Question

Choose the correct answer $\frac{7\mathrm{x}}{38}\mathrm{of}(\frac{\mathrm{x}}{4}+\frac{4\mathrm{x}}{3})$equals:

• A. $\frac{\mathrm{x}}{3}$
• B. $\frac{7{\mathrm{x}}^2}{3}$
• C. $\frac{7{\mathrm{x}}^2}{24}$
• D. $\frac{1}{38}$

Answer 1

The correct option is C

$\frac{7{\mathrm{x}}^2}{24}$

To simplify: $\frac{7\mathrm{x}}{38}\mathrm{of}(\frac{\mathrm{x}}{4}+\frac{4\mathrm{x}}{3})$

Solving for $(\frac{\mathrm{x}}{4}+\frac{4\mathrm{x}}{3})$, convert the given algebraic fractions into like fractions by obtaining L.C.M of their denominators, we get

L.C.M of $4$ and $3=12$

$\frac{\mathrm{x}}{4}=\frac{\mathrm{x}\times 3}{4\times 3}=\frac{3\mathrm{x}}{12}$

$\frac{4\mathrm{x}}{3}=\frac{4\mathrm{x}\times 4}{3\times 4}=\frac{16\mathrm{x}}{12}$

$\frac{\mathrm{x}}{4}+\frac{4\mathrm{x}}{3}=\frac{3\mathrm{x}}{12}+\frac{16\mathrm{x}}{12}$

$=$$\frac{3\mathrm{x}+16\mathrm{x}}{12}$

$=$$\frac{19\mathrm{x}}{12}$

$\frac{7\mathrm{x}}{38}\mathrm{of}(\frac{\mathrm{x}}{4}+\frac{4\mathrm{x}}{3})$$=\frac{7\mathrm{x}}{38}\times$$\frac{19\mathrm{x}}{12}$

$=\frac{7\mathrm{x}}{2}\times \frac{\mathrm{x}}{12}$

$=\frac{7{\mathrm{x}}^2}{24}$ $({\mathrm{a}}^{\mathrm{m}}\times {\mathrm{a}}^{\mathrm{n}}={\mathrm{a}}^{\mathrm{m}+\mathrm{n}})$

Thus, option C is the correct answer