fractions and decimals problem solving year 4

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• Fractions to / from decimals

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Fractions to/from Decimals for Grade 4

Converting fractions to and from decimals worksheets.

These worksheets provide introductory exercises for converting fractions to and from decimals .  All fractions have a denominator of 10 or 100 for easy translation into decimals.  Mixed numbers are also used.

Sample Grade 4 converting fractions to decimals worksheet

More decimals worksheets

Find all of our decimals worksheets , from converting fractions to decimals to long division of multi-digit decimal numbers.

More fractions worksheets

Explore all of our fractions worksheets , from dividing shapes into "equal parts" to multiplying and dividing improper fractions and mixed numbers.

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Y4 Fractions and Decimals Lesson 12 - Word Problems - Year 4

Subject: Mathematics

Age range: 7-11

Resource type: Lesson (complete)

Last updated

6 September 2023

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This is a complete lesson pack with high quality resources for Year 4 Fractions and Decimals- Word Problems.

This lesson pack includes:

• Differentiated Activity Sheets

The lesson forms a part of a series of lessons on Fractions and Decimals . Other lessons in this series are:

• Lesson 1: Equivalent Fractions
• Lesson 2: Fractions of Amounts
• Lesson 3: Calculating Quantities
• Lesson 4: Addition
• Lesson 5: Subtraction
• Lesson 6: Tenths and Hundredths
• Lesson 7: Decimal Equivalents
• Lesson 8: Dividing by 10
• Lesson 9: Dividing by 100
• Lesson 10: Rounding Decimals
• Lesson 11: Comparing Decimals
• Lesson 12: Word Problems

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Y4 Unit Bundle Fractions and Decimals - Year 4

This is a complete unit pack with high quality resources for Year 4 Fractions and Decimals. It includes 12 lesson packs covering the following topics: * Lesson 1: Equivalent Fractions * Lesson 2: Fractions of Amounts * Lesson 3: Calculating Quantities * Lesson 4: Addition * Lesson 5: Subtraction * Lesson 6: Tenths and Hundredths * Lesson 7: Decimal Equivalents * Lesson 8: Dividing by 10 * Lesson 9: Dividing by 100 * Lesson 10: Rounding Decimals * Lesson 11: Comparing Decimals * Lesson 12: Word Problems Each lesson pack includes: * PowerPoint Presentation * Differentiated Activity Sheets * Challenge Cards * A4 Poster

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Count up and down in hundredths

They will also be expected to count up and down in hundredths mentally.

Solve problems involving quantities and non-unit fractions

Your child will calculate quantities involving fractions. For instance, they might be asked to find a fraction of a set of objects. They should be able to do this even when the answer is not a whole number. For example:

 of 22 = 3 

They will solve problems involving fractions to divide quantities, including non-unit fractions . For example:

  of 12 First they will find the value of     = 4. Then they will multiply this value by 2 to find     = 8.

Add and subtract fractions with the same denominator

Your child will use drawings, diagrams, and symbols to add and subtract fractions with the same denominator (the bottom number of a fraction). For example:

Use decimal equivalents of tenths or hundredths

In Year 4, your child will learn that decimals and fractions are different ways of expressing numbers and proportions.

Use decimal equivalents of ¼, ½, ¾, and tenths and hundredths

Your child will learn to use decimal equivalents of any number of tenths or hundredths. For example:

  is equivalent to 0.1.     is equivalent to 0.3.     is equivalent to 0.01.     is equivalent to 0.05.     is equivalent to 0.25.     is equivalent to 0.5.     is equivalent to 0.75.

Divide one- or two-digit numbers by 10 and 100

Your child will be able to divide numbers by 10 and 100.

They will know what happens when they divide a 1- or 2-digit number by 10 and 100, identifying the value of the digits in the answer as ones, tenths, and hundredths. For example:

3 ÷ 10 = 0·3 =   5 ÷ 100 = 0·05 =  

Round numbers with 1 decimal place

Your child will round numbers with decimals up and down to the nearest whole number. For example:

1.6 will round up to 2. 18.3 will round down to 18.

Compare numbers with up to 2 decimal places

Your child will learn to compare decimal numbers with up to two decimal places and say which one is bigger or smaller. At this stage, they will mainly be comparing numbers with the same number of decimal places. For example:

3.45 is smaller than 3.54. 8.8 is bigger than 8.5.

Solve simple measure and money problems

Your child will solve real-world problems involving fractions and decimals to 2 decimal places.

They will also represent numbers with one or two decimal places in several ways, such as on number lines .

How to help at home

There are lots of ways you can help your child to understand fractions. Here are just a few ideas.

1. Explore equivalent fractions

Equivalent fractions are different fractions that have the same value.

Fraction wall

When they have done this, ask them if they notice any patterns in the sequence of fractions. Help your child notice that you can change one fraction into an equivalent fraction by multiplying (or dividing) the numerator and the denominator by the same number.

2. Simplify fractions

Your child will learn to simplify fractions. Simplifying a fraction means reducing the fraction into its simplest form.

To simplify fractions, your child will find the highest common factor of the numerator and the denominator and then divide both numbers by it. The ‘highest common factor’ is the biggest number that can be divided equally into both the numerator and the denominator. For example:

Simplify  .   We know that 5 is the highest common factor of 5 and 25 (i.e. it is the biggest number that both 5 and 25 can be divided by to arrive at whole numbers).   We can therefore divide the numerator and the denominator by 5 to get the answer:  .

If the numerator and the denominator do not have a common factor, then they are fully simplified. See page three of our Fraction Calculations in School booklet for more information.

Fraction Calculations in School

3. Think about fractions while shopping

Shopping together can provide a useful opportunity to think about fractions as decimals.

Encourage your child to compare price tags. This is great practice for comparing numbers with two decimal places. For example, one item may cost £1.67 and another may cost £1.76. Ask your child to say which one is bigger and to explain how they know. They could even use the greater than > or less than < symbols to compare numbers up to two decimal places (for example, 5.67 < 5.71).

Try using place value charts to help your child compare numbers with two decimal places. Place value charts are a way of showing how big numbers are visually. For example:

By showing the numbers with a place value chart, your child can understand the value of the number more easily. For example, place value charts could help with this comparison:

4.20 has four ones, two tenths and zero hundredths. 4.76 has four ones, seven tenths and six hundredths. Therefore, 4.76 is greater than 4.20.

4. Round decimals

Your child will need to be able to round decimals with one decimal place to the nearest whole number.

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Fraction and Decimal Worksheets for Year 4 (age 8-9)

In Year 4 children will begin to work with hundredths, understanding that finding one hundredth is equivalent to dividing by 100 (e.g. one hundredth of 2 000 is equivalent to 2 000 divided by 100). They should also be shown the connection between hundredths and tenths and that hundredths arise by dividing tenths by ten (e.g 0.5 divided by ten is 0.05).

The relationship between fractions and decimals will also be extended and by the end of the year children should be able to recognise and write decimal equivalence of any number of tenths or hundredths (e.g. 6 hundredths is equivalent to 0.06).

An important part of this link between fractions and decimals is understanding the effect of dividing a one-digit or two-digit number by ten or one hundred and identifying the value of the digits in the answer as units, tenths and hundredths (e.g. 45 divided by 100 is 0.45 or 4 tenths and five hundredths or 45 hundredths). Each digit moves one place to the right when dividing by ten and two digits to the right when dividing by 100. There is more on this in our Year 4 Division category.

Of course, there is still plenty to do on equivalent fractions and children should be learning some of the more common families of equivalent fractions (e.g. one fifth is equivalent to two tenths). They should also know the decimal equivalents to a quarter (0.25), a half (0.5) and three quarters (0.75).

Addition of fractions with the same denominator continues but answers can be more than one whole one and should be simplified where possible. More work is also done with subtracting fractions with the same denominator. We have plenty of pages on both of these subjects.

If all of this is achieved by the end of Year 4 then your child will have a really good basic understanding of fractions and should be able to move on successfully next year.

Comparing and ordering decimals

Comparing and ordering decimals up to two decimal places.

Putting decimals in order of size, using tenths.

Putting numbers with two decimal places in order of size.

More decimals shown on scales, including numbers greater than one.

Complete the numbers shown on the scales.

Ordering decimals from smallest to largest.

Ordering larger numbers including decimals.

Writing decimals in order from smallest to greatest.

Finding the smallest number in a set of decimals.

Ordering decimals using a place value chart.

Using the < > to compare decimals less than one whole one.

Using the < > to compare decimals more than one whole one.

More comparing of decimals.

Comparing decimals up to 2 decimal places.

Harder comparisons of decimals using < > and =.

Order decimals in ascending and descending order, including mixed units of cm and metres.

Use digit cards to make the largest and smallest numbers including decimals.

Finding the value of digits and missing numbers.

Recognising tenths and hundredths

Recognising and writing decimal equivalents of tenths and hundredths. Ordering decimals.

Writing tenths with the help of place value charts.

Further work on understanding and writing tenths.

Writing tenths as decimals, fractions and in words.

Find the correct decimal that is displayed in each grid.

Write down the decimals that each set represents.

Counting on or back in tenths and hundredths.

Finding the number of hundredths in numbers up to 2 decimal places.

Making a whole one using part whole model with tenths

Making a whole one using part whole model with hundredths

Rounding decimals

Rounding decimals to the nearest whole one and the nearest tenth.

Round tenths to the nearest whole one.

Rounding Decimals to the Nearest Whole One.

Round decimals to the nearest tenth.

Decimals and fractions

Understanding the relationship between decimals and fractions.

Writing tenths as decimals.

practice converting tenths to their decimal equivalent.

Using images to help convert hundredths to ones and tenths.

More on hundredths written as decimals and fractions.

More on hundredths, including converting improper fractions to decimals.

Converting fractions shown in hundredths to decimals.

Converting hundredths to decimals.

Write decimal equivalents of tenths and hundredths

A look at the relationship between fractions and decimals.

Converting fractions to decimals, including dividing by ten with remainders written as fractions and then as a decimal.

Most primary school calculators cannot show fractions in the way they are usually written, but it is easy to change a fraction into a decimal fraction, as shown on these pages.

This set of worksheets is all about converting decimal fractions into fractions. Easy, if you understand tenths and hundredths.

Understanding fractions

Developing an understanding of the equivalence of fractions and how this can be used to order fractions.

More on equivalent fractions, with examples showing that 4 fifths is equivalent to 8 tenths etc.

More on equivalent fractions including quarters, thirds, fifths and tenths.

Use the digit cards as many times as you can to show equivalent fractions.

Find fractions equivalent to a half and a quarter.

Recognising fifths of shapes.

Working with equivalent fractions.

Completing fraction sequences.

More fraction sequences.

Complete the fraction sequences.

Finding fractions of pizzas.

Understanding improper fractions and mixed numbers.

Complete fraction sequences, simplifying fractions where possible.

Adding and subtracting fractions

Beginning to add and subtract fractions.

Making fractions add up to one whole one, including some tricky ones where the bottom numbers of the fractions are different!

Using bar models to add fractions.

Using bar models to show subtraction of fractions.

Adding fractions with the same denominator.

Adding fractions with the same denominator which total more than one.

Subtracting simple fractions.

Subtracting from one whole one.

More on fractions

More on fractions.

Finding fractions of numbers.

A little more on fractions and finding quarters, fifths, ninths etc.

Complete the shapes by colouring more squares.

Finding fractions of bars of chocolate.

Fractions problems all connected to food.

Dividing tenths by ten.

Dividing by 100, with decimal and fraction answers.

A quick look at the Programme of Study for fractions in Year 4.

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Year 4: Decimals and fractions

Pupils should be taught throughout that decimals and fractions are different ways of expressing numbers.

Pupils’ understanding of the number system and decimal place value is extended at this stage to tenths and then hundredths. This includes relating the decimal notation to division of whole numbers by 10 and later 100.

Pupils should learn decimal notation and the language associated with it, including in the context of measurements. They make comparisons and order decimal amounts and quantities that are expressed to the same number of decimal places. They should be able to represent numbers with one or two decimal places in multiple ways, such as on number lines.

New Maths Curriculum (2014): Year 4 objectives.

Recognise and write decimal equivalents of any number of tenths or hundredths

Recognise and write decimal equivalents to 1/4; 1/2; 3/4, find the effect of dividing a one- or two-digit number by 10 and 100, identifying the value of the digits in the answer as units, tenths and hundredths, round decimals with one decimal place to the nearest whole number, compare numbers with the same number of decimal places up to two decimal places, solve simple measure and money problems involving fractions and decimals to two decimal places.

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Year 4 – Fractions

Welcome to Year 4 Fractions, Decimals and Percentages at Primary Maths Hub. Here you will find a growing library of outstanding resources and activities to support fractions, decimals and percentages lessons in Year 4 and at home.

If there’s a resource you’d like to see here, just visit our ‘Request a Resource’ page and Primary Maths Hub will create the resource and add it to the site.

Do Now Tasks / Starters

Fraction of Numbers Do Now Tasks

Fraction Addition Do Now Tasks

Fraction Subtraction Do Now Tasks

Fraction Addition and  Subtraction Do Now Tasks

Differentiated questions sets.

Fraction of a Number Question Set

Adding Fractions Question Set

Adding Mixed Numbers Question Set

Decimal Subtraction Question Set

Decimal Addition  Question Set 

Fractions of a number.

Strips – Fractions of a Number

Find Fractions of a Number

Fading Scaffolding Strips- Fraction of a Number

Finding and shading fractions.

Shade Fraction of a Shape

Adding fractions.

Strips – Add Fractions with the same Denominator

Fading Scaffolding Strips- Add Fractions With The Same Denominator

Fading Scaffolding Strips- Add 3 Fractions With The Same Denominator

Add Fractions Same Denominator

Subtracting fractions.

Strips – Subtract Fractions with the same Denominator

Strips- Subtract Tenths

Adding and subtracting fractions.

Strips – Add and Subtract Fractions with the Same Denominator

Adding and Subtracting Fractions Greater Than 1 Part-Whole Model

Comparing fractions, adding mixed numbers.

Add Mixed Numbers Same Denominator

Mixed Number and Improper Fraction Matching Cards

Mixed numbers.

Understand Improper Fractions Equal to Whole Numbers

Convert Mixed Numbers to Improper Fractions

Partition Mixed Numbers

Fraction reasoning.

Add Two Fractions Reasoning

Add Two or More Fractions Reasoning

Compare and Order Mixed Number Reasoning

Partition a Mixed Number Reasoning

Understanding Improper Fractions Reasoning

Tenths on a Number Line Reasoning

Tenths on a Place Value Grid Reasoning

Fraction of a Number Reasoning

Making a Whole with Hundredths Reasoning

Making a Whole with Tenths Reasoning 

Fraction challenges and word problems.

Add Fractions Challenge- Greater Than 1

Add Fractions Challenge

Decimal Place Value

Decimal Place Value – Faded Scaffolding

Adding decimals.

Strips- Add Tenths

Adding Decimals with the same DP 

Subtracting decimals.

Subtracting Decimals with the same DP 

Add and subtract decimals.

Strips- Add and Subtract Tenths

Rounding decimals.

Rounding Numbers with 1 dp to Nearest Whole

Rounding Numbers with 1 dp to Nearest Whole- Faded Scaffolding

Dividing decimals.

Fading Scaffolding Strips- Divide 1- or 2- Digit Numbers by 10

Fading Scaffolding Strips- Divide 1- or 2- Digit Numbers by 10 or 100

Fading Scaffolding Strips- Divide 1- or 2- Digit Numbers by 100

Decimal reasoning.

Decimals as Tenths Reasoning

Divide a 1-Digit Number by 10 Reasoning

Divide a 1-Digit Number by 100 Reasoning

Divide a 2-Digit Number by 10 Reasoning

Divide a 2-Digit Number by 100 Reasoning

Flexibly Partition Decimal Numbers Reasoning 

Round Decimal Numbers to Nearest Whole Number Reasoning

Partition Decimal Numbers Reasoning 

Compare Decimal Numbers Reasoning 

Equality and inequality statements.

Equality and Inequality Statement Matching- Decimals

Equality and Inequality Statement Matching- Improper Fractions Equal to Whole

Tenths as Decimals- Equality and Inequality Statement Matching

Percentages, fractions, decimals and percentages.

Tenths as Decimals

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Fractions, Decimals and Percentages - Short Problems

Better Spelling

Weekly Problem 12 - 2010 Can Emily increase her average test score to more than $80$%? Find out how many more tests she must take to do so.

Valuable Percentages

Weekly Problem 23 - 2010 These numbers have been written as percentages. Can you work out which has the greatest value?

Bouncing Ball

A ball is dropped from a height, and every time it hits the ground, it bounces to 3/5 of the height from which it fell.

Percentage Mad

Weekly Problem 43 - 2013 What is 20% of 30% of 40% of £50?

Information Display

The information display on a train shows letters by illuminating dots in a rectangular array. What fraction of the dots in this array is illuminated?

Mean Sequence

Weekly Problem 38 - 2009 This sequence is given by the mean of the previous two terms. What is the fifth term in the sequence?

Ordering Fractions

Weekly Problem 46 - 2014 Which of these fractions has greatest value?

Jacob's Flock

How many sheep are in Jacob's flock?

Farthest Fraction

Which of these fractions is the largest?

Tommy's Tankard

Weekly Problem 4 - 2017 Tommy's tankard holds 480ml when it is one quarter empty. How much does it hold when it is one quarter full?

Multiplication Magic Square

Weekly Problem 32 - 2015 Can you work out the missing numbers in this multiplication magic square?

Smashing Time

Weekly Problem 58 - 2012 Once granny has smashed some of her cups and saucers, how many cups are now without saucers?

Talulah's Tulips

Weekly Problem 10 - 2017 Talulah plants some tulip bulbs. When they flower, she notices something interesting about the colours. What fraction of the tulips are white?

Smallest Fraction

Which of these is the smallest?

Three Blind Mice

Each of the three blind mice in turn ate a third of what remained of a piece of cheese. What fraction of the cheese did they eat in total?

Charlie's Money

How much money did Charlie have to begin with?

Can you find a number that is halfway between two fractions?

Pride of Place

Two fractions have been placed on a number line. Where should another fraction be placed?

Second Half Score

Boarwarts Academy played their annual match against Range Hill School. What fraction of the points were scored in the second half?

Between a Sixth and a Twelfth

The space on a number line between a sixth and a twelfth is split into 3 equal parts. Find the number indicated.

Magical Products

Can you place the nine cards onto a 3x3 grid such that every row, column and diagonal has a product of 1?

Tricky Fractions

Use this series of fractions to find the value of x.

Too Close to Call

Weekly Problem 24 - 2012 Can you put these very close fractions into order?

Slightly Outnumbered

If this class contains between $45$% and $50$% girls, what is the smallest possible number of girls in the class?

What fraction of this triangle is shaded?

Peanut Harvest

A group of monkeys eat various fractions of a harvest of peanuts. What fraction is left behind?

A Drink of Water

Weekly Problem 43 - 2015 Rachel and Ross share a bottle of water. Can you work out how much water Rachel drinks?

Entrance Exam

Dean finishes his exam strongly. Can you work out how many questions are on the paper if he gets an average of 80%?

Which of the cities shown had the largest percentage increase in population?

Test Scores

Ivan, Tibor and Alex sat a test and achieved 85%, 90% and 95% respectively. Tibor scored just one more mark than Ivan. How many marks did Alex get?

Tennis Club

Three-quarters of the junior members of a tennis club are boys and the rest are girls. What is the ratio of boys to girls among these members?

The Grand Old Duke of York

What percentage of his 10,000 men did the Grand Old Duke of York have left when he arrived back at the bottom of the hill?

Meeting Point

Malcolm and Nikki run at different speeds. They set off in opposite directions around a circular track. Where on the track will they meet?

How many rats did the Pied Piper catch?

To make porridge, Goldilocks mixes oats and wheat bran..... what percentage of the mix is wheat?

Petrol Station

Andrea has just filled up a fraction of her car's petrol tank. How much petrol does she now have?

Recurring Mean

What is the mean of 1.2 recurring and 2.1 recurring?

Itchy's Fleas

Itchy the dog has a million fleas. How many fleas might his shampoo kill?

Weekly Problem 11 - 2013 A shop has "Everything half price", and then "15% off sale prices". What is the overall reduction in cost?

What percentage of the truck's final mass is coal?

Percentage Unchanged

If the base of a rectangle is increased by 10% and the area is unchanged, by what percentage is the width decreased by ?

What fraction of customers buy Kleenz after the advertising campaign?

2011 Digits

Weekly Problem 10 - 2014 What is the sum of the first $2011$ digits when $20 \div 11$ is written as a decimal?

Pineapple Juice

What percentage of this orange drink is juice?

After playing 500 games, my success rate at Solitare is 49%. How many games do I need to win to increase my success rate to 50%?

Percentage of a Quarter

What percentage of a quarter is a fifth?

Fractions of 1000

Find a simple way to compute this long fraction.

Breakfast Time

Four hobbits each eat one quarter of the porridge remaining in the pan. How much is left?

Percentage Swap

What is 50% of 2007 plus 2007% of 50?

Antiques Roadshow

Last year, on the television programme Antiques Roadshow... work out the approximate profit.

Squeezed In

Weekly Problem 9 - 2017 What integer x makes x/9 lie between 71/7 and 113/11?

Producing an Integer

Multiply a sequence of n terms together. Can you work out when this product is equal to an integer?

Elephants and Geese

Yesterday, at Ulaanbaatar market, a white elephant cost the same amount as 99 wild geese. How many wild geese cost the same amount as a white elephant today?

The Property Market

A property developer sells two houses, and makes a 20% loss on one and a 20% profit on the other. Overall, did he make a profit or a loss?