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
=
- 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.
- So the question is which number goes into BOTH 3 and 9. 3 does — 3 = 3 × 1 and 9 = 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.
- 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.
- 02
So the question is which number goes into BOTH 3 and 9. 3 does — 3 = 3 × 1 and 9 = 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.