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Equivalent fractions, step by step

Two fractions can name the same amount even when the numbers look nothing alike.

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The question

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4×2=8
1×2=2
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  1. 1/4 and the answer have to be the SAME amount — so nothing may be added to either half of it. The one move that leaves a fraction's value alone is cutting every piece into the same number of smaller pieces.
  2. Quarters into eighths: 8 ÷ 4 = 2, so each piece is being cut into 2. There are 2 times as many pieces, and each is 2 times smaller.
  3. The top is a COUNT of those pieces, so it is cut the same way: 1 × 2 = 2. 1/4 = 2/8 — the same amount of cake, cut differently.

How it works.

  1. 01

    1/4 and the answer have to be the SAME amount — so nothing may be added to either half of it. The one move that leaves a fraction's value alone is cutting every piece into the same number of smaller pieces.

  2. 02

    Quarters into eighths: 8 ÷ 4 = 2, so each piece is being cut into 2. There are 2 times as many pieces, and each is 2 times smaller.

  3. 03

    The top is a COUNT of those pieces, so it is cut the same way: 1 × 2 = 2. 1/4 = 2/8 — the same amount of cake, cut differently.

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