Question

Please help find the value of the expression and show work thank you

Answer 1

First we need to find the least common multiple of the denominators.

40 is is divisible by 8, 5, and 4, so we will use it as our common denominator.

Then we need to multiply the numerators by the same amount we had to multiply each denominator by to get 40.

For example, 8 is the denominator of the first fraction. To make it 40, we multiply by 5. We need to also multiply the numerator 3 by the same 5 to keep the fraction the same. So the 3 becomes 3*5 = 15.

The numerators in order after doing this are 15, -32, -15, and 50. Now add these add.

15-32-15+50 = 18.

Put this sum over the common denominator to get the final answer.

18/40 which can be simplified to 9/20.

The answer is 9/20

Answer 2

3/8+(-4/5)+(-3/8)+5/4

Remember a positive and a negative will be negative.

=3/8-4/5-3/8+5/4

Now you need a common denominator for all of them, but if you notice that 3/8-3/8=0, you are left with:
=-4/5+5/4

5 and 4 both go into 20. So your common denominator is 20. 5 goes in to 20 four times (so 4*4=16 =16/20).
4 goes in to 20 five times (so 5*5=25/20).

Remember 4/5 was negative:
=-16/20+25/20
=9/20

9 and 20 do not have any common factors, so this is the answer.

Hope this helps!! :)