Fraction word problems

Read the story, draw a bar model, decide which operation it needs, then solve and check the answer makes sense.

Four steps for any fraction word problem

Read it twice. What is the whole? What is the question asking for?
Draw a bar model. A long bar is the whole; cut it into the parts the fraction describes.
Choose the operation: “of” usually means multiply, “altogether” add, “left” or “more than” subtract, “share” or “how many fit” divide.
Check: is the answer sensible? A fraction of 24 must be less than 24 when the fraction is less than 1.

See it: pictures to draw with your child

Copy these onto paper or a whiteboard. A quick sketch makes the idea concrete before any written method.

3/4 of 24: four groups of 6, take three, 18.

Finding the whole: if 2 parts are $12, each part is $6 and the whole is $30.

Maya and Leo together ate 5/8 of the pizza.

Type 1: a fraction of an amount

“3/4 of the 24 children have a pet. How many have a pet?” Draw 24 as a bar cut into 4 equal parts. Each part is 24 ÷ 4 = 6. Three parts: 3 × 6 = 18 children.

Divide by the bottom, multiply by the top. See fraction of a number.

Type 2: adding and subtracting fractions

“Maya ate 1/4 of a pizza and Leo ate 3/8. How much did they eat altogether?” 1/4 = 2/8, so 2/8 + 3/8 = 5/8 of the pizza. How much is left? 1 − 5/8 = 3/8.

Make sure the fractions are of the same whole: 1/2 of a small pizza plus 1/2 of a large one is not one pizza. See adding fractions and subtracting fractions.

Type 3: multiplying and dividing

“A recipe uses 2/3 cup of oats. How much for 3 batches?” 3 × 2/3 = 2 cups.
“A ribbon is 3 m long. How many 3/4 m pieces can be cut?” 3 ÷ 3/4 = 4 pieces.
“Half a cake is shared by 4 friends. How much does each get?” 1/2 ÷ 4 = 1/8 of the cake.

See fractions × whole numbers and dividing fractions.

Type 4: finding the whole

“Sam spent 2/5 of his money, which was $12. How much did he have?” In the bar model, 2 parts are $12, so 1 part is $6 and 5 parts are $30. These “backwards” problems are much easier with a picture than with a rule.

Two-step problems

“A class of 30 has 1/3 who walk to school and 1/5 who cycle. How many come another way?” Walk: 30 ÷ 3 = 10. Cycle: 30 ÷ 5 = 6. Another way: 30 − 10 − 6 = 14. Write each step on its own line, and label what each number means.

Quiz: fraction word problems

Read carefully and draw a bar model if it helps.

Where this fits: fractions step by step

What to say to your child

A short script for teaching it the first time. Pause after each line and let your child do the next step.

“There are 20 sweets. You get 2/5 of them. How many?”
“Let’s draw a bar for the 20 and cut it into 5 equal parts. How many in each?” (4.)
“You get 2 parts.” (8 sweets.)
“Does 8 make sense? Is it less than 20?” (Yes.)
“Draw, choose, solve, check.”

More worked examples

Example 1: fraction of an amount

2/3 of 27 stickers: 27 ÷ 3 = 9, × 2 = 18 stickers.

Example 2: adding

1/2 h of reading + 1/3 h of piano = 3/6 + 2/6 = 5/6 h.

Example 3: dividing

How many 1/4 kg bags from 3 kg of rice? 3 ÷ 1/4 = 12 bags.

Example 4: finding the whole

3/8 of a number is 15, so 1/8 is 5 and the number is 40.

Practice questions (answers below)

Ask these out loud or write them down. Check each answer, and ask “how did you get that?” for one or two.

1/2 of 18
3/4 of 20
2/5 of 35
A pie: 1/3 eaten, then 1/6. How much eaten?
A tank is 7/8 full; 3/8 is used. How full now?
4 children each drink 3/4 litre. How much in all?
How many 1/3-cup scoops in 4 cups?
1/4 of a number is 7. What is the number?
2/3 of the 24 pupils are girls. How many boys?
Stretch: 3/5 of the money is $45. How much in all?

Show the answers

9
15
14
1/2
4/8 = 1/2
3 litres
12
28
8
$75

Common mistakes

Using the wrong wholeFinds 3/4 of the remaining amount instead of the total.Fix: underline the whole in the question before starting.

Choosing the wrong operationAdds when the story says “of”.Fix: “of” usually means multiply: 3/4 of 24 = 18.

Answer that doesn’t make senseSays 3/4 of 24 is 32.Fix: a fraction less than 1 of a number is smaller than the number.

How to teach it at home

Kitchen problems

Make up questions while cooking: half of 3 cups, 3 × 1/4 tsp.

Pocket money

Spend 1/4 of the money. How much is left?

Sport scores

What fraction of the shots went in?

By grade

Grade 3: fractions of shapes and simple amounts.
Grade 4 (4.NF.B.3d, 4.NF.B.4c): add, subtract and multiply in stories.
Grade 5 (5.NF.A.2, 5.NF.B.6, 5.NF.B.7c): unlike denominators, multiplying and dividing.
Grade 6 (6.NS.A.1): divide fractions in stories.

More for each grade: Grade 3 math and the CBSE class 3 maths guide; Grade 4 math and the CBSE class 4 maths guide; Grade 5 math and the CBSE class 5 maths guide; Grade 6 math and the CBSE class 6 maths guide.