Inverse Cross Multiplication
Calculator and formulas for calculating the inverse cross multiplication
Inverse cross multiplication is a method of elementary arithmetic to calculate the value of a variable in an equation involving two multiplications or rational expressions (not to be confused with inverse cross product).
To perform the calculation, enter three values, then click on the 'Calculate' button.
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Description of the inverse cross multiplication
The inverse cross multiplication is used when one quantity increases while the other decreases, and vice versa. This is typical of proportional relationships where the relationship between the quantities is inversely proportional.
Example
Suppose 5 workers need 12 days to complete a task. How many days do 8 workers need to complete the same task?
As the number of workers increases, the number of days required decreases (inverse proportionality).
\(5\) workers \(× 12\) days \(=8\) workers \(× \ x\) days
Solve equation:
\[5×12=8×x\] \[60=8x\] \[x-\frac{60}{8}=7.5\text{days}\]
So 8 workers need 7.5 days to complete the task.
Formula
\[\text{size}_1 × \text{size}_2 = \text{size}_3 × \text{size}_x\] \[x=\frac{\text{size}_1 × \text{size}_2}{\text{size}_3}\]
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