Solving Equations Containing Fractions

VocabularyThe reciprocal of a fraction:• changes the places of the numerator and

denominator. (Flip the fraction upside down)• Is also called the multiplicative inverse.

A number times its reciprocal equals 1.

123

32

Ex. 1) 54

32

x The goal is to get 1x alone.

To do this, multiply

both sides by ,

which is the reciprocal

of .

23

32

23

54

32

23 x

Reduce fractions if possible.

2

1

Multiply fractions, and simplify.511

561 x

Ex. 2) 1497

x The goal is to get 1x

alone.

To do this, multiply

both sides by ,

which is the reciprocal

of .

79

97

7

91

1497

79 x

Reduce fractions if possible.

2

-1

Multiply fractions, and simplify.18

1181

x

Ex. 3) 15

4 x Subtract 4 from both sides

to get the x term alone.

4 4

Multiply both sides by 5 to get 1x alone.

Note:

so 5 is the reciprocal of .

xx51

5

51

5)( 5)(

25x

55

x

Ex. 4) 10322 x Add 2 to both sides to get

the x term alone.

2 2

23

23

181

18x

112

32 x Multiply both sides by ,

which is the reciprocal of .

23

32

Reduce fractions if possible.

6

1

Multiply fractions, and simplify.

Ex. 5) 47251211

x Subtract 25 from both sides to get the x term alone.

25 25

1112

1112

24124

x

122

1211 x Multiply both sides by ,

which is the reciprocal of .

1112

1211

Reduce fractions if possible.

2

1

Multiply fractions, and simplify.

Ex. 6) 32115 x Subtract 15 from both sides

to get the x term alone.

15 15

1

2 1

2

36136

x

118

21

x Multiply both sides by ,

which is the reciprocal of .

12

21

Reduce fractions if possible.

Multiply fractions, and simplify.