Equivalent Fractions — Practice for Grades 4–5
Two fractions are equivalent when they describe the same amount, even though the numbers look different.
Understanding equivalent fractions
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.
Key Idea
The rule that makes this work: if you multiply (or divide) the top number and the bottom number by the same number (any whole number except zero), 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.
More pieces. The same amount.
Cut every piece of the bar into smaller, equal pieces, or glue pieces back together. Watch the green part: it never moves, and neither does the pin on the number line. Mira the glassblower is here to help, and every challenge you solve lights panes of her window wall.
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.
A common mistake, and the fix
Adding the same number to the top and the bottom.
Adding 1 to each turns 1/2 into 2/3, but 2/3 is more than half a bar, so the amount has changed. Multiply or divide the top and bottom by the same number instead: 1/2 = 2/4 = 3/6.
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.
Try it in Numeris.
A short lesson, then practice with feedback on every answer.
Put the reasoning on paper.
Try six fraction, angle, perimeter and area questions with explained answers, for grades 4–6.
Free printable · 3 pagesText version (screen-reader friendly): Draw it. Explain it. Math sample
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