Question

Express $\dfrac{5}{8}$ as a rational number with numerator 15.
A. $\dfrac{15}{8}$
B. $\dfrac{15}{24}$
C. $\dfrac{15}{18}$
D. $\dfrac{15}{2}$

Answer 1

Hint: We solve this question by first looking at the numerator and check if it is less than or greater than the required numerator. In this case, since it is less, we need to scale it up or increase it by a factor to get the required number. But for us to maintain the same value, we need to multiply the denominator by the same value too. Then, we get the required rational number with a numerator equal to 15.

Complete step-by-step solution:
In order to solve this question, let us consider the given fraction which is
$\Rightarrow \dfrac{5}{8}$
Now, we need another rational number such that it has a numerator equal to 15. This rational number has to be obtained from the above fraction itself. In order to do so, we look at the numerator of the current fraction. It is smaller than 15 and can be scaled up to 15 by multiplying with 3.
But, if we multiply only the numerator by 3, the value of the given fraction would change. We do not want the value of the fraction to change. In order to do this, we multiply the denominator by a factor of 3 too. This is as good as multiplying the above fraction by $\dfrac{3}{3}$ which is the same as 1. So, the above fraction does not change.
Multiplying the numerator and denominator by 3,
$\Rightarrow \dfrac{5}{8}\times \dfrac{3}{3}$
Multiplying them we get,
$\Rightarrow \dfrac{15}{24}$
Hence, the rational number equivalent of the fraction $\dfrac{5}{8}$ with a numerator 15 is given by $\dfrac{15}{24}.$ Therefore, the correct option is B.

Note: We need to be careful to multiply even the denominator with the required factor else the fractions will not be in proportion and will lead to a wrong result. If the numerator should be reduced to a particular value, then we take common factors for the numerator and denominator and cancel them out in order to get the required numerator.