15 \\
+\quad 4 \\
\hline
\end{array}\)
This strategy of lining up the numbers is effective for adding a series of numbers as well.
1 + 2 + 3 + 2 = ?
\(\ \begin{array}{r} 1 \\2 \\ 3 \\ +2 \\ \hline 8 \end{array}\)
1 + 2 + 3 + 2 = 8
When adding whole numbers, a place-value position can have only one digit in it. If the sum of digits in a place value position is more than 10, you have to regroup the number of tens to the next greater place value position.
When you add, make sure you line up the digits according to their place values, as in the example below. As you regroup, place the regrouped digit above the appropriate digit in the next higher place value position and add it to the numbers below it.
45 + 15 = ?
\(\ \begin{array}{r} \color{blue}1\ \ \\ 45 \\ +15 \\ \hline \color{blue}0 \end{array}\) | Add the ones. Regroup as needed. The sum of 5 and 5 is 10. This is 1 ten and 0 ones. Write the number of ones (0) in the ones place and the 1 ten in the tens place above the 4. |
\(\ \begin{array}{l} &\color{blue}1 \\ &45 \\ +&15 \\ \hline &{\color{blue}6}0 \end{array}\) | Add the tens, 1 + 4 + 1 is 6 tens. The final sum is 60. |
45 + 15 = 60
You must add digits in the ones place first, the digits in the tens place next, and so on. Go from right to left.
4,576 + 698 = ?
\(\ \begin{array}{r} 4,576 \\ +\quad 698 \\ \hline \end{array}\) | First, write the problem with one addend on top of the other. Be sure you line up the place values! |
\(\ \begin{array}{r} \color{blue}1\ \ \\ 4,576 \\ +\quad 698 \\ \hline \color{blue}4 \end{array}\) | Add the numbers, 6 and 8, in the ones place. Since the sum is 14, write the ones value (4) in the ones place of the answer. Write the 1 ten in the tens place above the 7. |
\(\ \begin{array}{r} {\color{blue}1}1\ \ \\ 4,576 \\ +\quad 698 \\ \hline {\color{blue}7}4 \end{array}\) | Add the numbers in the tens place. Since the sum is 17 tens, regroup 17 tens as 1 hundred, 7 in the tens place in the answer and write the 1 hundred in the hundreds place above the 5. |
\(\ \begin{array}{r} {\color{blue}1}\ \ 11\ \ \\ 4,576 \\ +\quad 698 \\ \hline {\color{blue}2}74 \end{array}\) | Add the numbers in the hundreds place, including the 1. Again, the sum is more than one digit. Rename 12 hundreds as 2 hundreds and 1 thousand. Write the 2 in the hundreds place and the 1 above the 4 in the thousands place. |
\(\ \begin{array}{r} 1\ \ 11\ \ \\ 4,576 \\ +\quad 698 \\ \hline {\color{blue}5},274 \end{array}\) | Add the numbers in the thousands place, including the 1. The final sum is 5,274. |
4,576 + 698 = 5,274
Another way to add is the partial sums method. In the example below, the sum of 23 + 46 is found using the partial sums method. In this method, you add together all the numbers with the same place value and record their values (not just a single digit). Once you have done this for each place value, add their sums together.
23 + 46 = ?
\(\ \begin{array}{r} 23&\color{blue}20 \\ 46&\color{blue}+40\\ \hline &\color{blue}60 \end{array}\) | Let’s begin by adding the values in the tens position, the 2 and 4. The values are written as 20 and 40. |
\(\ \begin{array}{r} 23&\color{blue}3 \\ 46&\color{blue}+6\\ \hline &\color{blue}9 \end{array}\) | Add the values in the ones place, the 3 and 6. |
\(\ \begin{array}{r} \color{blue}60 \\ \color{blue}+\quad 9 \\ \hline \color{blue}69 \end{array}\) | Finally, add the two sums, 60 and 9, together. |
23 + 46 = 69
The next example adds a series of three numbers. Notice that hundreds is the greatest place value now, so hundreds are added before the tens. (You can add in any order that you prefer.) Also notice that in Step 3, the value in the ones column for 350 is zero, but you still add that in to make sure everything is accounted for.
225 + 169 + 350 = ?
\(\ \begin{array}{r} {\color{blue}2}25 & \color{blue}200 \\ {\color{blue}1}69 & \color{blue}100 \\ {\color{blue}3}50 &{\color{blue}+ 300}\\ \hline &\color{blue}600 \end{array}\) | Add the values represented by the digits 2, 1, and 3 in the hundreds place first. This gives a sum of 600. |
\(\ \begin{array}{r} 2{\color{blue}2}5 & \color{blue}20 \\ 1{\color{blue}6}9 & \color{blue}60 \\ 3{\color{blue}5}0&\color{blue}+50\\ \hline &\color{blue}130 \end{array}\) | Next, add the values from the digits in the tens place, the 2, 6, and 9. The sum is 130. |
\(\ \begin{array}{r} 22\color{blue}5 & \color{blue}5\\ | Add the values from the digits in the ones place, the 5, 9, and 0. The sum is 14. |
\(\ \begin{array}{r} \color{blue}600 \\ \color{blue}130 \\ \color{blue}+\quad 14 \\ \hline \color{blue}744 \end{array}\) | At this point, you have a sum for each place value. Add together these three sums, which gives a final value of 744. |
225 + 169 + 350 = 744
A local company built a playground at a park. It took the company 124 hours to plan out the playground, 243 hours to prepare the site, and 575 hours to build the playground. Find the total number of hours the company spent on the project.
When adding multi-digit numbers, use the partial sums method or any method that works best for you.
A polygon is a many-sided closed figure with sides that are straight line segments. Triangles, rectangles, and pentagons (five-sided figures) are polygons, but a circle or semicircle is not. The perimeter of a polygon is the distance around the polygon. To find the perimeter of a polygon, add the lengths of its sides, as in the example below.
One side of a square has a length of 5cm. Find the perimeter.
Draw the polygon and label the lengths of the sides. Since the side lengths of a square are equal, each side is 5cm. | |
\(\ \begin{array}{r} 5 \\ 5 \\ 5 \\ +\quad 5 \\ \hline 20 \end{array}\) | Add the lengths of each side, 5 + 5 + 5 + 5. |
The perimeter is 20cm.
The key part of completing a polygon problem is correctly identifying the side lengths. Once you know the side lengths, you add them as you would in any other addition problem.
A company is planning to construct a building. Below is a diagram illustrating the shape of the building’s floor plan. The length of each side is given in the diagram. Measurements for each side are in feet. Find the perimeter of the building.
\(\ \begin{array}{r} 50 \\ 20 \\ 20 \\ 10 \\ 10 \\ 40 \\ 40 \\ +30 \\ \hline 220 \end{array}\) | Add the lengths of each side, making sure to align all numbers according to place value. |
The perimeter is 220 feet.
Find the perimeter of the trapezoid in feet.
Addition is useful for many kinds of problems. When you see a problem written in words, look for key words that let you know you need to add numbers.
A woman preparing an outdoor market is setting up a stand with 321 papayas, 45 peaches, and 213 mangos. How many pieces of fruit in total does the woman have on her stand?
\(\ \begin{array}{r} 321 \\ 45 \\ +213 \\ \hline \end{array}\) | The words “how many… in total” suggest that you need to add the numbers of the different kinds of fruits. Use any method you like to add the numbers. Below, the partial sums method is used. |
\(\ \begin{array}{r} {\color{blue}3}21 & \color{blue}300\\ {\color{blue} 0}45&\color{blue}0\\ {\color{blue}2}13 &\color{blue}+200\\ \hline &\color{blue}500 \end{array}\) | Add the numbers represented by the digits in the hundreds place first, the 3, 0 and 2. This gives a sum of 500. |
\(\ \begin{array}{r} 3{\color{blue}2}1 & \color{blue}20 \\ 0{\color{blue}4}5 & \color{blue}40 \\ 2{\color{blue}1}3 &\color{blue}+ 10\\ \hline &\color{blue}70 \end{array}\) | Next, add the numbers represented by the digits from the tens place, the 2, 4, and 1. The sum is 70. |
\(\ \begin{array}{r} 32\color{blue}1 & \color{blue}1 \\ 04\color{blue}5 & \color{blue}5 \\ 21\color{blue}3 &+ \color{blue}3\\ \hline &\color{blue}9 \end{array}\) | Add the numbers from the ones, the 1, 5, and 3. |
\(\ \begin{array}{r} \color{blue}500 \\ \color{blue}70 \\ \color{blue}+\quad 9 \\ \hline \color{blue}579 \end{array}\) | Add together the three previous sums. The final sum is 579. |
The woman has 579 pieces of fruit on her stand.
Lynn has 23 rock CDs, 14 classical music CDs, 8 country and western CDs, and 6 movie soundtrack CDs. How many CDs does she have in all?
\(\ \begin{array}{r} 23 \\ 14 \\ 8 \\ +6 \\ \hline \end{array}\) | The words “how many… in all” suggest that addition is the way to solve this problem. To find how many CDs Lynn has, you need to add the number of CDs she has for each music style. |
\(\ \begin{array}{r} 2\ \ \\ 23 \\ 14 \\ 8 \\ +\quad 6 \\ \hline 51 \end{array}\) | Use whatever method you prefer to find the sum of the numbers. |
Lynn has 51 CDs.
The following phrases also appear in problem situations that require addition.
Add to | Jonah was planning a trip from Boston to New York City. The distance is 218 miles. His sister wanted him to visit her in Springfield, Massachusetts, on his way. Jonah knew this would 17 miles his trip. How long is his trip if he visits his sister? |
Plus | Carrie rented a DVD and returned it one day late. The store charged $5 for a two-day rental, a $3 late fee. How much did Carrie pay for the rental? |
Increased by | One statistic that is important for football players in offensive positions is . After four games, one player had rushed 736 yards. After two more games, the number of yards rushed by this player 352 yards. How many yards had he rushed after the six games? |
More than | Lavonda posted 38 photos to her social network profile. Chris posted 27 photos to his Lavonda. How many photos did Chris post? |
Lena was planning a trip from her home in Amherst to the Museum of Science in Boston. The trip is 91 miles. She had to take a detour on the way, which added 13 miles to her trip. What is the total distance she traveled?
The word “added” suggests that addition is the way to solve this problem.
To find the total distance, you need to add the two distances.
\(\ \begin{array}{r} 91 \\ +\quad 13 \\ \hline 104 \end{array}\)
The total distance is 104 miles.
It can help to seek out words in a problem that imply what operation to use. See if you can find the key word(s) in the following problem that provide you clues on how to solve it.
A city was struck by an outbreak of a new flu strain in December. To prevent another outbreak, 3,462 people were vaccinated against the new strain in January. In February, 1,298 additional people were vaccinated. How many people in total received vaccinations over these two months?
Drawing a diagram to solve problems is very useful in fields such as engineering, sports, and architecture.
A coach tells her athletes to run one lap around a soccer field. The length of the soccer field is 100 yards, while the width of the field is 60 yards. Find the total distance that each athlete will have run after completing one lap around the perimeter of the field.
The words “total distance” and “perimeter” both tell you to add. Draw the soccer field and label the various sides so you can see the numbers you are working with to find the perimeter. | |
\(\ \begin{array}{r} \color{blue}1\ \ \ \ \\ 100 \\ 100 \\ 60 \\ +\quad 60 \\ \hline 20 \end{array}\) | There is a zero in the ones place, and the sum of 6 and 6 in the tens place is 12 tens. Place 2 tens in the tens place in the answer, and regroup 10 tens as 1 hundred. |
\(\ \begin{array}{r} \color{blue}1\ \ \ \ \\ 100 \\ 100 \\ 60 \\ +\quad 60 \\ \hline {\color{blue}3}20 \end{array}\) | By adding the 1 hundred to the other digits in the hundreds place, you end up with a 3 in the hundreds place of the answer. |
Each athlete will have run 320 yards.
You can add numbers with more than one digit using any method, including the partial sums method. Sometimes when adding, you may need to regroup to the next greater place value position. Regrouping involves grouping ones into groups of tens, grouping tens into groups of hundreds, and so on. The perimeter of a polygon is found by adding the lengths of each of its sides.
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Use Place Value to Write Whole Numbers. In the following exercises, write each number as a whole number using digits. six hundred two. fifteen thousand, two hundred fifty-three. three hundred forty million, nine hundred twelve thousand, sixty-one. two billion, four hundred ninety-two million, seven hundred eleven thousand, two.
Multi-step word problems with whole numbers. Google Classroom. Microsoft Teams. After collecting eggs from his chickens, Dale puts the eggs into cartons to sell. Dale fills 15 cartons and has 7 eggs left over. Each carton holds 12 eggs.
So, the required two-digit number is 42. Problem 9 : A whole number consisting of two digits is four times the sum of its digits and if 27 be added to it, the digits are reversed. Find the whole number. Solution : Let xy be the required two-digit whole number. Given : The two-digit whole is equal four times the sum of its digits. xy = 4(x + y)
The four basic operations on whole numbers are addition; subtraction; multiplication and division. We will learn about the basic operations in more detailed explanations along with the examples. Worked-out problems related to Operations on whole numbers. 1. Solve using rearrangement: = (784 + 216) + 127. = 1000 + 127. = 1127. (b) 25 × 8 × 125 ...
Singapore Maths: Primary 5 - Whole Numbers, Word Problem Q4. Learn how to use models to understand and solve word problems on whole numbers. Example: Dave and Eli bought some DVDs and paid $96 altogether. If Eli bought 10 more DVDs than Dave and paid $20 more than him, find the number of DVDs that Dave bought. Next set of videos in this series.
In this article, you will learn how to solve various problems on whole numbers in simple methods and get accurate answers. What are whole numbers? In mathematics, whole numbers are defined as the set of numbers that include positive integers and 0. In other words, whole numbers are comprised of natural numbers and 0.
Example 5: apply a property of whole numbers. Fill in the blank using your knowledge of the commutative property of multiplication to make the equation true. \rule {0.5cm} {0.15mm} \, \times 15=15 \times 3 × 15 = 15 × 3. Recall the property. Show step.
1.6 Solving problems with whole numbers Order of operations. If you use "BODMAS" or "BEDMAS" correctly to remember the order of operations, you will get the same answer. But, evaluating an expression using terms will help more with algebra later on!
Number Word Problems Worksheets and Solutions. Objective: I can solve whole number word problems. Example: At a football match, there were 11 820 spectators. 8 256 of the spectators were adults. Of the remaining spectators, there were 3 times as many teenagers as young children. How many teenagers were there?
Solving a word problem on whole numbers using models. Example: Each month Li pays bills for electricity and water. If she pays $36 a month for electricity, and $720 a year for electricity and water together, find the amount of money she pays for water each month. Show Step-by-step Solutions.
This video provides several examples of solving word problems using whole number operations.Complete Video List: http://www.mathispower4u.yolasite.com
1.3: Multiplication and Division of Whole Numbers We begin this section by discussing multiplication of whole numbers. The first order of business is to introduce the various symbols used to indicate multiplication of two whole numbers. 1.4: Prime Factorization; 1.5: Order of Operations; 1.6: Solving Equations by Addition and Subtraction; 1.7 ...
4th Grade Resources - Use the four operations with whole numbers to solve problems. Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. Multiply or divide to ...
Practice Solving Word Problems Using Multiplication of Whole Numbers with practice problems and explanations. Get instant feedback, extra help and step-by-step explanations. Boost your Algebra ...
Multiply whole numbers by a power of 10. Use rounding to estimate products. Find the area of a rectangle. Solve application problems using multiplication. Introduction. Instead of adding the same number over and over again, an easier way to reach an answer is to use multiplication. Suppose you want to find the value in pennies of 9 nickels.
4.OA.A.3. Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation
Follow the steps here to solve a word problem involving division. Step 1: Determine the total number of objects that are being divided into groups. Step 2: Determine either (a) the number of ...
Round whole numbers word problems. The distance to the moon is an average of 384,400 kilometers. Round the distance to the nearest ten thousand. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free ...
Practice Solving a Word Problem with the Addition of Whole Numbers with practice problems and explanations. Get instant feedback, extra help and step-by-step explanations. Boost your Algebra grade ...
You will learn about different ways to express whole numbers as sums and products. You will learn about different ways of doing calculations, and different ways of recording your work when doing calculations. You will strengthen your skills to do calculations and to solve problems. Revision. Do not use a calculator at all in section 1.1.
It means, when we add or multiply two whole numbers, then the resulting value is also a whole number. If A and B are two whole numbers, then, A + B → W. A x B → W. Where W represents whole numbers. See some examples of closure property below: Closure property of Addition. Closure property of multiplication. 2 + 3 = 5.
Three Ways to Represent Division. 12 ÷ 3 = 4 ( with a division symbol; this equation is read "12 divided by 3 equals 4." 4 3\longdiv12 ( with a division or long division symbol; this expression is read "12 divided by 3 equals 4." Notice here, though, that you have to start with what is underneath the symbol.
Here you will find our selection of 1st Grade Addition Word Problems which will help your child learn to solve addition problems using numbers with a sum of up to 20. Addition Word Problems. Math Word Problems. Addition Words. Subtraction Word Problems. Math Problem Solving. Word Problem Worksheets.
In this article we will explain a number of sophisticated prompt engineering strategies, simplifying these difficult ideas through straightforward human metaphors. The techniques and their examples have been discussed to see how they resemble human approaches to problem-solving. Chaining Methods. Analogy: Solving a problem step-by-step.
Adding Whole Numbers without Regrouping. Adding numbers with more than one digit requires an understanding of place value. The place value of a digit is the value based on its position within the number. In the number 492, the 4 is in the hundreds place, the 9 is in the tens place, and the 2 is in the ones place. You can use a number line to add.