Cross Multiplication Calculator
Solve A/B = C/D using cross multiplication with step-by-step solution. See also Proportion Calculator and Fraction Calculator.
How to Use Cross Multiplication
Cross multiplication is a method for solving proportions. Given A/B = C/D, multiply diagonally: A × D = B × C. Then isolate the unknown variable by dividing both sides by the coefficient next to it. This technique works whenever you have two equal fractions with one unknown value.
Cross Multiplication Formula
Given: A/B = C/D
Cross multiply: A × D = B × C
To find A: A = (B × C) / D
To find B: B = (A × D) / C
To find C: C = (A × D) / B
To find D: D = (B × C) / A
Example
Solve: 3/4 = x/8
Step 1: Cross multiply → 3 × 8 = 4 × x
Step 2: 24 = 4x
Step 3: x = 24 ÷ 4
Step 4: x = 6
Verify: 3/4 = 6/8 = 0.75 ✓
Frequently Asked Questions
Why does cross multiplication work?
Cross multiplication works because multiplying both sides of A/B = C/D by B × D eliminates the denominators, giving A × D = B × C. This is a valid algebraic operation that preserves the equality.
Can I use cross multiplication with more than two fractions?
Cross multiplication only works directly with two fractions set equal to each other. For chains of equal fractions (A/B = C/D = E/F), solve them in pairs.
What if the answer is a fraction?
The result of cross multiplication can be any real number, including fractions and decimals. The calculator shows the exact decimal result.
Solved Examples — Cross Multiplication
Example: If 5 kg of apples cost $12, how much do 8 kg cost?
Solution:
Step 1: Set up: 5/12 = 8/x
Step 2: Cross multiply: 5 × x = 12 × 8
Step 3: 5x = 96
Step 4: x = 96/5 = 19.20
Answer: $19.20
Example: Solve for x: 7/12 = 21/x
Solution:
Step 1: Cross multiply: 7 × x = 12 × 21
Step 2: 7x = 252
Step 3: x = 252/7 = 36
Step 4: Verify: 7/12 = 0.583..., 21/36 = 0.583... ✓
Answer: x = 36
Example: A blueprint scale is 1/4 inch = 3 feet. If a wall measures 2.5 inches on the blueprint, how long is the actual wall?
Solution:
Step 1: Set up: 0.25/3 = 2.5/x
Step 2: Cross multiply: 0.25 × x = 3 × 2.5
Step 3: 0.25x = 7.5
Step 4: x = 7.5/0.25 = 30
Answer: 30 feet
Practice Questions
Try these on your own:
- Solve: x/9 = 20/36 (Answer: x = 5)
- Solve: 15/x = 45/12 (Answer: x = 4)
- If 4 painters paint a house in 6 days, how many days for 3 painters? (Answer: 8 days — inverse proportion)
- Solve: 2.5/7 = x/42 (Answer: x = 15)
- A car uses 8 gallons for 240 miles. How many gallons for 450 miles? (Answer: 15 gallons)
- Solve: 11/x = 33/27 (Answer: x = 9)
Common Mistakes to Avoid
The most frequent mistake is multiplying the wrong terms — in cross multiplication of A/B = C/D, you multiply diagonally (A×D and B×C), not straight across. Another common error is setting up the proportion incorrectly by mixing up which values correspond. Always make sure matching quantities are in matching positions: if the first fraction is price/quantity, the second must also be price/quantity. Students also sometimes apply cross multiplication to inequalities without remembering that multiplying by a negative number flips the inequality sign. Finally, always verify your answer by plugging it back in — both fractions should reduce to the same decimal value.
Key Takeaways
- Cross multiplication: if A/B = C/D, then A×D = B×C.
- This method solves for any one unknown when the other three values are known.
- Always set up ratios consistently — same type of quantity in same position on both sides.
- Cross multiplication only works for equations (=), not for comparing which fraction is larger.
- Verify answers by checking that both fractions give the same decimal value.
- Applications: unit pricing, scaling recipes, map distances, similar triangles, and currency conversion.