The Algebra Teacher\'s Guide to Reteaching Essential Concepts and Skills

Name Date

WORKSHEET 6.12: SOLVING EQUATIONS THAT HAVE

FRACTIONAL COEFFICIENTS

-------------------------------------------------------------------------------------

Follow the steps below to solve equations with fractional coefficients:

1. Find the least common denominator (LCD) of the fractions.
   
   
   • Express each denominator using prime factorization with exponents.
   
   
   • Find the product of the prime numbers selecting the largest exponent of each prime
     number.
   
   
   
   


2. Multiply both sides of the fraction by the least common denominator.


3. Solve the equation.

EXAMPLE

x+ 1

4

+

5

6

=

9

2

.Solveforx.

Because 4 = 22 ,6= 21 · 31 ,and 2 = 21 ,theLCDis 22 · 3 or 12. Multiply both sides of the

equation by 12.

12

[

x+ 1

4

+

5

6

=

9

2

]

→12(x+ 1)+

4

12 · 5 =

6

12 · 9

2

3

111

26

→ 3 x+ 3 + 10 = 54 → 3 x+ 13 = 54 →

3 x= 41 →x= 13

2

3

DIRECTIONS: Solve each equation.

1.

x

6

+

x

4

=

5

6

2.

x

3

−

x

4

=−

5

4

3.

x

2

−

x+ 5

3

=

1

2

4.

3 x

5

−

x

4

=

1

20

5. 
   

3

8

+

x+ 2

4

=

x

2

CHALLENGE:Denny solved

x

4

+

x

12

=

1

6

by multiplying the equation by 12, the

least common denominator. Tara found a common denominator, 24, and

multiplied the equation by 24. Will they get the same answer? Explain your

reasoning.

247

Copyright

©

2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.