Question

what is $-\frac{5}{6}+4.2$?
a) $3\frac{11}{30}$
b) $3\frac{11}{15}$
c) $4\frac{19}{30}$
d) $5\frac{1}{30}$

Explanation:

Step1: Convert fraction to decimal

$-\frac{5}{6}\approx - 0.833$ (rounded to three - decimal places)

Step2: Perform addition

$-0.833 + 4.2=3.367$

Step3: Convert decimal to fraction

$3.367 = 3+\frac{367}{1000}$
Let's do it in a non - decimal way. First, convert $4.2$ to a fraction: $4.2=\frac{42}{10}=\frac{21}{5}$
Then find a common denominator for $\frac{21}{5}$ and $-\frac{5}{6}$. The common denominator of 5 and 6 is 30.
$\frac{21}{5}=\frac{21\times6}{5\times6}=\frac{126}{30}$
$-\frac{5}{6}=-\frac{5\times5}{6\times5}=-\frac{25}{30}$
$\frac{126}{30}-\frac{25}{30}=\frac{126 - 25}{30}=\frac{101}{30}=3\frac{11}{30}$

Answer:

A. $3\frac{11}{30}$