Equivalent Fractions

Study Sheet

Equivalent Fractions

Simplifying to lowest terms

Lowest Terms

Concept
The Big Idea
6 of 8 parts shaded

A fraction is in lowest terms when the top and bottom share no factor except 11. Divide both by their greatest common factor to get there in one step.

Example
Simplifying 68\dfrac{6}{8}

Both share the factor 22: 6÷28÷2=34\dfrac{6 \div 2}{8 \div 2} = \dfrac{3}{4}. The picture shows the same shaded amount.

In Plain Terms & More Examples

Concept
In plain terms

A fraction is in lowest terms when the top and bottom share no common factor but 11. Divide both by the biggest factor they share.

Example
Simplifying 812\dfrac{8}{12}

Both share 44: 8÷412÷4=23\dfrac{8 \div 4}{12 \div 4} = \dfrac{2}{3}.

Example
Simplifying 915\dfrac{9}{15}

Both share 33: 9÷315÷3=35\dfrac{9 \div 3}{15 \div 3} = \dfrac{3}{5}.