Question

Simplify:$\frac{7}{3}+2\frac{3}{4}-\frac{1}{7}$

Answer 1

Simplify the given expression

First simplify the mix fraction into improper fraction,

$2\frac{3}{4}=\frac{11}{4}$ [Multiply $4$ by $2$ and then add $3$]

$\frac{7}{3}+2\frac{3}{4}-\frac{1}{7}=\frac{7}{3}+\frac{11}{4}-\frac{1}{7}$

To solve this, find the LCM of the denominators i.e., LCM$(3,4,7)=84$

Now, make the denominator of each fraction same

$\begin{array}{rcl}\frac{7}{3}+\frac{11}{4}-\frac{1}{7}& =& \frac{7\times 28}{3\times 28}+\frac{11\times 21}{4\times 21}-\frac{1\times 12}{7\times 12}\\ & =& \frac{196+231-12}{84}\\ & =& \frac{415}{84}\end{array}$

Therefore, $\frac{7}{3}+2\frac{3}{4}-\frac{1}{7}=\frac{415}{81}$