Fractions: practice sheet

Part 1: What a fraction means

Remember: A fraction names equal parts of a whole. In 3/4 the denominator 4 says the whole is cut into 4 equal parts, and the numerator 3 says how many parts we have.

1. 1. Warm-up A chocolate bar has 12 pieces and you eat 5. What fraction did you eat?

2. 2. Warm-up Write 2 3/5 as an improper fraction.

3. 3. Core Write 23/6 as a mixed number.

4. 4. Core What fraction of an hour is 20 minutes? (simplest form)

5. 5. Stretch 🔥 What fraction of a day is 9 hours? (simplest form)

6. 6. Stretch 🔥 Which is longer: 45 cm or 3/5 of a metre? (answer 45cm or 3/5)

Part 2: Equivalent fractions and simplest form

Remember: Multiply or divide the numerator and denominator by the same number and the value does not change: 2/3 = 4/6 = 8/12.

1. 7. Warm-up Simplify 6/9.

2. 8. Warm-up 4/5 = ?/20. What is the missing number?

3. 9. Core Simplify 42/56.

4. 10. Core Which of 9/12, 6/10 and 12/16 is NOT equal to 3/4?

5. 11. Stretch 🔥 3/7 = 15/?. What is the missing number?

6. 12. Stretch 🔥 Simplify 84/126.

Part 3: Comparing and ordering fractions

Remember: Same denominator: the bigger numerator is bigger. Same numerator: the smaller denominator is bigger (bigger pieces).

1. 13. Warm-up Which is bigger, 3/5 or 2/5?

2. 14. Warm-up Which is bigger, 1/6 or 1/4?

3. 15. Core Which is bigger, 5/8 or 3/5?

4. 16. Core Which is the smallest: 2/3, 3/5 or 7/10?

5. 17. Stretch 🔥 Which fraction is exactly halfway between 1/3 and 1/2?

6. 18. Stretch 🔥 Order 5/6, 7/9 and 3/4 from the smallest (write them with commas).

Part 4: Adding, subtracting and multiplying

Remember: To add or subtract, make the denominators the same, then add or subtract only the numerators. Simplify at the end.

1. 19. Warm-up 1/5 + 2/5 = ?

2. 20. Warm-up 5/8 − 3/8 = ? (simplest form)

3. 21. Core 1/4 + 2/3 = ?

4. 22. Core 5/6 − 1/4 = ?

5. 23. Core 2/3 × 3/4 = ? (simplest form)

6. 24. Stretch 🔥 2 1/2 + 1 2/3 = ? (as a mixed number)

7. 25. Stretch 🔥 What is 3/4 of 3/5 of 40?

Activity 1: Party recipe

A recipe for 4 people uses 3/4 cup of sugar, 1/2 cup of butter, 2 1/4 cups of flour and 2/3 cup of milk. Rewrite it for 6 people.
Steps: 6 people is 6/4 = 3/2 of the recipe, so multiply every amount by 3/2. · Turn mixed numbers into improper fractions before multiplying. · Simplify and write answers bigger than 1 as mixed numbers.

1. 26. Sugar for 6 people (cups)

2. 27. Butter for 6 people (cups)

3. 28. Flour for 6 people (cups)

4. 29. Milk for 6 people (cups)

Activity 2: Pizza party

3 pizzas are each cut into 8 equal slices. Riya eats 3/8 of a pizza, Kabir eats 5/8 of a pizza and Asha eats 1 1/4 pizzas.
Steps: Add what the three ate (use eighths). · Take it away from 3 whole pizzas. · Share the leftover equally between 3 friends.

1. 30. How many pizzas did they eat altogether? (mixed number)

2. 31. What fraction of a pizza is left?

3. 32. How many slices are left?

4. 33. If 3 friends share the leftover equally, what fraction of a pizza does each get?

Activity 3: Fraction detective

Each clue describes exactly one fraction. Find it.
Steps: Write what each clue tells you about the numerator and denominator. · Use equivalent fractions to find the numbers. · Check your fraction against every clue.

1. 34. I am equal to 2/3 and my denominator is 21.

2. 35. I am equal to 3/5 and my numerator and denominator add up to 40.

3. 36. My denominator is 24 and I am between 1/4 and 1/3.

4. 37. Half of me is 3/8. Who am I? (simplest form)

Homework

1. 38. Simplify 45/60.

2. 39. Which is bigger, 7/12 or 5/8?

3. 40. 3/8 + 5/12 = ?

4. 41. A tank holds 60 litres and is 2/3 full. How many litres are in it?

5. 42. Write 4 2/7 as an improper fraction.

Project: Fraction recipe card

Pick a simple recipe your family makes for 4 people (lemonade, a sandwich, a salad, a smoothie). Rewrite it so it serves 2 people and 6 people.

Recipe: ______________________
Ingredient | 4 people | 2 people (× 1/2) | 6 people (× 3/2)
__________ | ________ | ________ | ________
__________ | ________ | ________ | ________
__________ | ________ | ________ | ________
Fraction-bar drawings for two amounts:
Why multiplying by 3/2 gives the amounts for 6 people: ____________________