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🍕 Fractions

Grade 3 · Halves, Quarters, Thirds, Eighths · Cambridge Primary Stage 3

Unit Fractions

1/2, 1/3, 1/4, 1/8 — one part of a whole

Fraction of a Shape

Shading equal parts of a whole shape

Fraction of an Amount

Finding 1/2 of 12, 1/4 of 20...

Equivalent Fractions

1/2 = 2/4 = 4/8

Comparing Fractions

Which is bigger: 1/2 or 3/4?

Adding Fractions

Adding fractions with the same denominator

1. Unit Fractions

A unit fraction has 1 as its numerator (top number). It means one equal part of a whole.

12 = one half  |  13 = one third  |  14 = one quarter  |  18 = one eighth
The denominator (bottom) tells you how many equal parts the whole is split into.
The numerator (top) tells you how many parts you have.

1/4 means: split into 4 equal parts, take 1.
🍕 Think of a pizza! 1/4 means cut into 4 equal slices and take 1 slice.

2. Fraction of a Shape

To show a fraction of a shape, split it into equal parts and shade the number shown by the numerator.

To shade 3/4 of a rectangle:
1. Split into 4 equal parts
2. Shade 3 parts
3. Check: all parts are the same size!
🍰 Equal parts is the key — all pieces must be the same size, like equal slices of cake!

3. Fraction of an Amount

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

Fraction of amount = total ÷ denominator × numerator
Find 1/4 of 20:
Step 1: Divide by denominator: 20 ÷ 4 = 5
Step 2: Multiply by numerator: 5 × 1 = 5

Find 3/4 of 20:
Step 1: 20 ÷ 4 = 5
Step 2: 5 × 3 = 15
🍬 For unit fractions (top = 1), you just divide! 1/3 of 12 = 12 ÷ 3 = 4.

4. Equivalent Fractions

Equivalent fractions look different but are worth the same amount.

1/2 = 2/4 = 4/8
To find equivalent fractions, multiply (or divide) both numerator and denominator by the same number:
1/2 × 2/2 = 2/4 ✓
1/4 × 2/2 = 2/8 ✓
2/4 ÷ 2/2 = 1/2 ✓
🌈 Think of it like doubling a recipe — if you use twice as many pieces but also cut twice as many, the amount stays the same!

5. Comparing Fractions

To compare fractions with the same denominator, just compare the numerators. For different denominators, convert to decimals or use a fraction wall.

Same denominator: 3/8 vs 5/8 → 5/8 is bigger (5 > 3)

Different denominators: 1/2 vs 3/4
Convert: 1/2 = 0.5, 3/4 = 0.75 → 3/4 is bigger
🍭 The bigger the denominator, the smaller each piece is! So 1/8 < 1/4 < 1/2.

6. Adding Fractions (Same Denominator)

When fractions have the same denominator, just add the numerators — the denominator stays the same!

1/4 + 2/4 = 3/4 (add tops, keep bottom)
1/8 + 3/8 = 4/8 = 1/2
1/3 + 1/3 = 2/3
2/8 + 3/8 = 5/8
🎂 You can only add fractions directly when the denominators are the same — like adding slices from the same size pizza!

Example 1 — Fraction of an Amount

Find 1/2 of 12.

Divide by denominator: 12 ÷ 2 = 6
Multiply by numerator: 6 × 1 = 6

Example 2 — Equivalent Fractions

Fill in the gap: 1/2 = ?/4

Multiply denominator 2 by 2 to get 4.
Multiply numerator by the same: 1 × 2 = 2. Answer: 2/4

Example 3 — Comparing Fractions

Which is bigger: 1/2 or 3/4?

1/2 = 0.5 (as a decimal)
3/4 = 0.75 (as a decimal)
0.75 > 0.5, so 3/4 is bigger

Example 4 — Adding Fractions

1/4 + 2/4 = ?

Same denominator (4), so add numerators: 1 + 2 = 3
Answer: 3/4 (as a decimal: 0.75)

Example 5 — Fraction of Amount (harder)

Find 3/4 of 12.

Divide by denominator: 12 ÷ 4 = 3
Multiply by numerator: 3 × 3 = 9

🍕 Fraction Bar Shading Tool

Choose a denominator, then click segments to shade them. See your fraction update live!

Click segments above to shade them!

Exercise 1 — Fractions of Amounts

1. What is 1/2 of 12?

2. What is 1/4 of 16?

3. What is 1/3 of 15?

4. What is 1/4 of 12?

5. What is 1/2 of 16?

6. What is 1/3 of 36?

7. What is 1/4 of 36?

8. What is 1/3 of 45?

9. What is 1/2 of 4?

10. What is 1/2 of 20?

Exercise 2 — Equivalent Fractions (find the missing numerator)

1. 1/2 = ?/4

2. 1/2 = ?/8

3. 1/4 = ?/8 (hint: what is 1×2?)

4. 3/4 = ?/8

5. 1/4 = ?/8

6. 2/4 = ?/8

7. 3/4 = ?/8

8. 4/4 = ?/8

9. 3/8 = ?/8 (already same — what is the numerator?)

10. 1/2 = ?/4 (same as q1 but check you remember!)

Exercise 3 — Which is Larger? (type the larger fraction as a decimal)

Tip: 1/2=0.5, 1/4=0.25, 3/4=0.75, 1/3≈0.333, 1/8=0.125, 3/8=0.375, 5/8=0.625, 7/8=0.875

1. 1/2 or 1/4? Type the larger as a decimal.

2. 3/4 or 1/2? Type the larger as a decimal.

3. 1/2 or 3/8? Type the larger as a decimal.

4. 5/8 or 1/2? Type the larger as a decimal.

5. 1/4 or 1/2? Type the larger as a decimal.

6. 3/4 or 5/8? Type the larger as a decimal.

7. 1/2 or 3/8? Type the larger as a decimal.

8. 3/4 or 3/8? Type the larger as a decimal.

9. 1/2 or 1/4? Type the larger as a decimal.

10. 7/8 or 3/4? Type the larger as a decimal.

Exercise 4 — Add Fractions (same denominator, type answer as decimal)

Add the fractions, then write your answer as a decimal. e.g. 3/4 = 0.75

1. 1/4 + 2/4 = ? (decimal)

2. 1/8 + 4/8 = ? (decimal)

3. 1/3 + 1/3 = ? (decimal, use 0.667)

4. 3/8 + 4/8 = ? (decimal)

5. 1/4 + 1/4 = ? (decimal)

6. 2/8 + 4/8 = ? (decimal)

7. 1/8 + 3/8 = ? (decimal)

8. 1/8 + 4/8 = ? (decimal)

9. 1/3 + 1/3 = ? (decimal, use 0.667)

10. 3/8 + 4/8 = ? (decimal)

Exercise 5 — Fraction of an Amount (harder)

1. 3/4 of 12 = ?

2. 3/4 of 8 = ?

3. 1/2 of 40 = ?

4. 3/4 of 20 = ?

5. 3/4 of 16 = ?

6. 3/4 of 24 = ?

7. 1/2 of 20 = ?

8. 5/8 of 40 = ?

9. 1/4 of 32 = ?

10. 3/4 of 28 = ?

🏋️ Practice — 20 Questions

Questions 11–18 need decimal answers. Tip: 1/2=0.5, 1/4=0.25, 3/4=0.75, 1/3≈0.333, 1/8=0.125

1. 1/2 of 12 = ?

2. 1/4 of 32 = ?

3. 1/4 of 12 = ?

4. 1/3 of 36 = ?

5. 1/3 of 15 = ?

6. 1/4 of 16 = ?

7. 1/4 of 36 = ?

8. 1/2 of 4 = ?

9. 1/3 of 45 = ?

10. 1/2 of 20 = ?

11. 1/2 as a decimal = ?

12. 1/4 as a decimal = ?

13. 3/4 as a decimal = ?

14. 1/3 as a decimal (use 0.333) = ?

15. 1/8 as a decimal = ?

16. 5/8 as a decimal = ?

17. 7/8 as a decimal = ?

18. 2/3 as a decimal (use 0.667) = ?

19. 1/4 of 16 = ?

20. 3/4 of 8 = ?

🏆 Challenge — 8 Questions (decimal answers)

Type all answers as decimals.

1. 1/2 as a decimal = ?

2. 1/4 as a decimal = ?

3. 3/4 as a decimal = ?

4. 1/8 as a decimal = ?

5. 3/8 as a decimal = ?

6. 5/8 as a decimal = ?

7. 7/8 as a decimal = ?

8. 1/3 as a decimal (use 0.333) = ?