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

Teaching Notes 6.12: Solving Equations That Have

Fractional Coefficients

To many students, equations with fractional coefficients appear to be very confusing.

Fortunately, these equations can be relatively easy to solve if students multiply both sides of the

equation by the least common denominator (LCD) before attempting to solve.

1. Review the multiplication property of equality, whichstates that multiplying both sides of
   an equation by the same nonzero number does not change the value of the solution. Depend-
   ing on the abilities of your students, you may wish to review 3.3: ‘‘Solving Equations by
   Multiplying or Dividing.’’


2. Explain that when an equation has fractional coefficients,students must multiply both sides
   of the equation by the least common denominator of the coefficients. This will eliminate
   the fractions and students can then solve the equation. Depending on the abilities of your
   students, review the process for finding the least common denominator by providing some
   examples such as the following: Find the LCD of 18 and 20. 18= 32 · 2 ; 20 = 22 ·5 The LCD
   is 2^2 · 32 ·5 or 180.


3. Review the information and example on the worksheet with your students. Be sure that your
   students understand the use of prime factorization for finding the least common denomina-
   tor. Also be sure that they understand all of the steps for solving the equation.

EXTRA HELP:

Express the product of the least common denominator and each term in factored form. This will

make it easier to cancel common factors and make computation easier.

ANSWER KEY:

(1)x= 2 (2)x=− 15 (3)x= 13 (4)x=

1

7

(5)x= 3

1

2

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(Challenge)Yes, provided their work is correct. Both will find thatx=

1

2

.

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246 THE ALGEBRA TEACHER’S GUIDE