Question

2/5 (1/3x - 15/8) - 1/3(1/2 - 2/3x)

Answer 1

Your question presented was: $\frac{2}{5} (\frac{1}{3} x-\frac{15}{8} )-\frac{1}{3} (\frac{1}{2} -\frac{2}{3}x)$

Okay, lets distribute this problem and break it into two parts. We will distribute 2/5 and -1/3 to the numbers in parenthesis. This is the distributive property.

Step 1.
$\frac{2}{5} (\frac{1}{3} x-\frac{15}{8} )$ when distributed is $\frac{2}{15} x - \frac{30}{40}$

Please note that -1/3 can be rewritten as + -1/3. So you must distribute the negative.

Step 2.
$\frac{-1}{5} + \frac{2}{9} x$
So..lets put the 2 parts of the equation together

$\frac{2}{15} x - \frac{30}{40}$ + $\frac{-1}{5} + \frac{2}{9} x$ can be simplified by getting the common denominator.

You can only add like terms, so those fractions with x can only be combined with x.
Step 3.
Lets reformat while we're at it
$\frac{6}{45} x + \frac{10}{45} x -\frac{30}{40} -\frac{8}{40}$

We got 45 because the LCM (Lowest Common Multiple) of 15 and 9 was 45. We multiplied both sides of the fraction by 3 for 2/15x and we multiplied by 5 on both parts of the fraction for 2/9x.

Now we combine.
Step 4.
$\frac{16}{45}x-\frac{38}{40}$. We can still simplify!
Step 5.
-38/40 can be simplified by a common factor, 2! So our final answer is
$\frac{16}{45}x-\frac{19}{20}$

I hope this helps you, heart if it helps.