Equivalent Fractions — Practice for Grades 4–5
Two fractions are equivalent when they describe the same amount, even though the numbers look different. Picture half a chocolate bar: you can call it 1/2, or you can score that same half into more pieces and call it 2/4, or 3/6 — it's still the same amount of chocolate. The name changes; the amount doesn't.
Understanding equivalent fractions
Two fractions are equivalent when they describe the same amount, even though the numbers look different. Picture half a chocolate bar: you can call it 1/2, or you can score that same half into more pieces and call it 2/4, or 3/6 — it's still the same amount of chocolate. The name changes; the amount doesn't.
The rule that makes this work: if you multiply (or divide) the top number and the bottom number by the same number, the fraction's value stays the same — because you're just cutting each piece into more (or fewer) equal pieces. So 1/2 = 2/4 because both top and bottom were multiplied by 2.
Why it matters: equivalent fractions are the key that unlocks comparing, adding, and simplifying fractions later. A child who sees that 1/2 and 3/6 are the same amount is ready for everything that follows.
Key Idea
The rule that makes this work: if you multiply (or divide) the top number and the bottom number by the same number, the fraction's value stays the same — because you're just cutting each piece into more (or fewer) equal pieces. So 1/2 = 2/4 because both top and bottom were multiplied by 2.
More pieces. The same amount.
Keep the whole the same size. Split each half into smaller, equal pieces and watch the shaded amount stay put.
(1 × 2) / (2 × 2) = 2 / 4. Both fractions shade half of the same whole.
Why not add 1 to the top and bottom?
1/2 and 2/3 cover different amounts. Adding 1 changes the shaded share. Multiplying both numbers by the same positive whole number splits all the pieces equally.
Explain it together: If you split each half into 3 pieces, why are 3 of the 6 pieces shaded?
Seeing it in action
Worked example
Is 3/6 equivalent to 1/2?
Start with 1/2. Multiply top and bottom by 3: (1×3)/(2×3) = 3/6.
So yes — 3/6 = 1/2. The bars below show the same whole divided into different-sized pieces; the shaded lengths match.
Worked example 2: simplifying
Write 4/8 in simplest form.
4 and 8 share a common factor of 4. Divide both: (4÷4)/(8÷4) = 1/2. So 4/8 = 1/2.
Try a few
Fill in: 2/3 = ?/6.
so 2/3 = 4/6; multiply top & bottom by 2.
Is 2/5 equivalent to 4/10?
×2 top and bottom.
Simplify 6/9.
divide both by 3.
Mosaic Province
A calm area-model game for making and matching equivalent fractions.
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Practice equivalent fractions in Numeris with instant feedback.
Put the reasoning on paper.
Try six fraction, angle, perimeter and area questions with explained answers, for grades 4–6.
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