What Are Equivalent Fractions?
Equivalent fractions are different fractions that represent the same value. They look different but are mathematically equal. For example, 1/2 and 3/6 are equivalent because both equal 0.5.
How to Find Equivalent Fractions
Multiply both the numerator (top) and denominator (bottom) by the same number:
- 3/7 × 2/2 = 6/14
- 3/7 × 3/3 = 9/21
- 3/7 × 4/4 = 12/28
- 3/7 × 10/10 = 30/70
The key rule: whatever you do to the numerator, you must do to the denominator.
Simplifying to Lowest Terms
Any fraction can be reduced to its simplest form by dividing both parts by their greatest common divisor (GCD).
- 6/14 → GCD(6, 14) = 2 → 3/7
- 15/35 → GCD(15, 35) = 5 → 3/7
- 24/56 → GCD(24, 56) = 8 → 3/7
All of these fractions are equivalent. The simplest form is the one where the GCD of numerator and denominator is 1.
Equivalent Fractions with Mixed Numbers
To find equivalent fractions for a mixed number, first convert it to an improper fraction:
- 2 3/4 = (2 × 4 + 3)/4 = 11/4
- Equivalents: 22/8, 33/12, 44/16, ...
Checking If Two Fractions Are Equivalent
Cross-multiply: a/b = c/d if and only if a × d = b × c.
- Is 3/7 = 9/21? → 3 × 21 = 63 and 7 × 9 = 63 → Yes
- Is 2/5 = 3/8? → 2 × 8 = 16 and 5 × 3 = 15 → No
Real-World Uses
- Cooking: Doubling a recipe that calls for 3/4 cup means using 6/8 (or 3/4 × 2 = 6/4 = 1 1/2 cups)
- Measurement: 1/2 inch = 8/16 inch on a ruler with 16ths markings
- Comparison: To compare 2/5 and 3/7, convert to common denominator: 14/35 vs 15/35
- Education: Understanding equivalence is fundamental to adding/subtracting fractions with different denominators