Solving Literal Equations and Formulas
GOAL: I can solve for variables that have fractional coefficients.
Text reference: Chapter 2, section 5, pages: 109 ─ 114  Illinois learning standard: 8.C.3  NCTM standard: XXXX

Lesson Vocabulary  
 Literal Equation
 A literal equation is an equation that has two or more variables in it.
 Some examples include:
y = 3/2x + 2
3/4x ─ 2y = 10
2/7x = 7x ─ 16
 Formula  Formulas are special types of literal equations.
 A formula is an equation that gives the relationship between the variables.
 Some examples include:
P = 2•L + 2•W
A = L • W
C = 2 π r

Strategies and Content Practice  Notes 
Fractional Coefficients

Fractional Coefficients are fractions that precede variables.  The following are some examples:
In the first example of solving for X, the 3/4 needs to be eliminated to get X all alone.
In the second example of solving for
Y, the 5/3 needs to be eliminated to get Y all alone.
In the third example of solving for A, the 3/7 needs to be eliminated to get A all alone.
This can be accomplished with a two-step process of multiplying and dividing but there's a more elegant way.

Here again, a Super-Hero algebra tool needs to be introduced and used to get the variables X,
Y, and A all alone on one side of the equal sign.

Engage The Super-Hero tool needed to solve for variables with fractional coefficients is the reciprocal.

The example problems above can be solved using a two-step (multiplication and division) process.  Unfortunately, that leads to the possibility of making an error.  The reciprocal trick eliminates both the multiplication and the division in one step.  For example, here is how the first problem can be solved using the reciprocal trick.

The following is how the reciprocal trick can be used on the last problem.
Give students selected problems from the practice worksheets below.
Circulate to check for understanding.
Select students to work their problems at the board and have them explain their answers.
Apply  Practice Assignments.

Worksheet 2-5, Verion C.

Worksheet 2-5, Version D.

Answers to the Practice Assignments.

Answers to Worksheet 2-5, Version C.

Answers to Worksheet 2-5, Version D.