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.
If they get stuck
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 around.
How this one works
One question from a sheet like this one, worked a step at a time — with a sentence saying what just happened and why.
Solving proportions, step by step