To solve a proportion, cross multiply the two ratios, simplify the resulting equation, and divide to isolate the unknown value. For example, in 2/3 = 8/x, cross multiplication gives 2x = 24, so x = 12.
Enter three values and leave one blank to solve a proportion, or enter all four values to check whether the ratios are equal.
The proportion 2/3 = 8/x is solved by making the two cross products equal.
What Is a Proportion?
A proportion is an equation stating that two ratios have the same value.
It may be written as a/b = c/d, where b and d cannot be zero.
The Proportion Calculator can solve for any one missing position.
The Basic Proportion Rule
When two ratios are equal, their cross products are equal.
Multiply the numerator of the first ratio by the denominator of the second ratio.
Multiply the denominator of the first ratio by the numerator of the second ratio.
Step 1: Identify the Unknown Value
Locate the letter or blank position that must be calculated.
In 2/3 = 8/x, the second denominator is unknown.
Keep the order of both ratios unchanged.
Step 2: Cross Multiply
Multiply two by x to obtain 2x.
Multiply three by eight to obtain 24.
The resulting equation is 2x = 24.
Step 3: Isolate the Unknown
Divide both sides of 2x = 24 by two.
This leaves x by itself on the left side.
The answer is x = 12.
Step 4: Check the Answer
Substitute 12 into the original proportion.
The completed ratios are 2/3 and 8/12.
Both cross products equal 24, confirming that the answer is correct.
Example: Solve x/5 = 6/15
Cross multiply x and 15, then multiply five and six.
This creates 15x = 30.
Divide by 15 to get x = 2.
Example: Solve 4/x = 10/15
Cross multiplication gives four times 15 equals 10 times x.
This simplifies to 60 = 10x.
Divide by 10 to obtain x = 6.
Example with Decimal Values
Consider 1.5/3 = x/10.
Cross multiplication gives 1.5 times 10 equals three times x.
The equation 15 = 3x produces x = 5.
Can a Proportion Have a Negative Answer?
Yes. Negative values follow the same algebraic rules.
For example, minus two over three equals eight over x produces minus 2x = 24.
Dividing by minus two gives x = minus 12.
How to Check Two Completed Ratios
When all four values are known, compare the cross products.
Equal cross products mean the ratios are proportional.
Different cross products mean the ratios do not form a proportion.
Common Mistakes When Solving Proportions
Do not multiply values on the same horizontal line and call them cross products.
Do not reverse only one ratio.
Do not use zero as a denominator.
Do not round intermediate values too early.
Check the solution in the original equation.
Conclusion
Cross multiply, simplify the equation, and divide to isolate the unknown.
Substitute the answer back into the proportion to verify it.
Use the Proportion Calculator to solve the equation and display the working.
FAQs
What is the fastest way to solve a proportion?
Cross multiply, form a one-variable equation, and divide to isolate the unknown.
How do I check a proportion answer?
Substitute the answer and confirm that the two cross products are equal.
Can the unknown appear anywhere?
Yes. The same cross-product rule can solve for any of the four positions.
Can a denominator equal zero?
No. Division by zero is undefined.
Can proportions contain decimals?
Yes. Decimal values are solved using the same method.