Solving Proportions
Free printable solving proportions worksheets. Find x in 3/4 = x/12, with whole-number answers and an answer key.
Each question is a proportion with one number missing: 3/4 = x/12. The first fraction is complete, and x is always the top of the second. Work out what the bottom was multiplied by - 4 times 3 is 12 - do the same to the top, and x is 9.
The first fraction is always in lowest terms and made from the numbers 1 to 9. The second is the first scaled up by a whole number from 2 to 12, so every x is a whole number and nothing on the sheet is larger than 50.
What this worksheet covers
- Solve a proportion for a missing value
- Scale a fraction by a whole-number factor to make an equivalent one
Common Core standards
- 6.RP.A.3 Use ratio and rate reasoning to solve problems.
Frequently asked questions
How do you solve a proportion?
Find the factor that turns one denominator into the other, then apply it to the numerator. In 5/3 = x/21, 3 became 21 by multiplying by 7, so x is 5 × 7, which is 35.
What about cross-multiplying?
It gives the same answer: 5 × 21 = 3 × x, so 3x = 105 and x = 35. It works because the two fractions are equal, and it is the method to reach for once the factor stops being a whole number. On these sheets the factor always is one, so the shortcut and the reasoning agree.
Is the missing number always in the same place?
Yes. x is always the top of the second fraction, so every question has the same shape and the work is the scaling, not finding where the gap is.
What grade is this?
Sixth grade, as a way to solve ratio problems, and again in seventh grade, where proportional relationships are written as equations.