# What is the sum of 3 1/6 + (-5.5), expressed as a mixed number in simplest form?

Mar 7, 2018

= color(green)( -2(1/3)

#### Explanation:

$3 \left(\frac{1}{6}\right) = \frac{\left(6 \cdot 3\right) + 1}{6} = \frac{19}{6}$

$5.5 = \frac{5.5 \cdot 10}{10} = {\cancel{55}}^{\textcolor{b r o w n}{11}} / {\cancel{10}}^{\textcolor{b r o w n}{2}} = \frac{11}{2}$

L C M of denominator of the numbers 2,6 is 6.

$\therefore \left(\frac{19}{6}\right) - \frac{11}{2} = \left(\frac{19}{6}\right) - \left(\frac{11 \cdot 3}{2 \cdot 3}\right)$

$\implies \left(\frac{19}{6}\right) - \left(\frac{33}{6}\right) = \frac{19 - 33}{6} = - {\cancel{14}}^{\textcolor{b r o w n}{7}} / {\cancel{6}}^{\textcolor{b r o w n}{3}}$

=> -(7/3) = color(green)( -2(1/3)