Overview: This lesson applies the strategies for solving multiplication equations to equations with a fraction as the coefficient of the variable.
Objectives: Students will learn how to use multiplication by reciprocals, to solve multiplication equations in which the coefficient of the variable is a fraction.
California Content Standards: 1.2 Students add, subtract, multiply, and divide, rational numbers (integers, fractions, and terminating decimals) and take positive rational numbers to whole-number powers.
2.0 Students calculate, and solve problems involving addition, subtraction, multiplication, and division.
3.3 Develop generalizations of the results obtained and the strategies used and apply them to new problem situations.
Warm-Up Activity: Ask students what the word reciprocal means. (If the product of two numbers is 1, then each factor is the reciprocal of the other).
Ask students to identify the reciprocals of the following numbers: 1/4, 3/5, 7/8 and 1/n
Encourage students to describe what they know about the product of these numbers and their reciprocals (the product equals 1).
Direct instructions for all students: Write the first example , 1/4h = 6 on the overhead projector. Ask students how they can change the coefficient of h from 1/4 to 1. Lead students to conclude that multiplying the left side of the equation by 4 will give h a coefficient of 1.
Remind students that to keep the equation true, they will need to multiply the right side of the equation by 4/1 as well.
Solve the example, showing each of the steps indicated. 1/4h = 6
(4/1)1/4 h = 6/1 (4/1) (4/1)1/4 h = 6/1 (4/1) 4/4 h = 24/1 h = 24
Solve the second example showing each of the steps indicated: -2/5x = -20 (-5/2)(-2/5) x = -20(-5/2) (10/10) x = 100/2 x = 50
Working in small groups: Divide class into small groups. Students will work in pairs by helping each other, developing strategies and sharing the answers (in each pair one student must have good math skills).
Group Problem Solving: Have small groups of students consider the following situation.
Havermill School needs to increase its students reading and math scores. Currently 1/7 of the school, 30 students, score above average in reading and math. By the end of the year, the school would like 1/5 of its students to score above average. If the school meets its goal, how many students will score above average?