Simplifying fractions, step by step

A fraction in lowest terms is the tidiest way to write an amount.

The question

= ?

3 =3×1
9 =3×3
3 =3×1
9 =3×3
=
  1. 3/9. Simplifying is making an equivalent fraction run backwards: instead of cutting the pieces smaller, glue them back into bigger ones. The amount does not change, only how it is cut.
  2. So the question is which number goes into BOTH 3 and 9. 3 does — 3 = 3 × 1 and 9 = 3 × 3.
  3. Take that 3 off both: 3 ÷ 3 = 1 and 9 ÷ 3 = 3, so 3/9 = 1/3. Nothing but 1 goes into both 1 and 3 now, which is how you know the pieces are as big as they get.

How it works.

  1. 01

    3/9. Simplifying is making an equivalent fraction run backwards: instead of cutting the pieces smaller, glue them back into bigger ones. The amount does not change, only how it is cut.

  2. 02

    So the question is which number goes into BOTH 3 and 9. 3 does — 3 = 3 × 1 and 9 = 3 × 3.

  3. 03

    Take that 3 off both: 3 ÷ 3 = 1 and 9 ÷ 3 = 3, so 3/9 = 1/3. Nothing but 1 goes into both 1 and 3 now, which is how you know the pieces are as big as they get.