Two ratios form a proportion when they represent the same value. The fastest test is to compare their cross products. For a/b and c/d, calculate a × d and b × c. If the products are equal, the ratios are proportional.
Enter three values and leave one blank to solve a proportion, or enter all four values to test whether two ratios are equal.
The ratios 4/10 and 6/15 form a proportion because both cross products equal 60.
What Does It Mean for Ratios to Be Proportional?
Proportional ratios represent the same relationship even when their numbers differ.
For example, 2/5 and 6/15 both equal 0.4.
You can enter all four values into the Proportion Calculator to test them.
Cross-Product Test
Write the ratios as a/b = c/d.
Multiply a by d and multiply b by c.
The ratios form a proportion only when the two products are equal.
Example: Are 4/10 and 6/15 Proportional?
Multiply four by 15 to get 60.
Multiply 10 by six to get 60.
Because both products are equal, the ratios form a proportion.
Example of Ratios That Are Not Proportional
Consider 3/5 and 8/10.
The cross products are three times 10, which is 30, and five times eight, which is 40.
Because 30 does not equal 40, the ratios are not proportional.
Test Ratios by Simplifying
Simplify each ratio to its lowest terms.
The ratio 4/10 simplifies to 2/5, while 6/15 also simplifies to 2/5.
Matching simplified ratios confirm a proportion.
Test Ratios Using Decimal Values
Divide each numerator by its denominator.
Four divided by 10 equals 0.4, and six divided by 15 also equals 0.4.
Equal decimal values indicate proportional ratios.
Test Ratios Using a Scale Factor
Look for one number that multiplies both parts of the first ratio to produce the second ratio.
Multiplying 2/5 by three gives 6/15.
Because the same scale factor applies to both values, the ratios are proportional.
Works quickly for any pair of valid ratios.
Matching simplest forms confirm equal values.
Equal quotients mean the ratios are proportional.
Both parts must change by an identical factor.
Which Proportion Test Is Best?
Cross multiplication is the most general method because it does not require simplifying or finding a visible scale factor.
Simplification is convenient when both ratios reduce easily.
Decimal comparison can be useful, but repeating or rounded decimals may make exact equality harder to recognise.
Ratios with Decimal Values
The same tests work when ratios contain decimals.
For 1.5/3 and 5/10, the cross products are 15 and 15.
The ratios are therefore proportional.
Ratios with Negative Values
Two ratios with the same sign pattern may form a proportion.
For example, minus 2/3 and 8/minus 12 both equal a negative value.
Apply the usual multiplication rules when comparing cross products.
Zero in a Ratio
A numerator may equal zero, producing a ratio value of zero.
A denominator cannot equal zero because division by zero is undefined.
Two valid zero-valued ratios may form a proportion when both numerators are zero.
Proportion Test Examples
The table shows several completed cross-product comparisons.
| Ratios | Cross products | Result |
|---|---|---|
| 2/3 and 8/12 | 24 and 24 | Proportional |
| 4/10 and 6/15 | 60 and 60 | Proportional |
| 5/8 and 15/24 | 120 and 120 | Proportional |
| 3/5 and 8/10 | 30 and 40 | Not proportional |
| 7/9 and 14/20 | 140 and 126 | Not proportional |
Common Mistakes
Do not compare only the numerators or only the denominators.
Do not use different scale factors for the two parts of a ratio.
Avoid treating rounded decimals as exact when precision matters.
Do not allow zero in a denominator.
Conclusion
Compare the cross products to determine whether two ratios form a proportion.
Simplification, decimal comparison, and scale factors provide alternative checks.
Use the Proportion Calculator to enter all four values and see the result.
FAQs
How do I know whether two ratios are proportional?
Their cross products must be equal.
Can I simplify both ratios instead?
Yes. Matching simplified forms show that the ratios are proportional.
Can decimals be used to compare ratios?
Yes, although exact cross products avoid problems caused by rounding.
Can proportional ratios contain negative values?
Yes, provided both ratios represent the same signed value.
Can a ratio have a zero denominator?
No. Division by zero is undefined.