Cross Multiplication Calculator - Solve Proportions & Ratios with Step-by-Step Solutions
Free cross multiplication calculator. Solve proportions, fractions, and ratios using cross multiplication method with step-by-step solutions. Our calculator uses algebraic principles to determine all proportion relationships from any given inputs.
Last updated: October 19, 2025
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2 / 3 = 4 / 6
Cross multiplication form
2
Calculated result
✓ Valid
12 = 12
Given: 2 / 3 = 4 / 6
Cross multiply: 2 × 6 = 3 × 4
Calculate: 12 = 12
Check: 12 = 12
Result: Valid proportion
Cross Multiplication
Multiply diagonally and set equal
Proportion
Use proportion a/b = c/d
Ratio
Compare ratios using cross multiplication
Applications:
- • Solving proportions
- • Scaling recipes
- • Unit conversions
- • Percentage calculations
Cross Multiplication Calculator Types & Features
Method used
a/b = c/d → a×d = b×c
Solves proportions by cross multiplying
Method used
Cross Multiply & Solve
Solves fraction equations efficiently
Method used
Cross Product Comparison
Compares ratios by cross multiplying
Method used
Proportional Conversion
Converts units using proportions
Method used
Proportional Scaling
Scales recipes proportionally
Features
Variable Solving
Solves for unknown variables
Quick Example Result
For proportion 2/3 = 4/6:
Cross Multiply
2 × 6 = 12
Cross Multiply
3 × 4 = 12
Result
Valid ✓
How Our Cross Multiplication Calculator Works
Our cross multiplication calculator uses the fundamental principles of algebra to solve proportion problems from any given inputs. The calculation applies algebraic methods and proportion theory to determine solutions, verify results, and provide step-by-step explanations.
The Fundamental Cross Multiplication Formula
a/b = c/d → a × d = b × cCross multiply diagonallySet products equalSolve for unknownThis formula forms the foundation of proportion solving and allows calculation of any unknown value in a proportion. It applies to fractions, ratios, and algebraic expressions.
Shows the diagonal multiplication pattern for solving proportions
Algebraic Foundation
Cross multiplication is a fundamental algebraic technique for solving proportion problems. It's based on the principle that if two ratios are equal, their cross products are also equal. This method is essential for solving real-world problems involving proportional relationships.
- Cross multiplication works by multiplying diagonally across a proportion
- If a/b = c/d, then a × d = b × c (cross products are equal)
- This method can solve for any unknown in a proportion
- It's particularly useful for unit conversions and scaling
- Cross multiplication preserves the equality of ratios
- It's applicable to fractions, decimals, and algebraic expressions
Sources & References
- Algebra and Trigonometry - Jay AbramsonComprehensive coverage of algebraic methods including cross multiplication
- Precalculus - OpenStaxMathematical foundations for proportion and ratio problems
- Khan Academy - Solving ProportionsEducational resources for understanding cross multiplication
Need help with other algebraic calculations? Check out our proportion calculator and fraction calculator.
Get Custom Calculator for Your PlatformCross Multiplication Calculator Examples
Given Information:
- Proportion: 2/3 = 4/6
- Method: Cross Multiplication
- Goal: Verify if proportion is valid
- Check: Cross products equality
Calculation Steps:
- Cross multiply: 2 × 6 = 12
- Cross multiply: 3 × 4 = 12
- Compare: 12 = 12
- Result: Valid proportion
Result: 2 × 6 = 3 × 4 → 12 = 12 ✓ Valid Proportion
The proportion 2/3 = 4/6 is valid because the cross products are equal.
Solving for Unknown
Proportion: 3/4 = x/8
Solution: x = 6
Ratio Comparison
Compare 2:3 and 4:6
Result: Equal ratios
Frequently Asked Questions
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