Fractions describe parts of a whole, but they can also describe parts of a quantity.
Find \dfrac{1}{12} of 36.
We can also work this out using arithmetic. We know that \dfrac{1}{12} of 36 can be written using multiplication, \dfrac{1}{12} \times 36.
This is the same as 1 \times \dfrac{36}{12} and \dfrac{1 \times 36}{12}. The third expression is the most useful.
First, if we evaluate the multiplication in the numerator we get \dfrac{36}{12}. Then we can cancel the greatest common factor from the numerator and denominator. In this case it is 12. This gives us \dfrac{3}{1} which is the same as 3.
We can check this answer by multiplying back. 12 \times 3 = 36, so we know that 3 is \dfrac{1}{12} of 36.
Evaluate \dfrac25\times35.
Find 3 groups of \dfrac45.
Find \dfrac{5}{7} of 5 weeks in days.
Finding the fraction of a quantity is the same as multiplying a whole number by a fraction.
To multiply a whole number by a fraction, multiply the whole number by the numerator.
It is often easier to cancel common factors in the numerator and denominator before evaluating the multiplication.