One amount, many names

Fold a paper strip in half. Shade one side with a pencil. Fold the strip again. Now it has 4 parts. The shading has not moved.

The rule

Cut every part in half. The shading stays where it is. So 1/2 and 2/4 are two names for one amount.

Multiply the top and the bottom by the same number. The amount does not change.

Two names for one amount are equivalent fractions. Divide top and bottom by the same number above 1. Repeat until no number above 1 works. The result is the simplest form. 4/8 becomes 1/2.

In simplest form, top and bottom share no factor except 1. A factor divides a number exactly.

Example

3/4 = ?/8. The ? is the missing top number.

The bottom is 4 × 2 = 8. So multiply the top by 2 too.

3 × 2 = 6. So 3/4 = 6/8.

Try the lab to finish this lesson.