Question

The rational number equivalent to the rational number \[\dfrac{7}{19}\] is:-
(a) \[\dfrac{17}{119}\]
(b) \[\dfrac{14}{57}\]
(c) \[\dfrac{21}{38}\]
(d) \[\dfrac{21}{57}\]

Answer 1

Hint: Before solving this question, we must know about rational numbers. A rational number is a number that can be expressed in the form of \[\dfrac{p}{q}\] , where ‘q’ is a non – zero integer. Since ‘q’ may be equal to 1, every integer is a rational number. In this question, we have to consider each option one by one. Then, we have to check if the numerator is a multiple of 7 and denominator is a multiple of 19. Then, we must find an option such that we can multiply numerator and denominator with the same number and it results in the fraction \[\dfrac{7}{19}\] when simplified.

Complete step-by-step answer:
Let us now solve this question. To find an equivalent fraction, we shall multiply the numerator and denominator by the same number. For solving this question, we shall consider every option.
Option (a) is given as \[\dfrac{17}{119}\]. We know that 17 is not a multiple of 7, so 17 cannot be obtained by multiplying any whole number with 7. So \[\dfrac{17}{119}\] cannot be an equivalent fraction of \[\dfrac{7}{19}\] .
Now, considering option b, we have \[\dfrac{14}{57}\]. When we divide 14 by 7, we obtain 2; this means that when we will multiply 7 by 2, then the product is 14. When we divide 57 by 19, we obtain 3; this means that when we multiply 19 by 3, then the product is 57.
We can see that when we multiply 7 by 2, then the product is 14, and when we multiply 19 by 3, then the product is 57. This means that we cannot obtain \[\dfrac{14}{57}\] by multiplying the same number to the numerator and denominator of \[\dfrac{7}{19}\] . Hence, \[\dfrac{14}{57}\] cannot be an equivalent fraction of \[\dfrac{7}{19}\] .
Now, taking the next option, c as \[\dfrac{21}{38}\]. When we divide 21 by 7, we obtain 3; this means that when we will multiply 7 by 3, then the product is 21. When we divide 38 by 19, we obtain 2; this means that when we multiply 19 by 2, then the product is 38.
We can see that when we multiply 7 by 3, then the product is 21, and when we multiply 19 by 2, then the product is 38. This means that we cannot obtain \[\dfrac{21}{38}\] by multiplying the same number to the numerator and denominator of \[\dfrac{7}{19}\] . Hence, \[\dfrac{21}{38}\] cannot be an equivalent fraction of \[\dfrac{7}{19}\] .
Now, we have the next option d as \[\dfrac{21}{57}\] . When we divide 21 by 7, we obtain 3; this means that when we will multiply 7 by 3, then the product is 21. When we divide 57 by 19, we obtain 3; this means that when we multiply 19 by 3, then the product is 57.
We can see that when we multiply 7 by 3, then the product is 21, and when we multiply 19 by 3, then the product is 57. This means that we can obtain \[\dfrac{21}{57}\] by multiplying the same number to the numerator and denominator of \[\dfrac{7}{19}\] . Hence, \[\dfrac{21}{57}\] is an equivalent fraction of \[\dfrac{7}{19}\] .
So, we have got the correct option for this question as (d) \[\dfrac{21}{57}\] .
Hence, \[\dfrac{21}{57}\] is an equivalent fraction of \[\dfrac{7}{19}\] .

So, the correct answer is “Option d”.

Note: We can also solve this question by multiplying the given fraction with the same number on the numerator and denominator such that it results in any of the options. So, we can start with 2, we will get $\dfrac{7}{19}\times \dfrac{2}{2}\Rightarrow \dfrac{14}{38}$ . Since it is not matching, we go for 3 and we get $\dfrac{7}{19}\times \dfrac{3}{3}\Rightarrow \dfrac{21}{57}$. Since this matches with option d, we conclude it as the answer.