RatiosSolve a proportion
Name: Date:
Find the missing number in each proportion.
13 : = 24 : 64
21 : 3 = 4 :
35 : 6 = 10 :
43 : 4 = 15 :
54 : 5 = 32 :
61 : 4 = 2 :
72 : = 16 : 24
82 : 5 = 14 :
93 : = 15 : 40
103 : = 18 : 30
Solving proportions worksheets
A proportion is two ratios set equal with one term missing, and finding it is a scale factor away. These free printable worksheets give three of the four numbers and ask for the fourth.
Kid stuck on one? You don’t just get the sheet.
Solving proportions
The answer key prints on a separate page.
What's on this sheet
3 : __ = 24 : 64 is solved by noticing that 3 became 24, which is eight times bigger, so whatever pairs with 3 must be eight times smaller than 64. Finding that scale factor first is much less error-prone than cross-multiplying, and it keeps the arithmetic inside the times tables where a child can check it.
Why this sheet works
Cross-multiplication is the method most textbooks reach for and it is worth knowing, but it is worth knowing second. Taught first it becomes a procedure with no meaning attached, and a child who has only that has no way to notice when they have set the proportion up the wrong way round.
How this one works
One question from this sheet, worked through a step at a time.
3 : 8 = 24 : 64
3 : ▢=24 : 64
3× 8 =24
64÷ 8=8
- 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.
- 3 became 24, so everything was multiplied by 8.
- The blank is on the ratio that was scaled UP from, so it is reached by going back down: 64 ÷ 8 = 8. Not "take the difference away" — a ratio scales, it does not shift.