Cross Multiplication Calculator
Solve proportions and equations with fractions using cross multiplication
Cross Multiplication
Solution
Example Problems
Scale Model Problem
Problem: A model airplane is built on a 1:100 scale. If the model is 3.5 inches long, how long is the real airplane?
Setup: model_length/real_length = scale_ratio
Equation: 3.5/x = 1/100
Cross multiply: 3.5 × 100 = x × 1
Solution: x = 350 inches
Answer: The real airplane is 350 inches (29.17 feet) long
Recipe Scaling Problem
Problem: A recipe for 4 people calls for 2 cups of flour. How much flour is needed for 6 people?
Setup: people/flour = people/flour
Equation: 4/2 = 6/x
Cross multiply: 4 × x = 2 × 6
Solution: 4x = 12, so x = 3
Answer: You need 3 cups of flour for 6 people
Cross Multiplication Rules
The Pattern
For A/B = C/D:
A × D = B × C
When to Use Cross Multiplication
Solving proportions and ratios
Finding missing values in fractions
Scaling problems (maps, models, recipes)
Rate and ratio calculations
Comparing fractions
Understanding Cross Multiplication
What is Cross Multiplication?
Cross multiplication is a method for solving equations that involve fractions or proportions. When you have an equation of the form A/B = C/D, you can "cross multiply" to get A × D = B × C.
Why Does it Work?
Cross multiplication works because it's actually just multiplication done twice. When you multiply both sides of A/B = C/D by B, you get A = (C × B)/D. Then, when you multiply both sides by D, you get A × D = C × B, which is the cross multiplication result.
Step-by-Step Method
- 1.Write the equation in the form A/B = C/D
- 2.Multiply the numerator of the first fraction by the denominator of the second
- 3.Multiply the denominator of the first fraction by the numerator of the second
- 4.Set these products equal to each other
- 5.Solve for the unknown variable
Remember: Cross multiplication only works when you have one fraction equal to another fraction. If you have more complex expressions, simplify them first.