Question

Express $\dfrac{3}{5}$ as rational number with numerator,
(i) -21
(ii) 150

Answer 1

Hint: Consider each subpart of the question one by one. To convert the numerator of $\dfrac{3}{5}$ into -21 multiply the numerator with -7 and to balance this change, multiply the denominator also with the same number. Simplify the product to get the answer. Now, to convert the numerator of $\dfrac{3}{5}$ into 150, multiply the numerator with 50 and similarly to balance the effect, multiply the denominator also with 50.

Complete step by step answer:
Here we have been provided with the fraction $\dfrac{3}{5}$ and we are asked to write it as a rational number whose numerator will be equal to (i) -21 and (ii) 150. Let us consider each subpart one by one.
(i) Now, when we divide the number -21 by 3 then we will get -7 that means to convert the numerator into -21 we have to multiply it with -7. This process will change the value of the fraction and that is why to balance this change we have to multiply the denominator also with -7. Therefore we get,
$\begin{align}
  & \Rightarrow \dfrac{3}{5}=\dfrac{3}{5}\times \dfrac{\left( -7 \right)}{\left( -7 \right)} \\
 & \therefore \dfrac{3}{5}=\dfrac{-21}{-35} \\
\end{align}$
Clearly the numerator of the above fraction is -21 so it is our answer.
(ii) Further, here the numerator should be 150. On dividing 150 by 3 we get 50 that means 50 must be multiplied to the numerator and to balance this change 50 must also be multiplied with the denominator. Therefore we get,
$\begin{align}
  & \Rightarrow \dfrac{3}{5}=\dfrac{3}{5}\times \dfrac{50}{50} \\
 & \therefore \dfrac{3}{5}=\dfrac{150}{250} \\
\end{align}$
Clearly the numerator of the above fraction is 150 so it is our answer.

Note: Note that in the answer obtained for part (i) of the question which is $\dfrac{-21}{-35}$ do not cancel the minus sign because if we will do so then the numerator will become 21 but we need -21, so it will change the answer. The fractions that we have obtained as answers are the equivalent fractions of $\dfrac{3}{5}$ because their simplest form is the same.