A fraction a/b represents the total of a equal unit fractions, each 1/b: a/b=1/b+⋯+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>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 1, such as 41.
To write a fraction as a sum of unit fractions:
Look at the denominator. It tells the size of each unit fraction.
Look at the numerator. It tells how many unit fractions to use.
Write that many copies of the unit fraction and add them.
Example: Write 47 as a sum of unit fractions.
The denominator is 4, so each unit fraction is 41.
The numerator is 7, so use seven copies of 41.
47=41+41+41+41+41+41+41
This means that 47 is made of seven equal fourths. Four fourths make one whole, and the other three fourths extend past that whole. The denominator stays 4 because every part is the same size.
Learn by doing: Interpret a fraction as a sum of unit fractions
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Practice:
Number Line - Simple Fractions (Not Simplified), Read Number - Labelled