Choosing the operation
Fraction word problems use the same thinking as whole-number problems. Decide what’s happening in the story, then choose the operation.
| The story… | Operation | Example |
|---|---|---|
| Combines parts | Add | 1/3 of the pizza plus 1/4 more |
| Takes away or compares | Subtract | How much more is 3/4 than 1/2? |
| Asks for a fraction of an amount | Multiply | 2/3 of 24 students |
| Repeats an amount | Multiply | 5 bottles of 3/4 L each |
| Asks how many parts fit | Divide | How many 1/4 kg bags from 3 kg? |
| Shares an amount equally | Divide | 3/4 of a cake shared by 3 people |
Draw a bar model
A bar model turns the story into a picture. Draw a bar for the whole, split it into equal parts, and label what you know.
Problem: A class has 30 students. 2/5 walk to school. How many walk?
Draw a bar of 30 split into 5 parts of 6. Two parts = 12 students.
Example 1: Remaining amounts
Problem: Ali had 3/4 of a tank of gas. He used 1/3 of the tank. What fraction is remaining?
3/4 − 1/3 = 9/12 − 4/12 = 5/12 of a tank.
Example 2: Fraction of a fraction
Problem: 2/3 of the students in a club are girls. 1/2 of the girls play chess. What fraction of the club are girls who play chess?
1/2 × 2/3 = 1/3.
Example 3: Fraction of the rest
Problem: Maya spent 1/4 of her $80 on a book and 1/3 of the rest on lunch. How much is left?
- Book: 1/4 × 80 = $20. Rest = $60.
- Lunch: 1/3 × 60 = $20. Left = $40.
Watch "of the rest": the second fraction is of the remainder, not the original.
Example 4: Division
Problem: A ribbon is 4 1/2 m long. How many 3/4 m pieces can be cut?
9/2 ÷ 3/4 = 9/2 × 4/3 = 36/6 = 6 pieces.
Example 5: Finding the whole
Problem: 3/8 of a number is 24. What is the number?
- 1/8 is 24 ÷ 3 = 8.
- 8/8 is 8 × 8 = 64.
Worked examples
Example 1: A recipe needs 2/3 cup of flour per batch. How much for 4 batches?
4 × 2/3 = 8/3 = 2 2/3 cups.
Example 2: Jo ran 2 1/2 km and Sam ran 1 3/4 km. How much farther did Jo run?
5/2 − 7/4 = 10/4 − 7/4 = 3/4 km.
Example 3: 5/6 of a pizza is shared equally by 5 friends. How much does each get?
5/6 ÷ 5 = 1/6 of the pizza.
Common mistakes
- Using the original whole when the problem says "of the rest".
- Choosing multiply when you should divide, and vice versa. Ask: am I finding part of something, or how many parts fit?
- Forgetting units in the answer.
Try it yourself
- 3/4 of 36 people like pizza. How many?
- A jug holds 2 L. How many 1/4 L glasses can it fill?
- Leo ate 1/5 of a cake and Mia ate 1/2. How much is left?
- 2/3 of a number is 18. Find the number.
- Sara has $60. She saves 1/2 and spends 1/3 of the rest. How much did she spend?
Answers: 1) 27 2) 8 3) 3/10 4) 27 5) $10
Quick recap
- Decide the operation from the story.
- Use a bar model to see the whole and its parts.
- Watch for "of the rest" and for finding the whole from a part.