Proportion calculator
Enter the three known terms of the proportion a : b = c : x and the calculator finds the fourth by cross-multiplication.
In the proportion 3 : 4 = 9 : x the missing value is 12.
Formula
The proportion a : b = c : x means a · x = b · c. Rearranged, x = (b · c) ÷ a.
How we got there
Check it: substitute the answer back and compare the two ratios — they must be equal.
How to solve a proportion by hand
- Write the proportion on one line
a : b = c : x, that is 3 : 4 = 9 : x.
- Cross-multiply
The products of the outer and inner terms are equal: 3 · x = 4 · 9.
- Divide by the coefficient of x
x = 36 ÷ 3 = 12.
- Check the answer
3 ÷ 4 = 0.75 and 9 ÷ 12 = 0.75. The ratios match, so the solution is right.
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Frequently asked questions
Cross-multiply and divide. For 3 : 4 = 9 : x you get x = (4 · 9) ÷ 3 = 12.
It is shorthand for multiplying the outer and inner terms, whose products are equal in a proportion.
Yes — for scaling recipes, map scales, exchange rates and mixtures. Anywhere two quantities are directly proportional.
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