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

(Marvins-Underground-K-12) #1
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





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.

Free download pdf