Proportion Calculator: Solve a/b = c/d for the Missing Value
Percent & ratioFreeNo sign-up
In 3/4 = 9/x, cross multiply to get 3x = 36, so x = 12.
In the proportion 3 / 4 = 9 / 12, the missing value d is 12. Cross multiplying gives a × d = b × c, which is 36 = 36.
Show the steps
- Write the proportion: 3 / 4 = 9 / 12.
- Cross multiply: a × d = b × c.
- Solve for d: d = b × c ÷ a = 12.
Proportion
a / b = c / d means a × d = b × c
a = b × c ÷ d, b = a × d ÷ c, c = a × d ÷ b, d = b × c ÷ a
- A proportion says two ratios are equal. It works with any units as long as both sides use them the same way.
Estimates for planning and learning, not financial, tax, legal or medical advice. Check figures with your lender, tax preparer or doctor before you act.
About this calculator
A proportion says that two ratios are equal, such as 3/4 = 9/12. When one of the four numbers is missing, you can find it with cross multiplication: a × d = b × c. This is the quickest way to scale a recipe, convert units, work out a map distance or solve a similar-triangle problem.
Pick which letter you want to solve for, type the other three numbers, and the calculator gives the answer, the matching cross products, the scale factor and every step.
How to use it
- Choose which value to find: a, b, c or d.
- Type the three numbers you know. Decimals and negatives work.
- Read the missing value and the cross products, and open Show the steps to see the algebra.
Cross multiplication
If a/b = c/d, multiply both sides by b and d to get a × d = b × c. Then isolate the unknown. For example, 5/8 = x/40 gives 8x = 200, so x = 25.
Word problems
Put matching units in matching places. If 3 notebooks cost 7.50 dollars, then 3/7.50 = 10/x finds the cost of 10 notebooks: x = 25 dollars. Check that both ratios compare the same things: notebooks to dollars on each side.
Direct and inverse proportion
This calculator is for direct proportions, where both quantities grow together. In an inverse proportion, one grows as the other shrinks, and the products stay equal: a × b = c × d.
Sources
Quick check: test yourself
Solve 2/3 = 6/x.
Correct answer: 9. Cross multiply: 2x = 18, so x = 9.
If 3 pens cost 15 dollars, what do 9 pens cost?
Correct answer: 45 dollars. The price per pen is 5 dollars, so 9 pens cost 45.
In a/b = c/d, which two products are equal?
Correct answer: a × d and b × c. Cross multiplication: a × d = b × c.
Pick an answer for each question.
Common questions
How do I solve a proportion?
Cross multiply and divide. For 2/3 = x/9, 3x = 18, so x = 6.
What is a proportion in math?
An equation that states two ratios are equal, such as 1/2 = 4/8.
What if the unknown is on the bottom?
Cross multiplication still works. For 3/x = 9/12, 9x = 36, so x = 4.
Can proportions use decimals or negatives?
Yes. The cross products rule works for any numbers, as long as no denominator is zero.
How do I know if two ratios form a proportion?
Cross multiply. If a × d equals b × c, the ratios are equal.
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