by another node which identifies the start of another task, or the beginning of any slack time, that is, waiting time between tasks.

Each task is connected to its successor tasks in this manner forming a network of nodes and connecting lines. The chart is complete when all final tasks come together at the completion node. When slack time exists between the end of one task and the start of another, the usual method is to draw a broken or dotted line between the end of the first task and the start of the next dependent task.

A PERT chart may have multiple parallel or interconnecting networks of tasks. If the scheduled project has milestones, checkpoints, or review points (all of which are highly recommended in any project schedule), the PERT chart will note that all tasks up to that point terminate at the review node. It should be noted at this point that the project review, approvals, user reviews, and so forth all take time. This time should never be underestimated when drawing up the project plan. It is not unusual for a review to take 1 or 2 weeks. Obtaining management and user approvals may take even longer

Consider the planning stage of a large-scale project (for example, the construction of Disneyland in HK). Successful completion of the project requires completion of hundreds of different activities by several different groups or companies (e.g. MTR builds the rail links, HK Government builds roads, KMB builds bus routes, SHK builds hotels, a roller-coaster company from Japan builds one ride in the park, McDonald’s builds some restaurants, etc.) Ideally, we want to complete the project as soon as possible.

This could be done if each activity was completed in parallel. However, it is often impossible to begin some activities before some other activity has been completed. For example, construction of buildings cannot begin until the forest cover over the Penny Bay area (site of Disneyland) has been cleared. Thus the entire project is broken into a set of well-defined activities. Further, the time taken to complete each activity is to be estimated.

The questions that the CPM/PERT analysis can answer include the following.

  • What is the earliest time to complete the entire project?
  • Given an activity, what is the earliest time to do it?
  • Which activities are the bottlenecks? These are activities that, if their completion is delayed, the entire project will be delayed.
  • What is the latest time that to begin an activity, and still not delay the project?

For example, it will take six months to hire and train a set of people to wear stuffed animal costumes and dance on the street; Disneyland will open in December 2008. So hiring and training need not begin until the summer of 2005.

In classical modeling of CPM/PERT as graphs, it is convenient to represent each activity as an edge. The weight of the edge indicates the time required to complete it. Each node represents a milestone, which is the point in time when a particular activity is completed and/or some activity is begun. The edges are directed, and the head of the edge is incident on the node representing the milestone corresponding to the completion of the activity.

The requirement that some activity cannot begin before another activity has been completed imposes a precedence relationship . Therefore, the arrows in our graph will depict the sequence in which the activities can be completed (equally: the paths indicate the sequence in which milestones can be achieved).

The graph also models the precedence relations of the milestones. If activity u must be completed before starting activity v, we indicate this by an arrow from the milestone (complete u) to the milestone (begin v). However, there may be no real activity between these two events – in which case this edge will have a weight = 0; such edges are called dummy edges since they only represent precedence, but not a real activity.

To successfully model a project in terms of a PERT network, we must first list out all precedence relationships. It is sufficient, for each activity, to identify its immediate predecessors.

Consider a project to construct a small Hydroelectric Power Plant. The details of the different activities, their precedence constraints, and the estimated times are shown in the table below.

ActivityDescriptionImmediate
Predecessor
Duration
aEcological survey6.2
bFile environmental impact report; get approvala9.1
cEconomic feasibility studya7.3
dPreliminary design and cost estimationc4.2
eProject approval and funding commitmentsb, d10.2
fCall quotation for equipment (turbines, generators)e4.3
gSelect supplier for equipmentf3.1
hThe final design of the projecte6.5
iSelect construction contractore2.7
jArrange construction materials supplyh, i5.2
kDam buildingj24.8
lPower station buildingj18.4
mPower lines erectiong, h20.3
nTurbines, generators installationg, l6.8
oBuild-up reservoir water levelk2.1
pCommission the generatorsn, o1.2
qStart supplying waterm, p1.1

Once the project plan data is in a form such as above, it can be expressed in the form of a directed graph using the following method.

  • Construct a node, s , representing the start of the project.
  • For each activity that has no immediate predecessor, make an edge incident from s .
  • Other activities are added to extend the graph according to the list of immediate predecessors; when there are two activities such that some of their immediate predecessors are the same, but some are not, we need to introduce a dummy activity to represent the precedence constraint.
  • In the end, all activities that have no successor are connected to a common node that represents the finish of the project.

Construct the graph for our hydroelectric plant project. In the graph, denote the edges by the activity names, in lower case letters. Each node represents the end of the activity or activities that are depicted by the edges incident to it; likewise, it depicts the point in time to begin any activity whose corresponding edge is incident from this node. The weight of the edge is the duration of the activity it represents. The dashed lines are the dummy edges: these edges are not given any name and have weight=0. They are used to depict the precedence constraints.

Figure 33a shows the first few steps in constructing the PERT graph. We begin with node s, and add the edge a, for activity a, which will take 6.2 weeks. Since activity a is an immediate predecessor for both b and c , so the edges for these two activities are incident from the node depicting the end of activity a , namely node A.

Figure 33b shows the situation where a dummy node is required. Activity c is an immediate predecessor of activity c . However, both activities b and d are immediate predecessors of task e . Therefore we need a dummy edge connecting the events depicted by nodes B and D. Since task e can only begin when all activities depicted by the edges incident to its starting node (namely node D in the figure), this dummy edge ensures that task b is also completed before task e begins.

Partial PERT graph for tasks a, b, c / Partial PERT chart for tasks b, c, d, e.

Figure 34. The entire graph is for the example. Once the PERT graph is completely constructed, we process it in two stages. In the first stage, called the Forward pass , the earliest possible start time for each activity is estimated. In the second stage, called the Backward pass , the latest allowed start time for each activity is estimated.

Forward pass

Begin from the start node, and compute the earliest time that each successive activity can begin. Earliest start time at node s = 0. Any edge (activity) that is incident from this node can be traversed in time equal to its weight. This gives the completion time of the activity. The maximum completion time due to each edge incident on a node is the earliest start time of any activity that begins from this node. This is the necessary and sufficient condition for all precedence constraints to be satisfied.

Thus in the graph, the earliest end time of activity a = 6.2; this is written in square brackets next to the node for “end of activity a ”, namely node A.

First few steps of the forward pass.

Notice that activity e has two immediate predecessors: b (which cannot be completed before 15.3), and d (which cannot be completed before 17.7). Thus, task e, which begins from node D, cannot begin before the maximum of these two , namely 17.7; therefore e cannot end before 17.7 + 10.2 = 27.9. Following this logic, the forward pass is completed as shown in Figure 36. From the graph, it is clear that the earliest time when we can complete the project is 68.8.

Forward pass for hydroelectric plant PERT example.

Backward pass

For the backward pass, begin at the finish node (in our case, node Q). The objective is to answer the following question: given the earliest completion time for the overall project , what is the latest time to begin a given activity, without causing any delay to the project?

Certainly, the project cannot be completed before 68.8 weeks. The last activity that we perform is q, which takes 1.1 weeks and cannot begin until all other activities are done. Thus if q is stated at any time after 68.8 – 1.1 = 67.7 weeks, then the project will get delayed. Since the start of activity q is at node M, we write this limit, 67.7, in the square bracket next to node M (see Figure 37a).

The latest allowed start time for each node is worked out using this logic. The only case where we need to pay some attention to this process is depicted in Figure 37b. Node L indicates that activity l ¸ whose duration is 18.4 weeks, must be completed no later than 59.7. Therefore it must begin at a time no later than 59.7 – 18.4 = 41.3 weeks. Using the same logic for activity k, the latest start time for activity k is 64.4 – 24.8 = 39.6. So which of these two figures, 41.3 and 39.6, is the correct figure for event J ? Clearly, we must pick the smaller of the two numbers – since if we denote the latest time at node J by 41.3, then we could only complete the activity k at 41.3 + 24.4 = 65.7, which will delay the project completion time (if we reach node K at any time later than 64.4, it will delay the project).

First few steps of Backward Pass / Logic at branch points.

Slack time: The slack time for an event is the difference between its latest and earliest time.

Completed PERT graph for the example problem.

While good in theory, CPM/PERT are sometimes less useful in practice because of two reasons.

  • It is often very difficult to estimate the exact time for any activity. Hence most modern PERT methods associate three-time values with each activity: the best case time, the expected time, and the worst-case time. Then a probabilistic model is built, using the worst case, best case, and expected duration of each task. However, such estimates are based on a series of assumptions, many of which may not be practically correct.
  • The second problem is that in constructing PERT graphs, we only consider the precedence relations between tasks. However, in real-life projects, several tasks may share some physical resources (e.g. cranes may be used in different tasks during the project). If two or more jobs require the same resource, it may not be possible to do them simultaneously. This type of constraint is not captured by PERT. To consider such cases, we must use a different type of problem model. Such models are studied in a different area of IELM, called resource-constrained scheduling. It is sometimes possible to construct LP formulations of such models.

R.K. Sharma, Operation Research – Theory and Application, First Edition, Macmillan Publishers.

V.Sunderasan, Resource Management Techniques, K.R. Publications.

Paneerselvam, Operation Research, second edition, Prentice Hall of India.

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Essays About Math: Top 10 Examples and Writing Prompts 

Love it or hate it, an understanding of math is said to be crucial to success. So, if you are writing essays about math, read our top essay examples.  

Mathematics is the study of numbers, shapes, and space using reason and usually a special system of symbols and rules for organizing them . It can be used for a variety of purposes, from calculating a business’s profit to estimating the mass of a black hole. However, it can be considered “controversial” to an extent.

Most students adore math or regard it as their least favorite. No other core subject has the same infamy as math for generating passionate reactions both for and against it. It has applications in every field, whether basic operations or complex calculus problems. Knowing the basics of math is necessary to do any work properly. 

If you are writing essays about Math, we have compiled some essay examples for you to get started. 

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1. Mathematics: Problem Solving and Ideal Math Classroom by Darlene Gregory 

2. math essay by prasanna, 3. short essay on the importance of mathematics by jay prakash.

  • 4.  Math Anxiety by Elias Wong

5. Why Math Isn’t as Useless as We Think by Murtaza Ali

1. mathematics – do you love or hate it, 2. why do many people despise math, 3. how does math prepare you for the future, 4. is mathematics an essential skill, 5. mathematics in the modern world.

“The trait of the teacher that is being strict is we know that will really help the students to change. But it will give a stress and pressure to students and that is one of the causes why students begin to dislike math. As a student I want a teacher that is not so much strict and giving considerations to his students. A teacher that is not giving loads of things to do and must know how to understand the reasons of his students.”

Gregory discusses the reasons for most students’ hatred of math and how teachers handle the subject in class. She says that math teachers do not explain the topics well, give too much work, and demand nothing less than perfection. To her, the ideal math class would involve teachers being more considerate and giving less work. 

You might also be interested in our ordinal number explainer.

“Math is complicated to learn, and one needs to focus and concentrate more. Math is logical sometimes, and the logic needs to be derived out. Maths make our life easier and more straightforward. Math is considered to be challenging because it consists of many formulas that have to be learned, and many symbols and each symbol generally has its significance.”

In her essay, Prasanna gives readers a basic idea of what math is and its importance. She additionally lists down some of the many uses of mathematics in different career paths, namely managing finances, cooking, home modeling and construction, and traveling. Math may seem “useless” and “annoying” to many, but the essay gives readers a clear message: we need math to succeed. 

“In this modern age of Science and Technology, emphasis is given on Science such as Physics, Chemistry, Biology, Medicine and Engineering. Mathematics, which is a Science by any criterion, also is an efficient and necessary tool being employed by all these Sciences. As a matter of fact, all these Sciences progress only with the aid of Mathematics. So it is aptly remarked, ‘Mathematics is a Science of all Sciences and art of all arts.’”

As its title suggests, Prakash’s essay briefly explains why math is vital to human nature. As the world continues to advance and modernize, society emphasizes sciences such as medicine, chemistry, and physics. All sciences employ math; it cannot be studied without math. It also helps us better our reasoning skills and maximizes the human mind. It is not only necessary but beneficial to our everyday lives. 

4.   Math Anxiety by Elias Wong

“Math anxiety affects different not only students but also people in different ways. It’s important to be familiar with the thoughts you have about yourself and the situation when you encounter math. If you are aware of unrealistic or irrational thoughts you can work to replace those thoughts with more positive and realistic ones.”

Wong writes about the phenomenon known as “math anxiety.” This term is used to describe many people’s hatred or fear of math- they feel that they are incapable of doing it. This anxiety is caused mainly by students’ negative experiences in math class, which makes them believe they cannot do well. Wong explains that some people have brains geared towards math and others do not, but this should not stop people from trying to overcome their math anxiety. Through review and practice of basic mathematical skills, students can overcome them and even excel at math. 

“We see that math is not an obscure subject reserved for some pretentious intellectual nobility. Though we may not be aware of it, mathematics is embedded into many different aspects of our lives and our world — and by understanding it deeply, we may just gain a greater understanding of ourselves.”

Similar to some of the previous essays, Ali’s essay explains the importance of math. Interestingly, he tells a story of the life of a person name Kyle. He goes through the typical stages of life and enjoys typical human hobbies, including Rubik’s cube solving. Throughout this “Kyle’s” entire life, he performed the role of a mathematician in various ways. Ali explains that math is much more prevalent in our lives than we think, and by understanding it, we can better understand ourselves. 

Writing Prompts on Essays about Math

Math is a controversial subject that many people either passionately adore or despise. In this essay, reflect on your feelings towards math, and state your position on the topic. Then, give insights and reasons as to why you feel this way. Perhaps this subject comes easily to you, or perhaps it’s a subject that you find pretty challenging. For an insightful and compelling essay, you can include personal anecdotes to relate to your argument. 

Essays about Math: Why do many people despise math?

It is well-known that many people despise math. In this essay, discuss why so many people do not enjoy maths and struggle with this subject in school. For a compelling essay, gather interview data and statistics to support your arguments. You could include different sections correlating to why people do not enjoy this subject.

In this essay, begin by reading articles and essays about the importance of studying math. Then, write about the different ways that having proficient math skills can help you later in life. Next, use real-life examples of where maths is necessary, such as banking, shopping, planning holidays, and more! For an engaging essay, use some anecdotes from your experiences of using math in your daily life.

Many people have said that math is essential for the future and that you shouldn’t take a math class for granted. However, many also say that only a basic understanding of math is essential; the rest depends on one’s career. Is it essential to learn calculus and trigonometry? Choose your position and back up your claim with evidence. 

Prasanna’s essay lists down just a few applications math has in our daily lives. For this essay, you can choose any activity, whether running, painting, or playing video games, and explain how math is used there. Then, write about mathematical concepts related to your chosen activity and explain how they are used. Finally, be sure to link it back to the importance of math, as this is essentially the topic around which your essay is based. 

If you are interested in learning more, check out our essay writing tips !

For help with your essays, check out our round-up of the best essay checkers

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Using Simple Math to Predict Your Business Future

Rolling averages can help shape your decisions..

Data analytics has become integral to running a business of any size. While using  data to make better decisions  used to be the domain of big companies, smaller businesses have gotten into the act. We can thank the impact of books like  Moneyball  by Michael Lewis for demonstrating how data analytics can give any team or business an edge over their competition.

The good news is that you don't need a math degree, a fancy algorithm, or even a massive data set to gain critical insights into your business. You can even  predict the future using metrics  from your business and basic statistical analysis like a rolling average.

Let me explain.

Embracing Trend Analysis

A rolling average, also known as a moving average, is a  simple statistical tool  you can use inside your business today to help predict the future.

Instead of considering all data points over time equally in the average, a rolling average focuses on a specific number of data points. It calculates the average of only those points. You can keep the average rolling by adding data from a new month while subtracting the data from the oldest month.

For example, we can use sales or revenue and then calculate a 12-month rolling average to see how your sales trend over those 12 months (total sales dollars / 12).

That immediately gives you a sense of the long-term revenue level inside the business. If the current month's sales are above the average, sales are growing.

You can combine that longer-term analysis by adding another trend line: a three-month rolling average.

As with the 12-month rolling average, you immediately see trends. Are sales going up or down?

Next, plot both trend lines on the same graph to see what insights you can learn. For instance, you might see that sales on the 12-month line are relatively flat, but the three-month line is trending down, which could spell trouble for your upcoming quarter.

Or, the 12-month average might be trending down while the three-month line shows a sharp spike upward, indicating that the business might be turning things around.

The three-month trend shows where the 12-month trend is headed.

What makes this powerful is its simplicity in creation and the immediate insights it can reveal with a picture. It also allows you to react somewhat slower than to the monthly results but quicker than to the six-month or annual results.

Embracing Flexibility

The beauty of this approach to data analysis is that you have the flexibility to use whatever data you need to look at the future. Use it with your profits, customer returns, website visits, or quality measures. Or whatever data you'd like to use to predict the future in ways that might give you an advantage over your competition.

Consider how a baseball team might use a rolling average of a player's offensive contributions to identify prime buy-low or sell-high candidates. By adjusting your timeline and using weeks or even days instead of months, I can track which players might be on the verge of breaking out--or breaking down.

Using this method, I might gain an advantage over other teams who might simply be looking at the sum of that player's statistics. While they might be looking to buy or sell based on those past results, I'm trying to gain an edge by predicting where the player's performance might be headed.

Gaining a Competitive Edge

In your business, perhaps you can use this to identify an acquisition target better or to help assess your performance compared with a competitor's. If everyone else is basing their actions on what's already happened, you might have an edge by using that data to see what might happen. And if you can do that, you are already one step ahead of the pack. Add these rolling averages to your key metrics today and see the insights you get.

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How to do IELTS

IELTS Essay: Maths

by Dave | Real Past Tests | 5 Comments

IELTS Essay: Maths

This is an IELTS writing task 2 sample answer essay on the topic of maths from the real IELTS exam.

Please consider supporting my efforts to creative high quality IELTS materials for students around the world by signing up for my Patreon (and don’t miss any of my exclusive IELTS Ebooks)!

To succeed in a business, one needs to know maths.

To what extent do you agree or disagree?

Many people claim that a key ingredient to success in the business world is a firm understanding of math. In my opinion, although there is some truth to this, it is not a crucial factor.

Proponents of the importance of math argue its usefulness in a variety of business contexts. For all business majors, mathematics courses in university are a requirement for graduation. This is because it is essential not only for those running a small business or shop to be able to do good book-keeping but also as a foundational skill for Wall Street brokers, bankers, entrepreneurs, accountants, and marketers. Without a solid understanding of the mathematical principles underlying the decision-making in those fields it is difficult to truly innovate and excel.

Nonetheless, there are more vital elements to business success. The math a business needs to prosper can be handled by dedicated specialists. It is more important for a potential business person to understand the nuances of the market, display leadership qualities, be decisive, and possess generally above-average intelligence. A good example of this would be an entrepreneur like Steve Jobs. He famously only hired quality specialists and prioritised for himself learning how to be an effective leader and motivate his employees well. The key to success is therefore segmenting a business into different areas all under the capable hands of a visionary leader.

In conclusion, mathematical ability can help inform businesses but it is not as essential as other management qualities. The ideal business person has an understanding of their strengths and weaknesses and brings together a team of strong complements.

1. Many people claim that a key ingredient to success in the business world is a firm understanding of math. 2. In my opinion, although there is some truth to this, it is not a crucial factor.

  • Paraphrase the overall essay topic.
  • Write a clear opinion. Read more about introductions here .

1. Proponents of the importance of math argue its usefulness in a variety of business contexts. 2. For all business majors, mathematics courses in university are a requirement for graduation. 3. This is because it is essential not only for those running a small business or shop to be able to do good book-keeping but also as a foundational skill for Wall Street brokers, bankers, entrepreneurs, accountants, and marketers. 4. Without a solid understanding of the mathematical principles underlying the decision-making in those fields it is difficult to truly innovate and excel.

  • Write a topic sentence with a clear main idea at the end.
  • Explain your main idea.
  • Develop it with specific examples.
  • Continue to develop it as fully as possible.

1. Nonetheless, there are more vital elements to business success. 2. The math a business needs to prosper can be handled by dedicated specialists. 3. It is more important for a potential business person to understand the nuances of the market, display leadership qualities, be decisive, and possess generally above-average intelligence. 4. A good example of this would be an entrepreneur like Steve Jobs. 5. He famously only hired quality specialists and prioritised for himself learning how to be an effective leader and motivate his employees well. 6. The key to success is therefore segmenting a business into different areas all under the capable hands of a visionary leader.

  • Write a new topic sentence with a new main idea at the end.
  • Explain your new main idea.
  • Include specific details and examples.
  • The more specific, the better.
  • Develop the example.
  • Conclude the paragraph or finish developing your last idea.

1. In conclusion, mathematical ability can help inform businesses but it is not as essential as other management qualities. 2. The ideal business person has an understanding of their strengths and weaknesses and brings together a team of strong complements.

  • Summarise your main ideas.
  • Include a final thought. Read more about conclusions here .

What do the words in bold below mean?

Many people claim that a key ingredient to success in the business world is a firm understanding of math . In my opinion, although there is some truth to this, it is not a crucial factor .

Proponents of the importance of math argue its usefulness in a variety of business contexts . For all business majors , mathematics courses in university are a requirement for graduation . This is because it is essential not only for those running a small business or shop to be able to do good book-keeping but also as a foundational skill for Wall Street brokers , bankers , entrepreneurs , accountants , and marketers . Without a solid understanding of the mathematical principles underlying the decision-making in those fields it is difficult to truly innovate and excel .

Nonetheless , there are more vital elements to business success. The math a business needs to prosper can be handled by dedicated specialists . It is more important for a potential business person to understand the nuances of the market, display leadership qualities , be decisive , and possess generally above-average intelligence . A good example of this would be an entrepreneur like Steve Jobs. He famously only hired quality specialists and prioritised for himself learning how to be an effective leader and motivate his employees well . The key to success is therefore segmenting a business into different areas all under the capable hands of a visionary leader .

In conclusion, mathematical ability can help inform businesses but it is not as essential as other management qualities . The ideal business person has an understanding of their strengths and weaknesses and brings together a team of strong complements .

key ingredient essential part

business world where business people work

firm understanding of math know math well

crucial factor important element

proponents supporters

usefulness practicality

variety of business contexts many different jobs

majors studying

requirement must do

graduation finishing school

running a small business having your own business

book-keeping keeping track of your earnings/spending

foundational skill needed

Wall Street brokers people who trade stocks

bankers people who work in banks

entrepreneurs people starting their own business

accountants people working with finances

marketers people working in advertising

solid understanding good grasp

mathematical principles underlying the math that underpins/supports

decision-making making decisions

fields jobs, areas

truly innovate think of new ideas

excel do better than others

nonetheless regardless

vital elements key parts

prosper do rewally well

handled by dedicated specialists dealt with by people who know it well

potential business person will get into business someday

nuances complexity

display leadership qualities are good leaders

decisive can make decisions

possess generally above-average intelligence are smart

entrepreneur person who starts a business

famously well-known

hired quality specialists employed experts

prioritised placed value on

effective leader good boss

motivate his employees well encourage those who work for him

key to success ingredient to doing well

segmenting a business dividing up a company

under the capable hands of under good leadership

visionary leader boss who can see the future

inform contribute to

not as essential as not as important as

management qualities leadership qualities

ideal perfect

strengths and weaknesses what you’re good and bad at

brings together combines

strong complements those who can support you

Pronunciation

kiː ɪnˈgriːdiənt   ˈbɪznɪs wɜːld   fɜːm ˌʌndəˈstændɪŋ ɒv mæθ ˈkruːʃəl ˈfæktə prəˈpəʊnənts   ˈjuːsfʊlnəs   vəˈraɪəti ɒv ˈbɪznɪs ˈkɒntɛksts ˈmeɪʤəz rɪˈkwaɪəmənt   ˌgrædjʊˈeɪʃən ˈrʌnɪŋ ə smɔːl ˈbɪznɪs   ˈbʊkˌkiːpɪŋ   faʊnˈdeɪʃən(ə)l skɪl   wɔːl striːt ˈbrəʊkəz ˈbæŋkəz ˌɒntrəprəˈnɜːz əˈkaʊntənts ˈmɑːkɪtəz ˈsɒlɪd ˌʌndəˈstændɪŋ   ˌmæθɪˈmætɪkəl ˈprɪnsəplz ˌʌndəˈlaɪɪŋ   dɪˈsɪʒən-ˈmeɪkɪŋ   fiːldz   ˈtruːli ˈɪnəʊveɪt   ɪkˈsɛl ˌnʌnðəˈlɛs ˈvaɪtl ˈɛlɪmənts   ˈprɒspə   ˈhændld baɪ ˈdɛdɪkeɪtɪd ˈspɛʃəlɪsts pəʊˈtɛnʃəl ˈbɪznɪs ˈpɜːsn   nju(ː)ˈɑːnsɪz dɪsˈpleɪ ˈliːdəʃɪp ˈkwɒlɪtiz dɪˈsaɪsɪv pəˈzɛs ˈʤɛnərəli əˈbʌv-ˈævərɪʤ ɪnˈtɛlɪʤəns ˌɒntrəprəˈnɜː   ˈfeɪməsli   ˈhaɪəd ˈkwɒlɪti ˈspɛʃəlɪsts   praɪˈɒrɪˌtaɪzd   ɪˈfɛktɪv ˈliːdə   ˈməʊtɪveɪt hɪz ˌɛmplɔɪˈiːz wɛl kiː tuː səkˈsɛs   sɛgˈmɛntɪŋ ə ˈbɪznɪs   ˈʌndə ðə ˈkeɪpəbl hændz ɒv   ˈvɪʒnəri ˈliːdə ɪnˈfɔːm   nɒt æz ɪˈsɛnʃəl æz   ˈmænɪʤmənt ˈkwɒlɪtiz aɪˈdɪəl   strɛŋθs ænd ˈwiːknɪsɪz   brɪŋz təˈgɛðə   strɒŋ ˈkɒmplɪmənts

Vocabulary Practice

Remember and fill in the blanks:

Many people claim that a k___________________t to success in the b___________________d is a f_________________________________h . In my opinion, although there is some truth to this, it is not a c___________________r .

P_____________________________s of the importance of math argue its u______________s in a v_____________________________s . For all business m__________s , mathematics courses in university are a r__________________t for g_____________________n . This is because it is essential not only for those r_________________________s or shop to be able to do good b__________________g but also as a f__________________________l for W______________________s , b_________s , e________________s , a_______________s , and m___________s . Without a s______________________g of the m_________________________________g the d____________________g in those f__________s it is difficult to t___________________e and e_____l .

N________________s , there are more v______________s to business success. The math a business needs to p___________r can be h___________________________s . It is more important for a p______________________n to understand the n____________s of the market, d________________________s , be d___________e , and p___________________________________________e . A good example of this would be an e____________r like Steve Jobs. He f____________y only h__________________________s and p_______________d for himself learning how to be an e_______________r and m______________________l . The k________________s is therefore s_____________________s into different areas all u_______________________________f a v________________r .

In conclusion, mathematical ability can help i__________m businesses but it is n________________________s other m_________________________s . The i______l business person has an understanding of their s________________________________s and b________________r a team of s________________________s .

Listening Practice

Learn more about this topic in the video below and practice with these activities :

Reading Practice

Read more about this topic and use these ideas to practice :

https://www.theatlantic.com/education/archive/2013/10/the-myth-of-im-bad-at-math/280914/

Speaking Practice

Practice with the following speaking questions from the real IELTS speaking exam :

  • Do you have a favourite number?
  • Will you use numbers at work in the future?
  • Were you good at math when you were younger?
  • Do you think numbers are important?

Writing Practice

Practice with the related topic below and then check with my sample answer:

Some think that climate change reforms will negatively affect business. Others feel they are an opportunity for businesses.

Discuss both sides and give your own opinion.

IELTS Essay: Climate Change and Business

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Anonymous

It was very helpful. However I need to practice a lot to accomplish my goal.

Anonymous

Recent IELTS QUESTION nowadays the way people doing online shopping has changed because of technology. has this become a positive or negative development?

Dave

Thank you – will try to get to writing it soon!

Yuliia

Technological advancements have caused a change in the way people do shopping. Over 1 million of purchases a day are made only on Amazon and eBay. It has become more common for customers to read reviews on the product, order things online and wait for the delivery at home. The tendency for internet shopping brings not only a possibility to choose from a wide variety of things but also saves our precious time.

One clear benefit that accrues from the e-commerce development is that customers can receive more information on the product, compare the quality and prices on other items and to choose the most suitable offer according to the budget. The most demanding individuals are in search of high-quality items at reasonable prices. For instance, such popular online stores as AliExpress, or eBay offer a number of different things at low prices that any person can find something useful.

Admittedly, nowadays people are pressed in time due to the tight work schedule, traffic jams and personal plans and not always have extra time to spend on doing groceries. Online shopping brings one more benefit for customers as saving their time. A person can order products from any supermarket just in several clicks and choose the time for delivery, in addition, some online stores offer free shipping and delivery that attract even more clients.

To sum up, the development of technologies has changed the way people do shopping enormously. It has brought many benefits for individuals as the ability to select things from a variety of different stores and to define the best offers as well as the possibility to spend time on more important duties such as self-development or family rather than shopping. 

nicole

Mathematics is a necessity to be well-established in business. Although there is little truth in this claim, I personally believe that it is not an absolute necessity.   Those who decry this claim point out the importance of mathematics as a fundamental concept for business ventures. Mathematics involves dealing with finances, profits, losses, and economic data that mainly constitutes the framework of business and therefore it is pertinent for a business individual to grasp the knowledge of mathematics to progressively understand the nuances of their establishments. For instance, when starting a business, one should estimate the gains and losses in the starting months in order to attract potential investors. As a result, one can benefit more as compared to someone who lacks an understanding of mathematics.   Nonetheless, most businesses require mathematics as a supporting element and instead, thrives on business management skills. There are many individuals from uneducated backgrounds that possess sharp intellectual minds, like making uninformed decisions promptly or offshoring and outsourcing their unique ideas for expansion, that creatively makes them economically more well-established as compared to one who only possesses mathematical skills. For instance, Mustafa, a famous store in Singapore, was first started as a textile shop by an uneducated individual but now, he expanded it into a three-levelled store ranging from jewelry to spices. Therefore, by honing the right business qualities, one can manage the ups and downs of businesses more effectively.   To encapsulate, though mathematics might seem the basics for businesses, it is not the main promising factor and also requires business capabilities to be successful. One should, however, be equipped with strong competence to excel further.

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To succeed in a business, one needs to know math’s. To what extent do you agree or disagree?

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  • Sentence 1 - Topic sentence
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Climate change is now an accepted threat to our planet but there is not enough political action to control excessive consumerism and pollution. Do you agree?'

The spread of a ‘global language’ such as english will threaten national languages. to what extent do you agree or disagree with this opinion, more and more young people are using drugs and alcohol and as a result, breaking the law. what are the causes of this problem what are some possible solutions, it is now possible for scientists and tourists to travel to remote natural environments, such as the south pole. what are the advantages and disadvantages of this development, you and some friends ate a meal at a restaurant to celebrate a special occasion, and you were very pleased with the food and service. write a letter to the restaurant manager.  in your letter: give details of your visit to the restaurant explain the reason for the celebration say what was good about the food and the service.

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Maths and business success - IELTS Writing Task 2 Opinion Essay

To succeed in a business, one needs to be good at maths..

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IMAGES

  1. Business MATH notes 1

    essay about business math

  2. The Five Point Essay Format

    essay about business math

  3. Introduction to Business Math

    essay about business math

  4. Importance Of Business Mathematics Free Essay Example

    essay about business math

  5. Contemporary Math Problem Essay

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  6. Best Ever Business Essay Example for Beginners on How to Compose it

    essay about business math

VIDEO

  1. 11 Business maths

  2. #14 Application of Matrices to Business and Economics

  3. Business Math // Mathematics of Finance // Class

  4. Business Mathematics

  5. Business Mathematics- NEB new model question (2079) solution

  6. business Mathematics and statistics

COMMENTS

  1. (PDF) An Introduction to Business Mathematics

    Germany. E-mail: [email protected]. E-Print: arXiv:1509.04333v2 [q-fin.GN] c. 2009-2015 Karlshochschule International University and Henk van Elst. Abstract. These lecture notes ...

  2. Business Mathematics Definition, Problems & Examples

    Business math is the study and use of mathematical concepts and skills related to business. It covers a wide range of topics, including finance, accounting, economics, statistics, and more ...

  3. Business Math Problem Description and Analysis Essay

    We will write a custom essay on your topic a custom Essay on Business Math Problem Description and Analysis. 808 writers online . Learn More . Problem Description. As a business major, one of the essential skills one needs to have is the ability to understand and interpret financial statements (Hosaka, 2019). Balance sheet is one of the most ...

  4. Business Math: A Step-by-Step Handbook

    Business Mathematics was written to meet the needs of a twenty-first century student. It takes a systematic approach to helping students learn how to think and centers on a structured process termed the PUPP Model (Plan, Understand, Perform, and Present). This process is found throughout the text and in every guided example to help students develop a step-by-step problem-solving approach.

  5. Business Mathematics

    Business Mathematics consists of Mathematical concepts related to business. It comprises mainly profit, loss and interest. Maths is the base of any business. Business Mathematics financial formulas, measurements which helps to calculate profit and loss, the interest rates, tax calculations, salary calculations, which helps to finish the business tasks effectively and efficiently.

  6. (PDF) Business Mathematics and Statistics

    See Full PDFDownload PDF. Licensed to: iChapters User fLicensed to: iChapters User Business Mathematics and Statistics Andre Francis BSc MSc Perinatal Institute Birmingham Andre Francis works as a medical statistician. He has previously taught Mathematics, Statistics and Information Processing to students on business and professional courses.

  7. What to Know About Business Math

    Business math is a type of mathematics course that is meant to teach people about money and provide them with the tools they need to make informed financial decisions. Business math not only teaches about the specifics of finances related to owning and operating a business but also offers helpful advice and information related to personal ...

  8. Business math

    Business Math and Logic: Important Tools in Living Studying Business Mathematics and Logic in this quarter has made a great impact to me and change my perspective in many things in life. It also made me realized that both of this is very beneficial to me and will play a big role in my life.

  9. 1.E: Succeeding in Business Mathematics (Exercises)

    Identify five specific activities or actions that you need to perform to succeed in your business math course. Consider how you will study for a math test. Develop three specific study strategies. Many students find it beneficial to work in study groups. List three ways that a study group can benefit you in your business math course.

  10. Business Mathematics: Course, Topics, Importance

    Business Mathematics is a specialized field of mathematics that deals with the application of mathematical concepts and techniques in business settings. It involves the use of mathematical tools and models to analyze business data, solve problems, and make informed decisions. ... Essays, letters of recommendation, ...

  11. Importance of Business Math in Business

    Importance of Business Math in Business. Business mathematics is mathematics used by commercial enterprises to record and manage business operations. Commercial organizations use mathematics in accounting, inventory management, marketing, sales forecasting, and financial analysis. Mathematics typically used in commerce includes elementary ...

  12. Business Mathematics

    Mathematics is considered to be the study of numbers, shapes & patterns and when this discipline is applied in a business, it becomes Business Maths. For a business, it is a vital subject that a student has to deal with. It acts as a tool that helps in solving and controlling various business problems. The basic objective to learn this subject ...

  13. Business Math

    Business Math. Improved Essays. 845 Words. 4 Pages. Open Document. Essay Sample Check Writing Quality. Show More. Business Math was first put into practice by industry leaders, George Dantzig and Harold Kuhn, in the 1950's. Business Mathematics is important in everyday life because not only does it help companies and organizations record and ...

  14. Mathematics and Business Relationship Research Paper

    Mathematics is a field of study which has been very useful in various sorts of analysis leading to business decision making. In this paper, the focus is on applying mathematical tools and techniques to business decision-making. The paper starts with a discussion of PERT and CPM Techniques. Then the use of this technique in project planning is ...

  15. Business Mathematics In The Real World

    1. Introduction: Business Math in the Real World. The whole concept of mathematics being used in the business field all started thousands of years ago. Mathematics started because of business, in other words. It started to facilitate commerce and trade and it could have not happened without having numbers. Banking, commerce and trade are the ...

  16. Mathematics

    Special Issue Information. Dear Colleagues, We are pleased to announce this Special Issue of the journal Mathematics entitled "Business and Economics Mathematics". This initiative focuses on the current changes that are taking place in the economic, social, and political environments of human society as a whole.

  17. Business Math

    Videos by the authors provide an excellent learning tool for students working on their own as well as a teaching tool for instructors. All learning units in each chapter and end-of-chapter summary practice tests are reviewed by the authors who provide step-by-step solutions and tips regarding the content making the learning process interactive while reaching the varied learning styles.

  18. MANCOSA

    Studying Business Mathematics at Management College of Southern Africa? On Studocu you will find 37 practice materials, practical, lecture notes, summaries, Skip to main content. ... Essays. Date Rating. year. Ratings. BEE Affidavit-EME-Gen. 2 pages 2021/2022 100% (1) 2021/2022 100% (1) Save. Project RISK Management - Assignment - POE. 9 pages ...

  19. To succeed in business, one needs to know math

    This essay has achieved this, with a balanced discussion on the role of math in business success and the importance of other factors. task achievement To increase clarity, ensure that the ideas presented are developed fully and are easy to understand, which this essay successfully demonstrates.

  20. Essays About Math: Top 10 Examples and Writing Prompts

    Math may seem "useless" and "annoying" to many, but the essay gives readers a clear message: we need math to succeed. 3. Short essay on the importance of Mathematics by Jay Prakash. "In this modern age of Science and Technology, emphasis is given on Science such as Physics, Chemistry, Biology, Medicine and Engineering.

  21. Using Simple Math to Predict Your Business Future

    Data analytics has become integral to running a business of any size. While using data to make better decisions used to be the domain of big companies, smaller businesses have gotten into the act.

  22. IELTS Essay: Maths

    Analysis. 1. Many people claim that a key ingredient to success in the business world is a firm understanding of math. 2. In my opinion, although there is some truth to this, it is not a crucial factor. Paraphrase the overall essay topic. Write a clear opinion. Read more about introductions here.

  23. To succeed in a business, one needs to know math

    Many authorities think that development of the progress is a crucial aim while others opine that there are some other kinds of improvements as same as vital. This essay discusses both viewpoints and I strongly agree with the latter opinion for the following reasons. 8. band.

  24. To succeed in a business, one needs to know math's

    Having a long life span of more than 100 years is now possible due to the advancments of science. While some people consider this phenomenon as a psitive matter since this can help individuals, especially those with a professional degree, to contribute more to their country, there are others who believe that providing old people a longer period of time will be cost an extra charge for governments.

  25. Maths and business success

    IELTS WRITING TASK 2 we have three important parts of education: reading, writing and maths. [4] ~ 2018 - Writing Feedback. Ielts Task 2 Topic: computer skills after writing, reading and maths [2] ~ 2017 - Writing Feedback. Task 2: To succeed in a business, one needs to know maths. To what extent do you agree or disagree [3] ~ 2020 - Writing ...

  26. Harvard Business School Announces 3 New Application Essays

    Harvard Business School announced a surprising departure from its single, open-ended application essay to three short essays with specific prompts. The HBS website sums up the kind of applicant ...

  27. The Role of Mathematics in Business Strategy

    Business Apps Based On Mathematics Strategic Planning. Strategic planning involves defining the long-term vision, setting objectives, and determining the best courses of action to achieve these ...