Idiot\'s Guides Basic Math and Pre-Algebra

Chapter 8: Variables and Expressions 107

What if there’s a variable in the denominator? To divide^6

t^2

t

, add your warning note, t { 0, and

then let the coefficient be and focus on the variables. This is where the rules for exponents come

in.

66

1

6

11

6

t^22

t

t

t

t

   t, provided t { 0. Unless the variable in the denominator is different from

the variable in the numerator, you should be able to do some simplifying with problems like this.

The next step is putting the pieces together. To divide

27

54

5

3

y

y

, start with the fact that y { 0 and

then group coefficients with coefficients and variables with variables.

27

54

27

54

5

3

5

3

y

y

y

y

 . Reduce the

fraction, and use the rules for exponents to simplify the variable part.

27

54

27

54

1

21

5

3

5

3

y^2

y

y

y

y

. You

can write your final answer as

y^2

2

or

1

2

y^2 , whichever you prefer, but remember to include y { 0.

Dividing with Other Operations

When addition or subtraction slips into the problem, things get a little more complicated. To

divide^257015

5

543

3

xxx

x

, you need to break it into three fractions. Each piece of the numerator is

going to be divided by the denominator.

Think for a minute about adding fractions, just regular fractions, like

1

2

2

3

. First you have to

change each fraction to an equivalent fraction with a common denominator, in this case, 6.

1

2

2

3

3

6

4

6

. Then you’ll add the 3 + 4 and put the answer over the common denominator of 6.

What you’re going to do with this variable division problem is step to when you had separate

fractions with the same denominator.^257015

5

543

3

xxx

x

 is going back to 25

5

70

5

15

5

5

3

4

3

3

3

x

x

x

x

x

x

.

Here’s how it works. Don’t forget: x { 0.

25 70 15

5

25

5

70

5

15

5

543

3

5

3

4

3

3

3

xxx

x

x

x

x

x

x

x

  

Simplify each of the three fractions by grouping coefficients with coefficients, reducing the

fraction, and then grouping variables with variables, using the rules for exponents.

So

25 70 15

5

5143

543

3

xxx 2

x

xx



, as long as x is not zero.

25 70 15

5

25

5

70

5

15

5

25

5

70

5

543

3

5

3

4

3

3

3

5

3

4

xxx

x

x

x

x

x

x

x

x

x

x

x^33

3

3

2

2

15

5

5

11

14

11

3

1

1

1

5143

x

x

xx

xx