To cross multiply a proportion, multiply the numerator of each ratio by the denominator of the opposite ratio. In a/b = c/d, the cross products are a × d and b × c. Set these products equal and solve the resulting equation.
Enter three values and leave one blank to solve a proportion, or enter all four values to check whether the ratios are equal.
In 2/3 = 8/x, the diagonal products are 2 × x and 3 × 8.
What Does Cross Multiplication Mean?
Cross multiplication forms two diagonal products from a pair of fractions or ratios.
For a/b = c/d, multiply a by d and multiply b by c.
Equal ratios have equal cross products.
Identify the Two Diagonals
The first diagonal connects the top-left value with the bottom-right value.
The second diagonal connects the bottom-left value with the top-right value.
Do not multiply the two numerators together or the two denominators together.
Example: Cross Multiply 2/3 = 8/x
The first diagonal is two times x.
The second diagonal is three times eight.
Set them equal to obtain 2x = 24.
Solve After Cross Multiplication
Once 2x = 24 has been formed, divide both sides by two.
This isolates x and gives x = 12.
The Proportion Calculator performs both the cross multiplication and division.
Cross Multiply When the Unknown Is a Numerator
Consider x/5 = 6/15.
The cross products are 15x and 30.
The equation 15x = 30 gives x = 2.
Cross Multiply When the Unknown Is a Denominator
Consider 4/x = 10/15.
The cross products are 60 and 10x.
The equation 60 = 10x gives x = 6.
Use Cross Multiplication to Check Ratios
Cross multiplication can test two completed ratios without solving for a variable.
For 4/10 and 6/15, the cross products are 60 and 60.
Because the products match, the ratios are proportional.
| Ratios | First product | Second product | Status |
|---|---|---|---|
| 2/3 and 8/12 | 2 × 12 = 24 | 3 × 8 = 24 | Proportional |
| 4/10 and 6/15 | 4 × 15 = 60 | 10 × 6 = 60 | Proportional |
| 3/5 and 8/10 | 3 × 10 = 30 | 5 × 8 = 40 | Not proportional |
Why Cross Multiplication Works
Begin with a/b = c/d.
Multiplying both sides by b and d removes both denominators.
The remaining equation is a × d = b × c.
Cross Multiplication with Decimals
Decimal values do not change the method.
For 1.5/3 = x/10, cross multiplication gives 15 = 3x.
Dividing by three gives x = 5.
Cross Multiplication with Negative Values
Follow the standard sign rules when multiplying.
A positive multiplied by a negative produces a negative product.
Keep the signs visible while isolating the unknown.
When Cross Multiplication Should Not Be Used
Cross multiplication applies to an equation containing two ratios.
It should not be used merely because two unrelated fractions appear in a problem.
First confirm that the fractions are stated or intended to be equal.
The method solves or verifies a proportion. It does not make unequal ratios equal.
Cross Multiplication Versus Equivalent Fractions
Equivalent-fraction methods multiply or divide both parts of one ratio by the same scale factor.
Cross multiplication compares diagonal products across two ratios.
Both approaches can confirm that two ratios represent the same value.
Useful for solving an unknown or checking two complete ratios.
Useful when the relationship between the ratios is easy to recognise.
Common Cross-Multiplication Mistakes
Do not multiply numerator by numerator and denominator by denominator.
Do not forget to set the two products equal.
Do not divide by the wrong coefficient after forming the equation.
Do not use a denominator of zero.
Check the final answer in the original proportion.
Conclusion
Multiply the top-left value by the bottom-right value and the bottom-left value by the top-right value.
Set the products equal and solve the resulting equation.
Use the Proportion Calculator to display the diagonals, cross products, and answer.
FAQs
Which numbers do I cross multiply?
Multiply the top-left value by the bottom-right value and the bottom-left value by the top-right value.
Why are the cross products equal?
Multiplying an equality of two ratios by both denominators produces equal diagonal products.
Can I cross multiply decimals?
Yes. The same method works with valid decimal values.
Can cross multiplication check two ratios?
Yes. Equal cross products show that the ratios are proportional.
Is cross multiplication always appropriate?
It applies when two ratios are being set equal or tested for equality.