Question

Fill in the blanks with the suitable value: $\frac{17}{-5}+[\frac{-3}{10}+\frac{-3}{8}]=[\frac{17}{-5}-\underset{–}{}]+\frac{-3}{8}$

• A. $\frac{10}{3}$
• B. $\frac{3}{10}$
• C. $\frac{-10}{3}$
• D. $\frac{-3}{10}$

Answer 1

The correct option is B $\frac{3}{10}$

A per the associative property of rational numbers for addition,
$(\frac{p}{q}+\frac{r}{s})+\frac{t}{u}=\frac{p}{q}+(\frac{r}{s}+\frac{t}{u})$
[Where $p,q,r,s,t,\text{and}u$ are integers]

So, we can write given expression $\frac{17}{-5}+[\frac{-3}{10}+\frac{-3}{8}]$ as $[\frac{17}{-5}+\frac{-3}{10}]+\frac{-3}{8}=[\frac{17}{-5}-\frac{3}{10}]+\frac{-3}{8}$

After comparing, the value in the blank should be $\frac{3}{8}$.
Hence, option with $\frac{3}{8}$ is the correct choice.