✖️ Cross Multiplication Calculator
Solve proportions using cross multiplication
a₁ / b₁ = a₂ / b₂
How to Use This Calculator
Enter Proportions
Input values for two proportions: a₁, b₁ for first ratio and a₂, b₂ for second ratio. Example: 2/3 and 4/6
Click Check Proportion
Press the "Check Proportion" button to see if the two proportions are equal using cross multiplication.
View Result
See if proportions are equal or not, plus the cross products a₁×b₂ and a₂×b₁ for verification.
Formula
For proportion a₁/b₁ = a₂/b₂:
If a₁ × b₂ = a₂ × b₁, then proportions are equal
Example 1: Check if 2/3 = 4/6
a₁ = 2, b₁ = 3, a₂ = 4, b₂ = 6
Check: a₁ × b₂ = 2 × 6 = 12
Check: a₂ × b₁ = 4 × 3 = 12
Since 12 = 12, proportions are equal
Example 2: Check if 3/4 = 6/10
a₁ = 3, b₁ = 4, a₂ = 6, b₂ = 10
Check: a₁ × b₂ = 3 × 10 = 30
Check: a₂ × b₁ = 6 × 4 = 24
Since 30 ≠ 24, proportions are not equal
About Cross Multiplication Calculator
The Cross Multiplication Calculator checks if two proportions (ratios) are equal by comparing their cross products. This is the fundamental method for verifying proportions and solving proportion equations.
When to Use This Calculator
- Math Problems: Verify if two fractions or ratios are equal
- Proportion Checks: Determine if proportions are equivalent
- Scaling Problems: Check recipe scaling or map proportions
- Educational Use: Learn cross multiplication method
- Real-World Applications: Verify price ratios, conversion rates
- Algebra: Solve proportion equations
Why Use Our Calculator?
- ✅ Instant Verification: Check proportions quickly
- ✅ Visual Results: See Equal/Not Equal clearly
- ✅ Cross Products Shown: See the calculations
- ✅ Educational: Learn the cross multiplication method
- ✅ Error Prevention: Avoid calculation mistakes
- ✅ Completely Free: No registration required
Understanding Cross Multiplication
Cross multiplication is a method to check if two proportions are equal. For proportions a₁/b₁ = a₂/b₂, multiply diagonally:
- Cross Product 1: a₁ × b₂ (top-left × bottom-right)
- Cross Product 2: a₂ × b₁ (bottom-left × top-right)
- If equal: The proportions are equivalent
- If different: The proportions are not equal
Real-World Applications
Recipes: Check if scaling 2 cups flour to 3 cups milk is the same as 4 cups flour to 6 cups milk. 2/3 = 4/6 ✓
Shopping: Verify if $10 for 5 items is the same rate as $18 for 9 items. 10/5 = 18/9 ✓
Maps: Check if 1 inch : 1 mile equals 2 inches : 2 miles. 1/1 = 2/2 ✓
Tips for Using This Calculator
- Make sure a₁ and a₂ are not zero (cannot divide by zero)
- Cross multiplication only works for checking if two proportions are equal
- Works with decimals and fractions
- Can be used to solve for unknown values in proportions
- If equal, you can substitute one proportion for the other
Frequently Asked Questions
What is cross multiplication?
Cross multiplication checks if two proportions are equal by multiplying diagonally: a₁×b₂ vs a₂×b₁. If products are equal, proportions are equivalent.
Why does cross multiplication work?
For a₁/b₁ = a₂/b₂, cross multiplying gives a₁b₂ = a₂b₁. This is the mathematical definition of equal proportions.
Can I use this to solve for unknown values?
Yes! Cross multiplication helps solve proportion equations. For a/b = c/d, cross multiply to get ad = bc, then solve for the unknown.
What if the proportions are not equal?
The calculator will show "Not Equal" and display the different cross products so you can see how close they are.
Can I use fractions or decimals?
Yes! The calculator works with any real numbers, including decimals and fractions entered as decimals.
Why can't a₁ or a₂ be zero?
Because you can't divide by zero. If a₁ or a₂ is zero, the proportion is invalid and undefined.