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Interpret a fraction as a sum of unit fractions

A fraction a/ba/b represents the total of aa equal unit fractions, each 1/b1/b: a/b=1/b++1/ba/b=1/b+\cdots+1/b. The denominator identifies the size of each equal part of one whole, while the numerator counts how many such parts are combined; this remains true when a>ba>b, with the quantity extending beyond one whole on a bar model or number line. Decompositions into unlike unit fractions are not included.

Detailed Explanation: Interpret a fraction as a sum of unit fractions

A unit fraction has a numerator of 11, such as 14\frac14.

To write a fraction as a sum of unit fractions:

  1. Look at the denominator. It tells the size of each unit fraction.
  2. Look at the numerator. It tells how many unit fractions to use.
  3. Write that many copies of the unit fraction and add them.

Example: Write 74\frac{7}{4} as a sum of unit fractions.

  • The denominator is 44, so each unit fraction is 14\frac14.
  • The numerator is 77, so use seven copies of 14\frac14.
74=14+14+14+14+14+14+14\frac{7}{4} = \frac14+\frac14+\frac14+\frac14+\frac14+\frac14+\frac14

This means that 74\frac74 is made of seven equal fourths. Four fourths make one whole, and the other three fourths extend past that whole. The denominator stays 44 because every part is the same size.

Learn by doing: Interpret a fraction as a sum of unit fractions

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Number Line - Simple Fractions (Not Simplified), Read Number - Labelled


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