Equivalent Fractions – Same Value, Different Look
Two fractions are equivalent if they represent exactly the same amount of a whole, even though they are written differently. Think of 1/2 and 2/4 — cut a pizza in 2 and take 1 piece, or cut it in 4 and take 2 pieces. You have the same amount of pizza.
Creating Equivalent Fractions
Multiply (or divide) both the numerator and denominator by the same non-zero number. This is like multiplying by 1 in a clever disguise.
Equivalent fractions of 2/3
×2: 4/6 ×3: 6/9 ×5: 10/15 ×10: 20/30
All equal to 2/3 ✓
Identifying Equivalent Fractions
Use cross-multiplication: if a/b = c/d, then a × d = b × c.
Are 3/4 and 9/12 equivalent?
3 × 12 = 36 4 × 9 = 36 Equal ✓ — they are equivalent.
Are 2/5 and 5/12 equivalent?
2 × 12 = 24 5 × 5 = 25 Not equal ✗ — not equivalent.
Finding a Missing Numerator or Denominator
3/5 = ?/20
Denominator multiplied by 4 (5 × 4 = 20). So numerator × 4 too: 3 × 4 = 12. Answer: 12/20.
Equivalent Fractions Table
| Base Fraction | Equivalent Fractions |
|---|---|
| 1/2 | 2/4, 3/6, 4/8, 5/10, 50/100 |
| 1/3 | 2/6, 3/9, 4/12, 10/30 |
| 3/4 | 6/8, 9/12, 15/20, 75/100 |
| 2/5 | 4/10, 6/15, 8/20, 40/100 |
Key Takeaways
- Multiply or divide both parts by the same number to create an equivalent fraction.
- Cross-multiply to test whether two fractions are equivalent.
- Equivalent fractions are the foundation for adding fractions and simplifying.
Practice Questions
- Write four fractions equivalent to 1/5.
- Find the missing number: 4/7 = ?/28.
- Are 6/10 and 9/15 equivalent? Use cross-multiplication.
- Find the missing number: 3/? = 15/25.
- Which of these is not equivalent to 2/3: 4/6, 6/9, 8/11, 10/15?