One quantity as a percentage of another

One quantity as a percentage of another

In “A as a percentage of B”, B represents 100%. A and B must measure the same kind of quantity. Dividing A by B gives the fraction of one reference amount that A represents. Use the same unit so the units cancel.

\(\text{Required percentage}=\dfrac{\text{quantity being compared}}{\text{reference quantity}}\times100\%\).

Example

Express 45 minutes as a percentage of 2 hours. Convert the reference: \(2\text{ h}=120\text{ min}\).

\(\dfrac{45}{120}\times100\%=37.5\%\).

Check that the reference is the amount after “of”. A result above 100% is possible when the quantity being compared is larger. The reference must be nonzero.