Question

Simplify:
$\frac{1}{4}(\frac{1}{4}+\frac{1}{3})-\frac{2}{5}$

Answer 1

Step 1: Solving the parentheses
$\frac{1}{4}(\frac{1}{4}+\frac{1}{3})-\frac{2}{5}$

=$\frac{1}{4}\left(\frac{1\times 3+1\times 4}{12}\right)-\frac{2}{5}$

[LCM of (3,4) = 12]

=$\frac{1}{4}\left(\frac{3+4}{12}\right)-\frac{2}{5}$

=$\frac{1}{4}\left(\frac{7}{12}\right)-\frac{2}{5}$

=$\frac{7}{48}-\frac{2}{5}$

Step 2: Simplifying further by making the denominator the same
Prime factors of 5 = 5
Prime factors of $48=2\times 2\times 2\times 2\times 3$
So,
LCM (5,48) =$2\times 2\times 2\times 2\times 3\times 5=240$

$\frac{7}{48}-\frac{2}{5}=\frac{7\times 5}{48\times 5}-\frac{2\times 48}{5\times 48}$

$=\frac{35}{240}-\frac{96}{240}$

$=\frac{35-96}{240}$

$=-\frac{61}{240}$

Hence, the given expression is equal to $=-\frac{61}{240}$