math calculator
Use our free cross multiplication calculator to solve equations with fractions. Shows step-by-step work for proportions and fraction comparisons.
Quick actions: Save inputs, view saved runs, print, share, or export results
Variable C = x
4
Animated arrows show the diagonal multiplication paths.
2 × 6 = 3 × x
2/3 = x/6
Solving for variable C = x
Start with the proportion:
Cross-multiply: x × 3 = 2 × 6
Divide both sides by 3:
Save this page for quick access when solving proportions, scaling problems, or fraction equations in class or at work.
Formula
A / B = C / D ⟹ A × D = B × CIn any proportion, the product of the extremes equals the product of the means. Select which variable to solve for and enter the other three values.
Step by step
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Summary
Solved Variable C
4
The unknown x.
Cross Products
2×6 = 3×x
Diagonal products are equal.
Solve Target
Variable C
The unknown term.
Guide
Cross multiplication is a method used to solve equations where two fractions are set equal to each other (proportions). You multiply the numerator of the first fraction by the denominator of the second, and the numerator of the second by the denominator of the first.
Simple example:
If 2/3 = x/6, then:
Check: 2/3 = 4/6 = 2/3 ✅
To use the calculator:
1. Enter the values for A, B, C, and D in the equation A/B = C/D.
2. Leave the unknown value blank (the one you want to solve for).
3. Click "Calculate" or observe the real-time feedback.
4. Review the step-by-step solution below.
Example Input:
Cross multiplication is a mathematical technique used to solve equations that involve fractions. When you have two fractions set equal to each other (called a proportion), cross multiplication lets you eliminate the fractions and solve for the unknown value. If you need to simplify standard ratios first, try our Simplify Fractions Calculator.
Think of it like this: If two fractions are equal, then their cross products (multiplying diagonally) are also equal.
Example:
2/3 = 4/6
You can use cross multiplication in three common situations:
The cross multiplication formula is simple:
If A/B = C/D, then: A × D = B × C
Where:
What this means:
1. Multiply the numerator of the first fraction (A) by the denominator of the second (D).
2. Multiply the denominator of the first (B) by the numerator of the second (C).
3. Set these two products equal to each other.
4. Solve for the unknown variable.
Problem: Solve for x: 2/3 = x/6
Answer: x = 4
Problem: Which is bigger: 2/3 or 3/4?
Answer: 3/4 is bigger than 2/3
Problem: You're building a model aircraft on a 1:100 scale. Your model is 3.5 inches long. How long is the real aircraft?
Answer: The real aircraft is 350 inches long (about 29 feet).
Our calculator with fractions can handle various types of fraction problems:
If you need to divide larger numbers manually, try using our Long Division Calculator.
A whole number fraction calculator helps with mixed numbers. Convert a mixed number to an improper fraction using: Mixed Number = (Whole Number × Denominator + Numerator) / Denominator.
Example: Multiply 2 1/4 × 1/3
1. Convert 2 1/4 to an improper fraction → 9/4.
2. Multiply fractions → 9/4 × 1/3 = (9 × 1) / (4 × 3) = 9/12.
3. Simplify → 9/12 ÷ 3/3 = 3/4.
To solve arithmetic with mixed numbers directly, try our Mixed Number Fraction Calculator.
The same cross multiplication process works for any unknown variable:
Example: If 2/3 = 4/x, find x (which is D): D = (B × C) ÷ A = (3 × 4) ÷ 2 = 12 ÷ 2 = 6.
This calculator CAN help with:
This calculator CANNOT do:
A cross multiplication calculator is essential for anyone working with equations that involve fractions. Whether you're solving for x, comparing fractions, or working with real-world proportions — cross multiplication makes it simple.
Remember the key formulas: A = (B × C) ÷ D, B = (A × D) ÷ C, C = (A × D) ÷ B, D = (B × C) ÷ A.
Start calculating now! Just enter your values above and get instant step-by-step results.
Proportions
An equation stating that two ratios or fractions are equal to each other.
Cross Product
The diagonal product of terms in a proportion equation.
Improper Fraction
A fraction where the numerator is larger than the denominator.