Math
Cross Multiplication Calculator
Set up a proportion a/b = c/d, choose which of the four positions is unknown, and solve it by cross multiplication.
The calculator writes the cross products, the resulting equation, the exact answer as a fraction and decimal, and checks that both cross products agree. The proportion calculator on mathcheck solves the a/b = c/x layout; this page handles any position.
First numerator.
First denominator.
Second numerator.
Try an example
Result
Missing term x
—
- Exact value
- —
- Solved proportion
- —
- Cross products
- —
- Scale factor
- —
Student quick launch
Grade planning, algebra checks, and formulas students reach for most.
Study path
Use this calculator with
Follow these when you want the formula behind the answer, a short lesson, or nearby tools in the same topic.
What cross multiplication does
Two ratios are equal when their cross products are equal. For a/b = c/d, multiply diagonally: a × d = b × c. This clears both The bottom number of a fraction; it says how many equal parts make one whole. in one move and leaves a simple equation. Put the unknown in any of the four positions, cross multiply, and divide to solve.
| Unknown | Equation | Solution |
|---|---|---|
| d | a × d = b × c | d = (b × c) / a |
| c | a × d = b × c | c = (a × d) / b |
| b | a × d = b × c | b = (a × d) / c |
| a | a × d = b × c | a = (b × c) / d |
Example: 3/4 = 9/x
Cross multiply: 3 × x = 4 × 9, so 3x = 36 and x = 12. Check: 3 × 12 = 36 and 4 × 9 = 36. Both ratios equal 0.75. Word problems with maps, recipes, similar triangles, and unit conversions all set up this way; keep matching quantities in matching positions.
How to use it
- Choose which of a, b, c, d is unknown.
- Type the three known values. Decimals and negatives are fine.
- Read x as a decimal and as an exact fraction, plus the solved proportion and matching cross products.
- Open Show the work for the diagonal products, the one-step equation, and the check.
How to read the answer
x is the value that makes both ratios equal. The cross-products line shows the two diagonal products agreeing, which is the proof. The scale factor tells how much the first ratio was multiplied to reach the second; a scale factor of 3 means the second ratio is three times the first.
Common mistakes and edge cases
- Multiply diagonally (a with d, b with c), not straight across.
- Keep like quantities in like positions: miles over miles, hours over hours, or miles over hours on both sides.
- If you divide by 0 to isolate x, the proportion has no unique solution.
- Cross multiplication only works with one fraction on each side of the equals sign.
- Rounding x early can make the check fail; the exact fraction is shown for that reason.
Worked examples
Missing denominator
3/4 = 9/x
Missing term x
12
Missing numerator
x/5 = 6/15
Missing term x
2
Fraction answer
2/3 = x/7
Missing term x
4.666667
Missing first denominator
5/x = 20/8
Missing term x
2
Decimals
1.5/2.5 = x/10
Missing term x
6
Negative
-3/4 = x/8
Missing term x
-6
Zero makes it unsolvable
0/4 = 9/x
Missing term x
Error
Zero denominator
3/0 = 9/x
Missing term x
Error
Frequently asked questions
How do you cross multiply?+
Multiply the numerator of each fraction by the denominator of the other and set the products equal: for a/b = c/d, a × d = b × c. Then solve the resulting equation.
Why does cross multiplication work?+
Multiplying both sides of a/b = c/d by b × d cancels each denominator, leaving a × d = c × b. It is just clearing fractions in one step.
Can the unknown be in the denominator?+
Yes. Cross multiply as usual; the unknown ends up multiplied by a known number, and you divide to isolate it.
Can I cross multiply to add fractions?+
No. Cross multiplication solves equations of the form fraction = fraction. Adding fractions needs a common denominator.
What if I get a decimal answer?+
That is normal. The calculator also shows the exact fraction, such as 14/3 for 2/3 = x/7.
How is this different from the proportion calculator?+
The proportion calculator solves the fixed layout a/b = c/x. This page lets the unknown sit in any of the four positions and shows the cross products explicitly.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- September 4, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
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Last updated: September 4, 2026