🍕 Fractions

Grade 5 · Number · Cambridge Primary Stage 5

What is a Fraction?

Numerator, denominator, parts of a whole

Equivalent Fractions

Multiply or divide top and bottom

Comparing Fractions

Same denominator, common denominator

Adding & Subtracting

Same and different denominators

Fractions of Amounts

Find 3/4 of 48 = 36

1. What is a Fraction?

A fraction shows a part of a whole. It is written as one number over another:

numeratordenominator  →  34 means 3 out of 4 equal parts
The denominator (bottom) tells you how many equal parts the whole is divided into.
The numerator (top) tells you how many of those parts you have.

Example: A pizza cut into 8 slices. You eat 3 slices → you ate 3/8 of the pizza.
💡 The word "denominator" has the word "de-nom-in-ator" — think of it as the name of the fraction (quarters, eighths, etc.)

2. Equivalent Fractions

Equivalent fractions have the same value but different numbers. To make one, multiply or divide both the top and bottom by the same number.

23 = 46 = 812   (×2, then ×4)
Simplifying fractions: Divide both top and bottom by their HCF (Highest Common Factor).
Example: Simplify 12/18. HCF of 12 and 18 is 6.
12 ÷ 6 = 2,   18 ÷ 6 = 3  →  2/3
💡 A fraction is in its simplest form when the top and bottom share no common factor other than 1.

3. Comparing and Ordering Fractions

To compare fractions:

Same denominator: just compare the numerators.
3/7 vs 5/7 → 3 < 5 → 3/7 < 5/7

Different denominators: convert to a common denominator first (use LCM).
Compare 1/3 and 2/5: LCM of 3 and 5 = 15.
1/3 = 5/15,   2/5 = 6/15 → 1/3 < 2/5
Mixed numbers and improper fractions:
A mixed number has a whole part and a fraction part: 2¾
An improper fraction has numerator ≥ denominator: 11/4
To convert: 2¾ → (2×4 + 3)/4 = 11/4  |  11/4 → 11÷4 = 2 remainder 3 → 2¾

4. Adding and Subtracting Fractions

Same denominator: add/subtract the numerators, keep the denominator.
38 + 28 = 58
Different denominators: find the LCD (Lowest Common Denominator), convert, then add.
13 + 14 : LCD = 12 → 412 + 312 = 712
Adding mixed numbers: add the whole parts, then add the fractions.
1½ + 2¼ → (1+2) + (2/4 + 1/4) = 3 + 3/4 = 3¾
💡 Always simplify your answer at the end if you can!

5. Fractions of Amounts

To find a fraction of an amount:

Divide by the denominator, then multiply by the numerator
Find 3/4 of 48:
Step 1: 48 ÷ 4 = 12 (find one quarter)
Step 2: 12 × 3 = 36 (multiply by numerator)
So 3/4 of 48 = 36
Find 2/5 of 35:
35 ÷ 5 = 7  →  7 × 2 = 14
💡 The word "of" in maths means multiply. So 3/4 of 48 = 3/4 × 48.

Example 1 — Equivalent Fractions

Find the missing number: 3/5 = ?/20
5 × 4 = 20, so multiply the top by 4 too: 3 × 4 = 12
Answer: 3/5 = 12/20

Example 2 — Simplifying

Simplify 15/20
HCF of 15 and 20 is 5. Divide both by 5: 15÷5 = 3, 20÷5 = 4
Answer: 3/4

Example 3 — Adding Fractions (different denominators)

Work out 2/3 + 1/4
LCD of 3 and 4 = 12. Convert: 2/3 = 8/12 and 1/4 = 3/12
8/12 + 3/12 = 11/12. Answer: 11/12

Example 4 — Fraction of an Amount

Find 5/8 of 64
64 ÷ 8 = 8. Then 8 × 5 = 40
Answer: 40

Example 5 — Converting Mixed ↔ Improper

Convert 3 2/5 to an improper fraction
Multiply whole by denominator: 3 × 5 = 15. Add numerator: 15 + 2 = 17
Answer: 17/5

Fraction Bar Comparator

Enter two fractions to compare them as bars.

Equivalent Fraction Finder

Enter a fraction to see its first five equivalents.

Exercise 1 — Equivalent Fractions

Find the missing number in each equivalent fraction. Enter your answer.

1. 2/3 = ?/9 → enter the missing number

2. 3/4 = ?/12 → enter the missing number

3. 4/5 = 12/? → enter the missing number

4. 1/2 = ?/10 → enter the missing number

5. 5/6 = ?/18 → enter the missing number

6. 2/7 = 6/? → enter the missing number

7. 3/5 = ?/20 → enter the missing number

8. 4/9 = ?/27 → enter the missing number

9. 1/4 = 5/? → enter the missing number

10. 6/8 = 3/? → enter the missing number (simplify)

Exercise 2 — Simplifying Fractions

Simplify each fraction fully. Enter the numerator of the simplified fraction.

1. Simplify 6/8 → enter the numerator

2. Simplify 10/15 → enter the numerator

3. Simplify 4/12 → enter the numerator

4. Simplify 9/12 → enter the numerator

5. Simplify 8/20 → enter the numerator

6. Simplify 6/9 → enter the numerator

7. Simplify 12/16 → enter the numerator

8. Simplify 15/25 → enter the numerator

9. Simplify 14/21 → enter the numerator

10. Simplify 18/24 → enter the numerator

Exercise 3 — Adding Fractions (Same Denominator)

Add the fractions. Enter only the numerator of the answer (denominator stays the same).

1. 3/8 + 2/8 = ?/8 → enter the numerator

2. 1/5 + 3/5 = ?/5 → enter the numerator

3. 2/9 + 4/9 = ?/9 → enter the numerator

4. 5/12 + 3/12 = ?/12 → enter the numerator

5. 7/10 − 3/10 = ?/10 → enter the numerator

6. 4/7 + 2/7 = ?/7 → enter the numerator

7. 9/11 − 5/11 = ?/11 → enter the numerator

8. 3/10 + 4/10 = ?/10 → enter the numerator

9. 6/13 + 5/13 = ?/13 → enter the numerator

10. 8/15 − 3/15 = ?/15 → enter the numerator

Exercise 4 — Fractions of Amounts

Find the fraction of each amount. All answers are whole numbers.

1. Find 1/2 of 48

2. Find 3/4 of 48

3. Find 2/5 of 35

4. Find 3/8 of 64

5. Find 5/6 of 36

6. Find 2/3 of 27

7. Find 4/5 of 60

8. Find 3/7 of 49

9. Find 5/8 of 40

10. Find 7/10 of 90

Exercise 5 — Mixed Numbers & Improper Fractions

Convert between mixed numbers and improper fractions as instructed.

1. Convert 7/3 to a mixed number. What is the whole number part?

2. Convert 11/4 to a mixed number. What is the whole number part?

3. Convert 2¾ to an improper fraction. What is the numerator?

4. Convert 3½ to an improper fraction. What is the numerator?

5. Convert 13/5 to a mixed number. What is the whole number part?

6. Convert 17/6 to a mixed number. What is the whole number part?

7. Convert 4⅖ to an improper fraction. What is the numerator?

8. Convert 19/4 to a mixed number. What is the whole number part?

9. Convert 5⅓ to an improper fraction. What is the numerator?

10. Convert 23/6 to a mixed number. What is the whole number part?

🏋️ Practice — Mixed Fractions (20 Questions)

1. 3/4 = ?/8 — find the missing number

2. Simplify 10/12 — enter the numerator

3. 2/7 + 3/7 = ?/7 — enter the numerator

4. Find 1/4 of 32

5. Convert 9/4 to a mixed number — enter the whole number part

6. 1/2 = ?/14 — find the missing number

7. Simplify 8/12 — enter the numerator

8. 5/9 − 2/9 = ?/9 — enter the numerator

9. Find 2/3 of 24

10. Convert 3⅔ to an improper fraction — enter the numerator

11. 2/5 = ?/15 — find the missing number

12. Simplify 16/20 — enter the numerator

13. 4/11 + 6/11 = ?/11 — enter the numerator

14. Find 3/5 of 40

15. Convert 15/4 to a mixed number — enter the whole number part

16. 3/8 = ?/24 — find the missing number

17. Simplify 14/21 — enter the numerator

18. Find 7/8 of 56

19. Convert 2⅘ to an improper fraction — enter the numerator

20. 11/13 − 5/13 = ?/13 — enter the numerator

🏆 Challenge — Multi-Step Fraction Problems (8 Questions)

1. Find 2/3 of 3/4 of 60. (First find 3/4 of 60, then find 2/3 of that)

2. Sam has 48 sweets. He gives away 3/8 of them. How many does he keep?

3. Which is larger: 5/8 or 3/5? Enter 1 if 5/8 is larger, enter 2 if 3/5 is larger.

4. A bag of flour weighs 2¾ kg. Another weighs 1⅝ kg. What is the total in kg × 8? (so enter your answer × 8 to make it a whole number — answer to 2¾+1⅝=4⅜ so ×8 = 35)

5. A class has 30 pupils. 2/5 are boys. How many girls are there?

6. Convert 4⅞ to an improper fraction. What is the numerator?

7. 1/3 of a number is 15. What is the whole number?

8. A recipe uses 3/4 cup of sugar. If you make 6 batches, how many cups of sugar do you need in total? (Give whole number — answer is 4 and a half, enter 4 for the whole number part)