½ Fractions

Grade 4 · Number · Cambridge Primary Stage 4

Parts of a Whole

Numerator and denominator explained

Equivalent Fractions

½ = 2/4 = 3/6 — same value, different look

Comparing Fractions

Which fraction is bigger?

Adding & Subtracting

Fractions with the same denominator

Fractions of Amounts

Find ¾ of 40 and similar problems

1. Numerator and Denominator

A fraction has two parts:

3
4
Numerator (top) — how many parts you have
Denominator (bottom) — how many equal parts in total
3/4 means: the whole is split into 4 equal parts, and we have 3 of them.
💡 Remember: Denominator is Down (bottom). Numerator is on top — it's the Number of parts you have.

2. Equivalent Fractions

Equivalent fractions have the same value even though they look different.

½ = 2/4 = 3/6 = 4/8 = 5/10
To find an equivalent fraction, multiply (or divide) both the numerator and denominator by the same number.

½ × 2/2 = 2/4   |   ½ × 3/3 = 3/6   |   1/3 × 2/2 = 2/6
💡 Think of it like zooming in on a pizza: cutting each slice into 2 pieces doubles both the number of pieces and total pieces — same amount eaten!

3. Comparing Fractions (same denominator)

When fractions have the same denominator, simply compare the numerators.

3/8 vs 5/8 → same denominator (8), so compare tops: 5 > 3, therefore 5/8 > 3/8
Examples:
4/7 vs 2/7 → 4 > 2, so 4/7 > 2/7
7/10 vs 3/10 → 7 > 3, so 7/10 > 3/10
💡 The bigger the numerator (when denominators are equal), the bigger the fraction — more pieces of the same-sized slice!

4. Adding and Subtracting Fractions (same denominator)

When denominators are the same, add or subtract the numerators only. The denominator stays the same.

1/5 + 2/5 = 3/5   |   4/5 − 1/5 = 3/5
2/7 + 3/7 = 5/7 (add numerators: 2+3=5, keep denominator 7)
6/7 − 2/7 = 4/7 (subtract numerators: 6−2=4, keep denominator 7)
💡 Think of the denominator as the "name" of the pieces (sevenths, eighths…). You're just counting how many of those pieces you have.

5. Fractions of Amounts

To find a fraction of an amount: divide by the denominator, then multiply by the numerator.

¾ of 40 = (40 ÷ 4) × 3 = 10 × 3 = 30
Examples:
½ of 24 = 24 ÷ 2 = 12
¼ of 32 = 32 ÷ 4 = 8
2/3 of 18 = (18 ÷ 3) × 2 = 6 × 2 = 12
3/5 of 25 = (25 ÷ 5) × 3 = 5 × 3 = 15
💡 Memory trick: Divide by the bottom, multiply by the top. Bottom first, top second.

Example 1 — Equivalent Fraction

Find the missing numerator: 1/2 = ?/4

Denominator went from 2 to 4 (×2). Do the same to numerator: 1 × 2 = 2.
Answer: 2/4

Example 2 — Comparing Fractions

Which is larger: 3/8 or 5/8?

Same denominator (8). Compare numerators: 5 > 3.
5/8 is larger

Example 3 — Adding Fractions

1/5 + 2/5 = ?

Same denominator. Add numerators: 1 + 2 = 3. Keep denominator.
Answer: 3/5

Example 4 — Subtracting Fractions

4/5 − 1/5 = ?

Same denominator. Subtract numerators: 4 − 1 = 3. Keep denominator.
Answer: 3/5

Example 5 — Fraction of an Amount

3/4 of 40 = ?

Step 1: 40 ÷ 4 = 10 (one quarter)
Step 2: 10 × 3 = 30 (three quarters)
Answer: 30

📊 Fraction Bar Model

🔁 Equivalent Fraction Finder

🎯 Fraction of an Amount

Exercise 1 — Equivalent Fractions (find the missing numerator)

1. 1/2 = ?/4

2. 1/3 = ?/6

3. 2/3 = ?/6

4. 1/4 = ?/8

5. 3/4 = ?/8

6. 1/2 = ?/10

7. 2/5 = ?/10

8. 1/3 = ?/9

9. 3/4 = ?/12

10. 2/3 = ?/9

Exercise 2 — Comparing Fractions (enter the larger numerator)

1. Which has a larger numerator: 3/8 or 5/8? Enter the larger numerator.

2. Which is larger: 4/7 or 2/7? Enter the larger numerator.

3. Which is larger: 1/6 or 5/6? Enter the larger numerator.

4. Which is larger: 7/10 or 3/10? Enter the larger numerator.

5. Which is larger: 2/5 or 4/5? Enter the larger numerator.

6. Which is larger: 6/8 or 3/8? Enter the larger numerator.

7. Which is larger: 5/9 or 8/9? Enter the larger numerator.

8. Which is larger: 1/4 or 3/4? Enter the larger numerator.

9. Which is larger: 9/10 or 7/10? Enter the larger numerator.

10. Which is larger: 4/6 or 1/6? Enter the larger numerator.

Exercise 3 — Adding Fractions (same denominator, give numerator of answer)

1. 1/5 + 2/5 = ?/5 — enter the numerator

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

3. 1/8 + 4/8 = ?/8 — enter the numerator

4. 3/10 + 4/10 = ?/10 — enter the numerator

5. 2/9 + 5/9 = ?/9 — enter the numerator

6. 1/6 + 4/6 = ?/6 — enter the numerator

7. 3/8 + 2/8 = ?/8 — enter the numerator

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

9. 1/7 + 5/7 = ?/7 — enter the numerator

10. 2/5 + 2/5 = ?/5 — enter the numerator

Exercise 4 — Subtracting Fractions (give numerator of answer)

1. 4/5 − 1/5 = ?/5 — enter the numerator

2. 6/7 − 2/7 = ?/7 — enter the numerator

3. 7/8 − 3/8 = ?/8 — enter the numerator

4. 9/10 − 4/10 = ?/10 — enter the numerator

5. 8/9 − 3/9 = ?/9 — enter the numerator

6. 5/6 − 2/6 = ?/6 — enter the numerator

7. 7/8 − 5/8 = ?/8 — enter the numerator

8. 8/10 − 5/10 = ?/10 — enter the numerator

9. 6/7 − 1/7 = ?/7 — enter the numerator

10. 4/5 − 3/5 = ?/5 — enter the numerator

Exercise 5 — Fractions of Amounts

1. 1/2 of 24 = ?

2. 1/4 of 32 = ?

3. 3/4 of 40 = ?

4. 1/3 of 30 = ?

5. 2/3 of 18 = ?

6. 3/5 of 25 = ?

7. 1/2 of 56 = ?

8. 3/4 of 60 = ?

9. 2/5 of 35 = ?

10. 4/5 of 50 = ?

🏋️ Practice — 20 Questions

1. 1/2 = ?/4 (missing numerator)

2. 1/3 = ?/6 (missing numerator)

3. 2/3 = ?/6 (missing numerator)

4. 1/4 = ?/8 (missing numerator)

5. 3/4 = ?/8 (missing numerator)

6. 1/2 = ?/10 (missing numerator)

7. 2/5 = ?/10 (missing numerator)

8. 3/8 vs 5/8 — larger numerator = ?

9. 7/10 vs 3/10 — larger numerator = ?

10. 2/5 vs 4/5 — larger numerator = ?

11. 1/5 + 2/5 = ?/5 — numerator = ?

12. 2/7 + 3/7 = ?/7 — numerator = ?

13. 1/8 + 4/8 = ?/8 — numerator = ?

14. 3/10 + 4/10 = ?/10 — numerator = ?

15. 4/5 − 1/5 = ?/5 — numerator = ?

16. 6/7 − 2/7 = ?/7 — numerator = ?

17. 1/2 of 24 = ?

18. 1/4 of 32 = ?

19. 3/4 of 40 = ?

20. 1/3 of 30 = ?

🏆 Challenge — 8 Questions

1. 1/2 = ?/20 (find the missing numerator)

2. 2/5 = ?/15 (find the missing numerator)

3. 9/12 − 6/12 = ?/12 — enter the numerator

4. 3/5 of 25 = ?

5. 4/5 of 50 = ?

6. 3/4 of 40 = ?

7. 1/2 of 48 = ?

8. 2/3 of 9 = ?