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

Teaching Notes 6.11: Solving Proportions

To solve proportions that have variables or variable expressions in the numerator or denominator,

students must multiply the whole expression by the numerator or denominator, not only one

term. This can result in confusion and errors.

1. Explain that a proportion is a statement that two ratios are equal.


2. Discuss solving proportions by providing this example:
   2 x
   5

=

3

7

. Explain that 2xand 7 are
called the ‘‘extremes,’’ and that 5 and 3 are called the ‘‘means.’’ In any proportion, the product
of the means is equal to the product of theextremes. Students should write and solve the
equation 2x· 7 = 5 ·3or14x=15. The solution isx= 1

1

14

.

3. Review the information and example on the worksheet with your students. Note the use of
   the distributive property in the example. Dependingon the abilities of your students, you
   may find it helpful to review solving linear equations.

EXTRA HELP:

Always use the distributive property to find the product of a polynomial and a number or variable.

ANSWER KEY:

(1)x= 6

1

2

(2)x= 1

7

8

(3)x= 5

3

4

(4)x=− 4

2

3

(5)x=

3

7

(6)x= 0 (7)x=− 1

3

7

(8)x=− 3

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(Challenge)Eddie is incorrect. He did not apply the distributive property correctly. The correct

equation is 2x+ 2 = 3 x.Thesolutionisx=2.

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244 THE ALGEBRA TEACHER’S GUIDE