What is equivalent fractions?
Two fractions are equivalent when they represent the same amount even though they look different. For example, 1/2 and 2/4 and 50/100 all describe the same half of a pizza.
Why it matters
Equivalent fractions unlock adding and subtracting fractions with unlike denominators, comparing fractions, simplifying answers, and converting between fractions and decimals. Without this, every fraction problem feels like a different puzzle.
Worked example
Find a fraction equivalent to 2/3 with a denominator of 12.
- 1
Ask: "what do I multiply 3 by to get 12?" Answer: 4.
You need to scale the denominator up to 12. Whatever you do to the bottom, you must do to the top.
- 2
Multiply the numerator (top) by the same number: 2 × 4 = 8.
Multiplying top and bottom by the same number is the same as multiplying by 1 — it doesn’t change the value.
- 3
Write the new fraction: 8/12.
- 4
Check: does 8/12 = 2/3? Divide top and bottom of 8/12 by 4: 8÷4 = 2, 12÷4 = 3. Yes — both reduce to 2/3.
Answer
8/12 (and you can verify because 8/12 reduces back to 2/3)
Common mistakes
- •Adding the same number to both top and bottom instead of multiplying — e.g. turning 1/2 into 2/3 by adding 1 to each. (1/2 ≠ 2/3.)
- •Forgetting that the SAME multiplier must apply to both top and bottom.
- •Reducing too aggressively — e.g. simplifying 6/9 to 1/1 because both digits "look the same."
- •Confusing equivalent fractions with mixed numbers (1/2 is not equivalent to 1 1/2).
How Briveli teaches equivalent fractions
Briveli’s Grade 3 and Grade 4 fraction units teach equivalent fractions visually — with fraction bars and number lines — before introducing the multiply-by-1 trick, so kids understand WHY it works.
Practice Grade 4 math on Briveli