Finding the equivalent fraction with the smallest terms is a very useful skill to use with common fractions.

This process is a subset of finding equivalent fractions, by which a common fraction is matched with other common fractions of the same value, or equal to the first.

The formal method for finding the simplest equivalent fraction involves working out the highest common factor (HCF) of the numerator and denominator. For example, to simplify the common fraction 12/32:

factors of 12: 1, 2, 3, 4, 6, 12

factors of 32: 1, 2, 4, 8, 16, 32

highest common factor: 4

12 divided by 4 = 3

32 divided by 4 = 8

12/32 = 3/8

When students are at the investigative stage of learning this process, we can show them a fraction using some sort of physical or pictorial model, as shown in the video, and they can be asked to explore alternative ways to divide the shape to find a simpler fraction (i.e., one with smaller numbers).

Extending These Activities:

Students can be asked to simpify more complicated fractions, with larger numerator and denominator. A decimal fraction or percentage could be converted to a common fraction then simplified. For example: