Solving proportions, step by step

A proportion is two ratios set equal with one term missing, and finding it is a scale factor away.

The question

1 : 5 = 7 : 35

1 : ▢=7 : 35
1× 7 =7
35÷ 7=5
  1. Two ratios are equal when both sides were scaled by the same amount. So the first job is to find that amount from the pair you CAN see.
  2. 1 became 7, so everything was multiplied by 7.
  3. The blank is on the ratio that was scaled UP from, so it is reached by going back down: 35 ÷ 7 = 5. Not "take the difference away" — a ratio scales, it does not shift.

How it works.

  1. 01

    Two ratios are equal when both sides were scaled by the same amount. So the first job is to find that amount from the pair you CAN see.

  2. 02

    1 became 7, so everything was multiplied by 7.

  3. 03

    The blank is on the ratio that was scaled UP from, so it is reached by going back down: 35 ÷ 7 = 5. Not "take the difference away" — a ratio scales, it does not shift.