Question

Simplify the algebraic fraction : $\frac{\mathrm{a}}{6}+\frac{3\mathrm{a}}{5}-\frac{\mathrm{a}}{15}$

Answer 1

To simplify: $\frac{\mathrm{a}}{6}+\frac{3\mathrm{a}}{5}-\frac{\mathrm{a}}{15}$

Convert the given algebraic fractions into like fractions by obtaining L.C.M of their denominators, we get

L.C.M of $6$ ,$5$ and $15=30$

$\frac{\mathrm{a}}{6}=\frac{\mathrm{a}\times 5}{6\times 5}=\frac{5\mathrm{a}}{30}$ ; $\frac{3\mathrm{a}}{5}=\frac{3\mathrm{a}\times 6}{5\times 6}=\frac{18\mathrm{a}}{30}$ ; $\frac{3\mathrm{a}}{15}=\frac{3\mathrm{a}\times 2}{15\times 2}=\frac{6\mathrm{a}}{30}$

$\frac{\mathrm{a}}{6}+\frac{3\mathrm{a}}{5}-\frac{\mathrm{a}}{15}$ $=\frac{5\mathrm{a}}{30}+\frac{18\mathrm{a}}{30}-\frac{6\mathrm{a}}{30}$

$=\frac{5\mathrm{a}+18\mathrm{a}-6\mathrm{a}}{30}$

$=\frac{23\mathrm{a}-6\mathrm{a}}{30}$

$=\frac{17\mathrm{a}}{30}$

Thus,$\frac{\mathrm{a}}{6}+\frac{3\mathrm{a}}{5}-\frac{\mathrm{a}}{15}=\frac{17\mathrm{a}}{10}$