Finding the fractions of a quantity simply means finding what quantity the fraction represents in the whole. Knowing long division is always helpful when finding the fraction of a quantity that represents the whole.

Finding the fraction of a quantity can be simply done in two ways, you can find the quantity of a fraction by multiplying the numerator of the fractions and dividing it by the denominator or one can find the fraction of a given quantity by dividing the numerator with the denominator and then Multiply the results by the quantity.

Let’s look at all the two ways of finding the fraction of a quantity and their examples.

## Finding the fraction of a quantity by multiplying the numerator with the quantity and dividing the results by the denominator.

Step 1. Multiply the numerator with the quantity.

step 2: Divide the results by the denominator. Using long division is easy when you are not allowed to use calculator.

Let’s look at an example of this method.

\text{Example: find }\space\frac{2}{7} \space \text{of}\space56\space\text{gallons of petrol}\\ Answer: \text{simply multiply the} \\ \text{numerator 2 with the quantity 56 }\\\text{ and divide the results by 7}\space=\frac{2}{7}×56\\=\frac{2×56}{7}=\frac{112}{7}\\ =16 \space\text{gallons of petrol}

## Finding the fraction of a quantity by dividing the numerator and the denominator and multiplying the results by the quantity.

step 1. Divide the numerator and denominator of the fraction

step 2. Multiply the results by the given quantity

Let’s look at an example under this method

\text{Example. Find }\space\frac{4}{5}\space \text{of 500 dollars}\\ Answer: \text{Note that }\\\text{the number that follows the 'of ' is the}\\\text{ quantity. Divide the numerator by the}\\\text{ denominator i.e 4÷5=0.8.}\\\text{Then multiply the results 0.8 by 500} \\\text{dollars = 0.8×500=400 dollars}

Practicing finding the fraction of a quantity. Try your hands on the following.

\text{Find the following}\space(a). \frac{4}{7}\space\text{of one week?}\space\\(b). \frac{1}{15}\space\text{of 2 hours?}\space(c). \frac{3}{4}\space\text{of 2 days?}