Equivalent Fractions
Discover how different fractions can name the same amount, learn to find and create equivalent fractions, and simplify fractions to their lowest terms.
What Are Equivalent Fractions?
Equivalent fractions are fractions that look different but represent exactly the same amount. Think of cutting a pizza: if you cut it into 4 pieces and eat 2, or cut it into 8 pieces and eat 4, you have eaten the same amount — half the pizza.
Visual: Fraction Bars
1/2
2/4
4/8
1/2 = 2/4 = 4/8 — All three shaded areas are equal!
Creating Equivalent Fractions
To create an equivalent fraction, multiply or divide both the numerator and denominator by the same number. This is like multiplying by 1 (e.g. 2/2 or 3/3), so the value stays the same.
Multiply Up (scaling up)
4 × 3 = 12, so multiply numerator by 3 too:
3 × 3 = 9
3/4 = 9/12
Divide Down (simplifying)
12 ÷ 4 = 3, so divide numerator by 4 too:
8 ÷ 4 = 2
8/12 = 2/3
Equivalent Fractions Family Table
| Simplest Form | ×2 | ×3 | ×4 |
|---|---|---|---|
| 1/2 | 2/4 | 3/6 | 4/8 |
| 1/3 | 2/6 | 3/9 | 4/12 |
| 2/3 | 4/6 | 6/9 | 8/12 |
| 3/4 | 6/8 | 9/12 | 12/16 |
Simplifying Fractions
A fraction is in its simplest form (also called lowest terms) when the only number that divides evenly into both the numerator and denominator is 1. We find the highest common factor (HCF) and divide both numbers by it.
Simplify 6/9
HCF of 6 and 9 = 3
6 ÷ 3 = 2 9 ÷ 3 = 3
6/9 = 2/3
Simplify 10/15
HCF of 10 and 15 = 5
10 ÷ 5 = 2 15 ÷ 5 = 3
10/15 = 2/3
Simplify 12/16
HCF of 12 and 16 = 4
12 ÷ 4 = 3 16 ÷ 4 = 4
12/16 = 3/4
Key Vocabulary
Equivalent Fractions
Fractions that have the same value even though they use different numbers. E.g. 1/2 = 2/4.
Numerator
The top number of a fraction — shows how many parts you have.
Denominator
The bottom number of a fraction — shows how many equal parts the whole is divided into.
Simplest Form
A fraction where the numerator and denominator share no common factor other than 1. E.g. 3/4 is simpler than 6/8.
Worked Examples
Find two fractions equivalent to 2/5.
Method: Multiply both numerator and denominator by the same number.
×2: 2×2 = 4 and 5×2 = 10, so 4/10
×4: 2×4 = 8 and 5×4 = 20, so 8/20
Answer: 2/5 = 4/10 = 8/20
Find the missing number: 3/4 = ?/20
Step 1: How did the denominator change? 4 × 5 = 20, so we multiplied by 5.
Step 2: Multiply the numerator by the same number: 3 × 5 = 15.
Answer: 3/4 = 15/20
Simplify 18/24 to its lowest terms.
Step 1: Find the HCF of 18 and 24. Factors of 18: 1, 2, 3, 6, 9, 18. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. HCF = 6.
Step 2: Divide both by 6: 18 ÷ 6 = 3 and 24 ÷ 6 = 4.
Answer: 18/24 = 3/4 (simplest form)
Knowledge Check
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Key Concepts Summary
- ●Equivalent fractions have the same value but different numerators and denominators.
- ●To find an equivalent fraction, multiply or divide both top and bottom by the same number.
- ●To simplify, find the Highest Common Factor (HCF) and divide both numbers by it.
- ●A fraction is in simplest form when the HCF of the numerator and denominator is 1.
- ●Use fraction bars or diagrams to visualise whether fractions are equivalent.