Question

Add the following rational numbers:-
$${\displaystyle \frac{5}{8}}$$ And $${\displaystyle \frac{-7}{12}}$$

Answer 1

Hint:-We are firstly going to make the denominators of these two rational numbers similar by calculating the L.C.M. of their denominators.
After making their denominators the same, we will add the rational numbers, and hence, then we will get the answer of this question.

Complete step-by-step answer:
As mentioned in the hint provided above, we are firstly going to make the denominators of these two rational numbers similar by calculating the L.C.M. of their denominators. So, let us calculate the L.C.M. of 8 and 12.
L.C.M. of 8 and 12:-

So, the L.C.M. of 8 and 12 = 2x2x2x3 = 4 x6 = 24
Now, we will multiply the denominators of these two rational numbers by suitable numbers, so that we can obtain 24 as the denominator in both the cases. As we are multiplying the denominators of these rational numbers, we will multiply their numerators also, by the same numbers.
$${\displaystyle \frac{5\times 3}{8\times 3}}={\displaystyle \frac{15}{24}}$$
$${\displaystyle \frac{-7\times 2}{12\times 2}}={\displaystyle \frac{-14}{24}}$$
So, the two rational numbers we get after making their denominators same are:
$${\displaystyle \frac{15}{24}}and{\displaystyle \frac{-14}{24}}$$
Now, we shall add these two rational numbers.
 $${\displaystyle \frac{15}{24}}+{\displaystyle \frac{-14}{24}}={\displaystyle \frac{15-14}{24}}={\displaystyle \frac{1}{24}}$$
Hence, the sum of these two rational numbers is $${\displaystyle \frac{1}{24}}$$ .
Therefore, the answer of this question is $${\displaystyle \frac{1}{24}}$$.

Note:-When we multiply any number by the denominator of a fraction or a rational number, then we have to multiply the same number with the numerator also. If we do not do so, then the answer can come out to be wrong. One must do all the calculations in this question very carefully.
Also not only in this question, the students must be very careful while solving any such questions as if there is any mistake in the calculus, then the answer can come out to be wrong.