Question

Express $\dfrac{4}{7}$ as a rational number with numerator 48.

Answer 1

Hint: We know that a rational number can be expressed as $\dfrac{p}{q}$ , where $p$ and $q$ are integers. So here we have to find a rational number with numerator, i.e. $p$ as 48. We know that $4\times 12=48$ . We will have to multiply the given number with 12 on both the numerator and denominator to get the final answer.

Complete step by step answer:
Before going to the solution, let us first understand the basic concepts.
A number is said to be a rational number if it can be expressed as $\dfrac{p}{q}$ , where $p$ and $q$ are integers. An integer is a number which includes natural numbers $\left\{ \left. 1,2,3\cdots \right\} \right.$, zero $\left\{ \left. 0 \right\} \right.$and negative of counting numbers $\left\{ \left. -1,-2.-3\cdots \right\} \right.$. Examples of integers are $-2,-9,0,26,5$ .
In the rational number, we know that $p$ is the numerator and $q$ is non zero denominator. Numerator is the number which is above the line of any fraction. Denominator is the number which is below the line of any fraction.
For example, if we have a rational number in the form of $\dfrac{8}{9}$ then it represents a fraction, where 8 is the numerator and 9 is the nonzero denominator (i. e $9\ne 0$).
Now, let us start with our solution. We have been given a number $\dfrac{4}{7}$. We can clearly see that the numerator of $\dfrac{4}{7}$ is 4.
Now, we have been asked to find a rational number with a numerator as 48. So, we must find out by which number should we multiply 4 to get 48.
We have to divide 48 by 4 to get the number as $\left( 48\div 4 \right)=12$ .
Now, it is clear from the above that we have to multiply the numerator (i. e 4) and denominator (i.e 7) by 12.
$\therefore \dfrac{4}{7}=\left( \dfrac{4\times 12}{7\times 12} \right)=\dfrac{48}{84}$

Hence, the required rational number is $\dfrac{48}{84}$.

Note: Here, we had multiplied both the numerator and denominator with 12 such that the given fraction remains unaltered and it gives us a form such that the numerator is 48. Most students do not multiply the denominator with 12 and directly obtain the final answer as $\dfrac{4\times 12}{7}=\dfrac{48}{7}$ , but this is not what is required. So, this kind of mistake must be avoided.