Question

The sum of the two rational number is $\dfrac{{127}}{{42}}$, if one of them is $\dfrac{{17}}{{21}}$, then find the other.

Answer 1

Hint: According to given in the question we have to find the other rational number when sum of the two rational number is $\dfrac{{127}}{{42}}$, if one of them is $\dfrac{{17}}{{21}}$. So, first of all we will let the required rational number is $x$ but before that we have to understand about the rational numbers which is explained below:
Rational number: A number that can be obtained by dividing two integers/numbers that can be positive or negative both and the word rational comes from the word ratio or rational numbers are represented in the form $\dfrac{a}{b}$ where the integer b in the denominator should not be zero. It is also a type of a real number so, any fraction with non-zero denominator is a rational number and we can represent it in so many ways as: $\dfrac{1}{2},\dfrac{1}{3},\dfrac{{ - 1}}{2},\dfrac{2}{5},......$
So, now as given in the question that sum of both the rational number is $\dfrac{{127}}{{42}}$
There we can obtain the other or required number as asked in the question by adding the number we let with the given number $\dfrac{{17}}{{21}}$ and after the same easy calculations we can obtain the value of the required number.

Complete step-by-step answer:
Given,
One number = $\dfrac{{17}}{{21}}$
Sum of numbers = $\dfrac{{127}}{{42}}$
Step 1: First of all we have to let that the other number is $x$
Step 2: Now, as we know that the sum of the numbers is $\dfrac{{127}}{{42}}$so now we have to add the number we let with the given number $\dfrac{{127}}{{42}}$.Hence,
$
   \Rightarrow x + \dfrac{{17}}{{21}} = \dfrac{{127}}{{42}} \\
   \Rightarrow x = \dfrac{{127}}{{42}} - \dfrac{{17}}{{21}} \\
    \\
 $
Step 3: Now, to obtain the value of x we have found the L.C.M. of the expression obtained in step 2.
$
   \Rightarrow x = \dfrac{{127}}{{42}} - \dfrac{{17}}{{21}} \\
   \Rightarrow x = \dfrac{{127 - 34}}{{42}} \\
   \Rightarrow x = \dfrac{{93}}{{42}} \\
   \Rightarrow x = \dfrac{{31}}{{14}} \\
 $

Hence, if the sum of the two rational number is $\dfrac{{127}}{{42}}$, if one of them is $\dfrac{{17}}{{21}}$, then the other rational number is $ = \dfrac{{31}}{{14}}$

Note: If the sum, multiplication, division or the subtraction of any two numbers is given and one of the numbers is also given so we can find the other number with the help of their sum, multiplication, division or the subtraction by assuming that number some variable.
Do remember to simplify the obtained rational number.
A number that can be obtained by dividing two integers/numbers that can be positive or negative both and the word rational comes from the word ratio or rational numbers are represented in the form $\dfrac{a}{b}$ where the integer b in the denominator should not be zero.