Cross multiplication
Calculator and formulas for calculating the cross multiplication
Cross multiplication is a method of elementary arithmetic to calculate the value of a variable in an equation involving two fractions or rational expressions (Not to be confused with Cross product).
To perform the calculation, enter the values of the varibles, then click the 'Calculate' button.
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Description with formula and example
The cross multiplication is a mathematical method for calculating proportional relationships. There are two types of cross multiplication problems: the direct and the inverse cross multiplication .
The formula for the cross multiplication consists of two pairs of values that are related to each other.
\[ a/b=c/x \ \ \ \text{or} \ \ \ \displaystyle\frac{a}{b}=\frac{c}{x}\]
To calculate, the formula is rearranged:
\[\displaystyle x=\frac{b ·c}{a}\]
Direct cross multiplication
In the direct cross multiplication, more of the quantity A leads to more of the quantity B (proportional relationship).
Example:
5 apples cost 2 euros. How much do 8 apples cost?
Solution steps:
- 5 apples = 2 euros
- 1 apple = 2 euros / 5 = 0.40 euros
- 8 apples = 0.40 euros × 8 = 3.20 euros
Answer: 8 apples cost 3.20 euros.
Inverse cross multiplication
The inverse cross multiplication applies: More of A leads to less of B (antiproportional relationship).
Example:
5 workers need 10 hours to build a wall. How long does it take 8 workers?
Solution steps:
- 5 workers = 10 hours
- 1 worker = 10 hours × 5 = 50 hours
- 8 workers = 50 hours / 8 = 6.25 hours
Answer: 8 workers need 6.25 hours.
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