Question

How do you simplify \[\dfrac{2}{3} \times 18\]?

Answer 1

Hint:
In the given question, we have been asked to calculate the product of two rational numbers – one is a fraction and the other is a natural number. When doing questions of such type, the first thing to do is check if the natural number and the denominator of the fraction have common factors. If they do, reduce it to the lowest term, i.e., cancel out all the common factors. Then multiply normally.

Complete step by step solution:
We have to calculate \[\dfrac{2}{3} \times 18\].
First, we are going to solve the denominator and the natural number, and we have
\[\dfrac{1}{3} \times 18 = \dfrac{{18}}{3} = 6\]

Hence, \[\dfrac{2}{3} \times 3 = 2 \times 6 = 12\]

Note:
In the given question, we had to multiply a natural number with a fraction. The procedure is very easy and pretty straight-forward – multiply the natural number with the numerator, but before multiplying, reduce the natural number and the denominator by cancelling out the common factors. Then, when there is no common factor between the denominator and the natural number, multiply the remaining part with the numerator. Here, we must pay close attention when we are reducing the denominator and the natural number part. We should not divide the numbers twice – once divided, they are not to be repeated.