What is 9/20+(-1/5) in simplest form?

steveschoen | Certified Educator

Hi, Robert.  I hope this can assist.

To add fractions, you need to have a common denominator.  There are several ways to find this.  The way I like to is this.

1) list the denominators

20

5

2) List their multiples

20: 20, 40, 60, 80. . .

5: 5, 10, 15, 20, 25. . .

3) Which number occurs first in each line

20 occurs first in both lines, so that is the common denominator

So, we need to write each fraction with the denominator being 20.  The first fraction has that already.  So, we need to convert -1/5 to a fraction with 20 on the bottom.  There are several ways to do this.  One way is to make a proportion:

-1/5 = x/20

Because, you know the bottom is 20, you just don't know the top number.  Solving the proportion, x = -4.  So, we would have:

9/20 + (-1/5)

9/20 + (-4/20)

For this, we add the top numbers, the bottom numbers stay the same.  So, 9 + (-4) = 5.  So, we have:

5/20 which reduces to 1/4

I hope this assist, Robert.  Good luck.

Steve

oldnick | Student

`9/20+(-1/5)= 9/20-1/5= 1/5(9/4-1)=1/5(9-4)/4=1/5 5/4=1/4`

chesspawn | Student

1. Give both fractions common denominators, because you're adding.

9/20 + (-4/20)

2. The new fraction you have is (9 + (-4)) / 20, which gives you 5 / 20

3. 5 goes into 20 four times, therefore the answer is 1 / 4