Question

Simplify the algebraic fraction : $1\frac{\mathrm{x}}{2}+2\frac{2\mathrm{x}}{3}-\frac{\mathrm{x}}{6}$

Answer 1

To simplify : $1\frac{\mathrm{x}}{2}+2\frac{2\mathrm{x}}{3}-\frac{\mathrm{x}}{6}$

Convert the above mixed algebraic fraction into an improper fraction, we get

$1\frac{\mathrm{x}}{2}+2\frac{2\mathrm{x}}{3}-\frac{\mathrm{x}}{6}$$=\frac{2+\mathrm{x}}{2}+\frac{6+2\mathrm{x}}{3}-\frac{\mathrm{x}}{6}$

Now let us find the L.C.M of denominators of the above algebraic fractions to convert them into like fractions, we get

L.C.M of $2$, $3$ and $6$ $=6$

$\frac{2+\mathrm{x}}{2}=\frac{(2+\mathrm{x})\times 3}{2\times 3}=\frac{3(2+\mathrm{x})}{6}$

$\frac{6+2\mathrm{x}}{3}=\frac{(6+2\mathrm{x})\times 2}{3\times 2}=\frac{12+4\mathrm{x}}{6}$

$1\frac{\mathrm{x}}{2}+2\frac{2\mathrm{x}}{3}-\frac{\mathrm{x}}{6}$ $=$$\frac{3(2+\mathrm{x})}{6}$$+\frac{12+4\mathrm{x}}{6}$$-\frac{\mathrm{x}}{6}$

$=$$\frac{6+3\mathrm{x}+12+4\mathrm{x}-\mathrm{x}}{6}$

$=\frac{18+6\mathrm{x}}{6}$

$=6\times \frac{(3+\mathrm{x})}{6}$ ( $6$ is taken common in numerator )

$=\mathrm{x}+3$

Thus,$1\frac{\mathrm{x}}{2}+2\frac{2\mathrm{x}}{3}-\frac{\mathrm{x}}{6}$$=\mathrm{x}+3$ . Answer