Question

Evaluate:
$\frac{-11}{12}+\frac{5}{16}+\frac{-3}{8}$

Answer 1

Step 1: Finding LCM of denominators of given numbers
Given,
$\frac{-11}{12}+\frac{5}{16}+\frac{-3}{8}$
$\therefore LCM\text{of}8,12,16=4\times 2\times 3\times 2=48.$

Step: 2 Making the denominators of the rational number equal to LCM i.e. 48
To make the denominators equal to 48 we have to multiply and divide the first fraction by 4, second by 3 and third 6.
$\frac{-11}{12}=\frac{-11\times 4}{12\times 4}=\frac{-44}{48}$ and
$\frac{5}{16}=\frac{5\times 3}{16\times 3}=\frac{15}{48}$ and
$\frac{-3}{8}=\frac{-3\times 6}{8\times 6}=\frac{-18}{48}$

Step 3: Adding $\frac{-14}{35}$ and $\frac{15}{35}$
Since, denominators are same, hence add the numerators. $\frac{-44}{48}+\frac{15}{48}+\frac{-18}{48}$
$=\frac{-62+15}{48}$
$=\frac{-47}{48}$
Hence, the required answer is $\frac{-47}{48}.$