Question

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

Answer 1

Your question presented was:
`(2)/(5) ((1)/(3) x-(15)/(8) )-(1)/(3) ((1)/(2) -(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.

`(2)/(5) ((1)/(3) x-(15)/(8) )` when distributed is
`(2)/(15) x - (30)/(40)`

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

Step 2.

`(-1)/(5) + (2)/(9) x`
So..lets put the 2 parts of the equation together

`(2)/(15) x - (30)/(40)` +
`(-1)/(5) + (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

`(6)/(45) x + (10)/(45) x -(30)/(40) -(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.

`(16)/(45)x-(38)/(40)`. We can still simplify!
Step 5.
-38/40 can be simplified by a common factor, 2! So our final answer is

`(16)/(45)x-(19)/(20)`

I hope this helps you, heart if it helps.