Question

Find the value of $[\frac{7}{21}{]}^3+[\frac{3}{5}{]}^3$.

Answer 1

Step 1: Write the fractions in their simplest form.

$\frac{7}{21}=\frac{1}{3}$ in its standard form and $\frac{3}{5}$ is already in standard form.

Step 2: Find the cubes of each fraction and then perform addition.

$(\frac{1}{3}{)}^3=\frac{1}{3}\times \frac{1}{3}\times \frac{1}{3}=\frac{1}{27}$
And $(\frac{3}{5}{)}^3=\frac{3}{5}\times \frac{3}{5}\times \frac{3}{5}=\frac{27}{125}$
Then $\frac{1}{27}+\frac{27}{125}=\frac{1\times 125+27\times 27}{27\times 125}$
$=\frac{125+729}{3375}$
$=\frac{854}{3375}$