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.
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. (Visual: a bar split in 2 with 1 shaded, beside a bar split in 6 with 3 shaded — 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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