Equivalent fractions: same amount, different numbers

A portion chart counts pizza in quarters, but you have one half. You can call the same share two quarters. No food appears or disappears; only the size of the pieces changes. Fractions such as 1/2 and 2/4 are equivalent.

Both bars stand for the same whole

The filled half and the two filled quarters cover the same share. Both bars have the same total size.

1/2

2/4

Name one half in quarters

Rewrite 1/2 using quarters.

Split each half into two

$2\times2=4$

The whole now has four equal pieces. Each new piece is a quarter.
Count the pieces you have

$\frac12=\frac{1\times2}{2\times2}=\frac24$

Your one half splits into two quarters. Double the top and the bottom, not just one of them.
Run the change backwards

$\frac68=\frac{6\div2}{8\div2}=\frac34$

Pair the eighths to make quarters. Six eighths and three quarters fill the same share. This gives the fraction a simpler name.

Why both numbers must change

The top number, or numerator, counts your pieces. The bottom number, or denominator, says how many equal pieces make the whole. A larger bottom number means smaller pieces of that same whole.

Multiplying top and bottom by 2 means multiplying the fraction by 2/2. That equals one, so the amount stays fixed. Changing only the top or bottom changes the share.

Use the same whole when you compare. Half a large pizza need not match half a small one. Equal fractions describe equal shares of a whole of the same size.

Try it yourself

Work out an answer and explain your reasoning. Then check the explanation.

Find an equivalent numerator

$\frac35=\frac{\square}{20}$

A chart uses twentieths. Rewrite three fifths in that form.

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$\frac{12}{20}$

Five became twenty after multiplying by four. Multiply three by four too.

Keep the value unchanged

$\frac23=\frac43$

Fix the fraction on the right without changing the original share. Explain what must change together.

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$\frac23=\frac46$

Doubling only the top number doubles the amount. Double the bottom number too.

Use this idea in fraction sums

The game offers mixed fraction arithmetic rather than an equivalence-only quiz. Use equal fractions when you need one piece size or a simpler answer.

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