Question

How do you evaluate $\dfrac{7}{8}+\dfrac{8}{7}$ ?

Answer 1

Hint: In this question, we have to solve the fractional terms to get a simplified answer. So, we will use the LCM method to get the solution. We first take the least common multiple of the denominator and then solve further by multiplying the first term of the numerator and the last term of the denominator, and then add the value to the next term, which is the multiplication of the next term of the numerator and the first term denominator. Then, we make further calculations, to get the required result to the solution.

Complete step-by-step answer:
According to the problem, we have to find the simplified value of a fractional number.
Since two fractional numbers are added to each other, therefore we will use the LCM method to get the result.
The fractional term given to us is $\dfrac{7}{8}+\dfrac{8}{7}$ -------- (1)
So, we will first take the least common multiple of the denominator of the equation (1), we get
$LCM(8,7)=2\times 2\times 2\times 7$
Therefore, we get
$LCM(8,7)=56$ ---------- (2)
So, we will write the LCM of (8,7) as the new denominator of the new fractional term.
Now, we will find the numerator of the new fractional number.
We will multiply the numerator of the first fractional number to the denominator of the second fractional number and then add that value to the multiplication of the numerator of the second fractional number to the denominator of the first fractional number, that is
$(7\times 7)+(8\times 8)$
Therefore, we get
$49+64$
$113$ --- (3)
Thus, the new fractional number will take values as the numerator from equation (3) and the denominator from equation (2), that is
$\dfrac{113}{56}$ which is our required answer.
Therefore, for the fractional number $\dfrac{7}{8}+\dfrac{8}{7}$ , its simplified value is equal to $\dfrac{113}{56}$

Note: While solving this problem, keep in mind the method you are using and do the step-by-step calculations to avoid confusion and mathematical error. One of the alternative methods to solve this problem is first to take the long division method, that is divide the numerator and denominator of both the fractions individually and then add both of them, which is our required solution to the problem.