This is simply adding and subracting fractions! Let's tackle this one step at a time:
- Let's rewrite all terms as fractions: (3/8) + (-4/5) + (-3/8) + (5/1) - (4/1)
- Let's simplify: (3/8) + (-3/8) = (3/8) - (3/8) = 0. Therefore, the terms with (3/8) cancel out and we have: (-4/5) + (5/1) - (4/1)
- Let's bring the negative signs outside of the parentheses (NOTE: 0 + (-4) = 0 - 4):
(5/1) - (4/1) - (4/5). I moved the (-4/5) all the way to right to make things prettier. We can do this because of the commutative law of addition/subtraction, which says a - b - c = a - c - b = -c + a - b, in other words, it's ok to shift terms when adding or subtracting them; it doesn't change the final answer. - Let's get a common denominator for all the terms to make addition/subtraction simple:
NOTE: (5/1) = (5/1)*(1) = (5/1)*(5/5) = (25/5); We want to multiply the terms by one so we don't change their overall value.
NOTE: A easy way to find the common denominator is to multiply all distinct (different) numbers in the denominator of each term.
In our case, the distinct values in the denominators of these numbers are: 5 & 1
5*1=5. So we'll multiply the denominator of each term by a number which gives us a product of 5, then we'll multiply the numerator by the same number so that all we're doing is multiplying the term by 1.
We have: [ (5/1)*(5/5) ] - [ (4/1)*(5/5) ] - [ (4/5)*(1/1) ] = (25/5) - (20/5) - (4/5) - Now do the addition/subtraction! Easy!:
(25/5) - (20/5) - (4/5)
= (5/5) - (4/5)
= (1/5) - We have the answer!------> (1/5)