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Unlike denominator word problems, step by step

Adding 2/3 and 1/12 is not hard once the denominators match — the work is noticing they do not.

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The question

How much more did Omar use than Kwame?

Omar worked the early shift and used 2/3 kilogram; Kwame came in later and used 1/12 kilogram.
2/3 − 1/12
8/12 − 1/12
7/12 kilogram
  1. Read it through once. Two amounts, one taken from the other — so the operation is the easy part. The work is that the two fractions are cut into different-sized pieces.
  2. You cannot subtract them as they stand: 2/3 − 1/12 counts pieces of two different sizes. Find a size they can BOTH be cut into.
  3. Rewritten over that common denominator: 8/12 − 1/12. Nothing has changed value — the same amounts, counted in the same-sized pieces.
  4. Now the numerators subtract, and the denominator stays put: 7/12 kilogram.

How it works.

  1. 01

    Read it through once. Two amounts, one taken from the other — so the operation is the easy part. The work is that the two fractions are cut into different-sized pieces.

  2. 02

    You cannot subtract them as they stand: 2/3 − 1/12 counts pieces of two different sizes. Find a size they can BOTH be cut into.

  3. 03

    Rewritten over that common denominator: 8/12 − 1/12. Nothing has changed value — the same amounts, counted in the same-sized pieces.

  4. 04

    Now the numerators subtract, and the denominator stays put: 7/12 kilogram.

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