How to find common denominator, please help!?

Question

How do you find common denominator and then solve for these problems? I need to show work and I can't figure it out.

1. 7/10 - (-5/6)

2. -11/15 - 2/9

3. 9/20(-4/15)

4. 8/5 divided by (-18/25)

5. -27.8 - 13.582

6. -32.84 divided by 4

7. -89.416 +21.32 - 478.91 + 298.213

Any help is greatly appreciated! Thank you!

Answer 1

I'll get you through the first one. Then you're on your own (but don't worry, there are always show offs to do all your work for you!)

1. 7/10 - (-5/6)

Now, let's make that a little easier

7/10 + 5/6

A common denominator is something both will divide into equally. In this case, 30 will work.

7/10 (3/3) + 5/6 (5/5) (remember 3/3 or 5/5 = 1, so you're not changing any value.

21/30 + 25/30 = 46/30

now divide 46/30

1 16/30

To help a bit more -- when multiplying fractions, no common denominator needed. Just multiply straight across. To divide, turn the second fraction upside down (the reciprocal) and multiply.

Answer 2

The easiest way is just to multiply the 2 bottom numbers together. It will be a common denominator - but not necessarily the lowest common denominator.

1)

10 X 6 = 60

so;

42/60 + 50/60 = 92/60 = 1 32/60 = 1 8/15

2)

15 X 9 = 135, but that is not the lowest common denominator. What number can be divided by 9 & 15? It's 45. That is the lowest.

so;

45/15 = 3, so 11 X 3 = 33. 45/9 = 5, so 5 X 2 = 10

then

-33/45 - 10/45 = -43/45.

3)

To multiply, multiply the top 2, then the bottom 2.

9 X -4 = -36, 20 X 15 = 300

so;

-36/300 = -18/150 = -9/75

4)

When dividing, invert the divider.

8/5 /  -18/25 is equal to

8/5 X -25/18

8 X -25 = -200, 5 X 18 = 90

so

-200/90 = -20/9 = -2 2/9

5)

-27.800 - 13.582 = -41.382

6)

-8.21

7)

-248.793