Question

Simplify $5\frac{1}{6}+2\frac{1}{3}-5\frac{11}{12}$.

Answer 1

Making the denominators of the fractions the same.

$12=3\times 2\times 2$

LCM $\left(6,3,12\right)=12$

$\begin{array}{rcl}& \Rightarrow & 5\frac{1}{6}+2\frac{1}{3}-5\frac{11}{12}=\frac{\left(5\times 6\right)+1}{6}+\frac{\left(2\times 3\right)+1}{3}-\frac{\left(5\times 12\right)+11}{12}\\ & =& \frac{31}{6}+\frac{7}{3}-\frac{71}{12}\\ & =& \frac{31\times 2}{6\times 2}+\frac{7\times 4}{3\times 4}-\frac{71}{12}\\ & =& \frac{62}{12}+\frac{28}{12}-\frac{71}{12}\\ & =& \frac{62+28-71}{12}=\frac{90}{12}=\frac{19}{12}\end{array}$

$\frac{19}{12}=1\frac{1}{12}$

Thus, $5\frac{1}{6}+2\frac{1}{3}-5\frac{11}{12}$ is $1\frac{1}{12}$.