Question
Simplify:
$3+1\frac{1}{5}+\frac{2}{3}-\frac{7}{15}$
$3+1\frac{1}{5}+\frac{2}{3}-\frac{7}{15}$
✓
Answer
$3+1\frac{1}{5}+\frac{2}{3}-\frac{7}{15}=\frac{3}{1}+\frac{1\times5+1}{5}+\frac{2}{3}-\frac{7}{15}$
$=\frac{3}{1}+\frac{6}{5}+\frac{2}{3}-\frac{7}{15}$
$=\frac{3\times15}{1\times15}+\frac{6\times3}{5\times3}+\frac{2\times5}{3\times5}-\frac{7\times1}{15\times1}$ (because $LCM$ of 1$, 5, 3$ and $15$ is $15)$
$=\frac{45}{15}+\frac{18}{15}+\frac{10}{15}-\frac{7}{15}$
$=\frac{45+18+10-7}{15}$
$=\frac{66}{15}$
$=\frac{22}{5}$
$=3\frac{7}{5}$
$=\frac{3}{1}+\frac{6}{5}+\frac{2}{3}-\frac{7}{15}$
$=\frac{3\times15}{1\times15}+\frac{6\times3}{5\times3}+\frac{2\times5}{3\times5}-\frac{7\times1}{15\times1}$ (because $LCM$ of 1$, 5, 3$ and $15$ is $15)$
$=\frac{45}{15}+\frac{18}{15}+\frac{10}{15}-\frac{7}{15}$
$=\frac{45+18+10-7}{15}$
$=\frac{66}{15}$
$=\frac{22}{5}$
$=3\frac{7}{5}$
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