Algebra

Lesson 3-3

Vocabulary:

• Multiplication Property of Equality: If each side of an equation is multiplied by the same number, then the resulting equation will be true.

• Division Property of Equality: If each side of an equation is divided by the same number, then the resulting equation will be true.

Examples:

1. Solve Using Multiplication by a Positive Number

     t/30 = 7/10                    equation

     30(t/30) =30(7/10)          multiply each side by 30

     t=21                             t/30(30) = t and 7/10(30)= 21

2. Solve Using Multiplication by a Fraction

     (2¼)g = 1½                       equation

     (9/4)g = 3/2                      rewrite each mixed number as an improper fraction

     (4/9)9/4g = (4/9)3/2           multiply each side by 4/9, the opposite of 9/4

     g = 12/18 or 2/3                the solution!

3. Solve Using Multiplication by a Negative Number

     42 = -6m                      equation

     (-1/6)42 = (-1/6)-6m      multiply each sid by -1/6, the reciprocal of -6

     -7 = m                         the solution!

4. Write and Solve an Equation Using Multiplication

     Words: One sixth times the weight on Earth equals the weight on the moon.

     Variable: Let w = the weight on Earth.

     Equation: One sixth times the weight on Earth equals the weight on the moon.

                        1/6      *                 w               =                    33

     1/6w = 33              equation

     6(1/6w) = 6(33)      multiply each side by 6

     w = 198                 1/6(6) = 1 and 33(6) = 198

5. Solve Using Division by a Positive Number

      13x = 195               equation

     13x/13 = 195/13      divide each side by 13

     x = 15                    13x/13 = x and 195/13 = 15

6.Solve Using Division by a Negative Number

     -3x = 12                 equation

     -3x/-3 = 12/-3        divide each side by -3

     x = -4                   -3x/-3 = x and 12/-3 = -4 

7.Write and Solve an Equation Using Division

     Words: Seven times a number equals -84.

     Variable: let n be the number

     Equation: Seven times a number equals 84

                       7       *          n        =     84    

     7n = 84            original equation

     7n/7 = -84/7     divide each side by 7

     N= -12             the result!

Additional Information:

     To check your answers, do this:

                    9y = 117

                    9(13) = 117

                    117 = 117

                    the solution is 13

Online resources:

algebra1.com

Pictures:

This page by: TB and SJ