Algebra Demystified 2nd Ed

14 alGebra De mystif ieD

To compute a

b

c

d

+ or a

b

c

d

− , we can “reverse” the simplification process

to rewrite the fractions so that they have the same denominator. This process

is called finding a common denominator. Multiplying a

b

by d

d

(the second denom-

inator over itself ) and dc by bb (the first denominator over itself ) gives us equiv-

alent fractions that have the same denominator. Once this is done, we can add

or subtract the numerators.

a

b

c

d

a

b

d

d

c

d

b

b

ad

bd

cb

bd

+=⋅+⋅= +

Nowwe can addthenuumerators.

=ad+cb

bd

a

b

c

d

a

b

d

d

c

d

b

b

ad

bd

cb

bd

−=⋅−⋅= −

Nowwe cansubtracttthenumerators.

=ad−cb

bd

Note that this is essentially what we did with the pie chart to find^14 +^13

when we divided the pie into 43 ×= 12 equal parts.

For now, we will use the formula ab±=dc adbd±cb to add and subtract two

fractions. Later, we will learn a method for finding a common denominator

when the denominators have common factors.

EXAMPLES

Find the sum or difference.

1

2

3

7

8

15

1

2

+

−

SOLUTIONS

In this sum, the first denominator is 2 and the second denominator is 7. We

multiply the first numerator and denominator of the first fraction,^12 , by 7

and the numerator and denominator of the second fraction, 73 , by 2. This

gives us the sum of two fractions having 14 as their denominator.

1

2

3

7

1

2

7

7

3

7

2

2

7

14

+=  ⋅







+⋅







= +=^6

14

13

14

8

15

1

2

8

15

2

2

1

2

15

15

−= ⋅











−⋅







=   16

30

15

30

1

30

−=

SOLUTIONS

In this sum, the first denominator is 2 and the second denominator is 7. We

✔

EXAMPLES

Find the sum or difference.