1. Ch 4 Sec 7: Slide #1 Columbus State Community College Chapter 4 Section 7 Problem Solving: Equations Containing Fractions

2. Ch 4 Sec 7: Slide #2 Problem Solving: Equations Containing Fractions 1.Use the multiplication property of equality to solve equations containing fractions. 2.Use both the addition and multiplication properties of equality to solve equations containing fractions. 3.Solve application problems using equations containing fractions.

3. Ch 4 Sec 7: Slide #3 Multiplication and Division Properties of Equality The multiplication property of equality says, if a = b, then a c = b c. Also, if a = b, then = as long as c is not 0. This is the division property of equality. In other words, you may multiply or divide both sides of an equation by the same nonzero number and it will still be balanced. a c b c

4. Ch 4 Sec 7: Slide #4 1 1 Using the Multiplication Property of Equality EXAMPLE 1 Using the Multiplication Property of Equality Solve each equation and check each solution. Multiply both sides by the reciprocal of. 1 3 – x=– 27 1 3 – x = 3 1 – 3 1 – 9 1 (a) 1 3 – x = 9

5. Ch 4 Sec 7: Slide #5 Using the Multiplication Property of Equality EXAMPLE 1 Using the Multiplication Property of Equality Solve each equation and check each solution. (a) 1 3 – x = 9 Check your solution ( x = – 27 ). 1 3 – x = 9 1 3 – ( – 27 ) 9 = 9 =9 Balances NOTE: – 27 is the correct solution ( not 9 ).

6. Ch 4 Sec 7: Slide #6 1 1 Using the Multiplication Property of Equality EXAMPLE 1 Using the Multiplication Property of Equality Solve each equation and check each solution. (b) 2 5 n = 10 Multiply both sides by the reciprocal of. 2 5 n=25 2 5 n = 5 2 5 2 10 1 1 1 1 5

7. Ch 4 Sec 7: Slide #7 Using the Multiplication Property of Equality EXAMPLE 1 Using the Multiplication Property of Equality Solve each equation and check each solution. Check your solution ( n = 25 ). 10= Balances NOTE: 25 is the correct solution ( not 10 ). 2 5 n = 10 (b) 2 5 n = 10 2 5 ( 25 ) = 10

8. Ch 4 Sec 7: Slide #8 1 1 Using the Multiplication Property of Equality EXAMPLE 1 Using the Multiplication Property of Equality Solve each equation and check each solution. Multiply both sides by the reciprocal of. 3 4 5 6 a= 1 1 2 1 3 4 a = 5 8 4 3 4 3 (c) 3 4 a = 5 8

9. Ch 4 Sec 7: Slide #9 Using the Multiplication Property of Equality EXAMPLE 1 Using the Multiplication Property of Equality Solve each equation and check each solution. Balances (c) 3 4 a = 5 8 Check your solution ( a = ). 5 6 3 4 a = 5 8 5 8 5 8 = 5 8 2 1 3 4 = 5 6

10. Ch 4 Sec 7: Slide #10 4 3 3 4 x =– 6 1 4 3 112 Using the Addition & Multiplication Properties of Equality EXAMPLE 2 Using the Addition & Multiplication Properties of Equality Solve each equation and check each solution. Subtract 7 from both sides. (a) 3 4 x =1 + 7 – 7 3 4 x =– 6 x =– 8 Multiply both sides by. 4 3 111

11. Ch 4 Sec 7: Slide #11 2 1 Using the Addition & Multiplication Properties of Equality EXAMPLE 2 Using the Addition & Multiplication Properties of Equality Solve each equation and check each solution. Check your solution ( x = – 8 ). (a) 3 4 x =1 + 7 =1 3 4 – 8 1 – 6 + 7 1 =1 =1Balances

12. Ch 4 Sec 7: Slide #12 3 2 2 3 b = 6 1 3 2 131 Using the Addition & Multiplication Properties of Equality EXAMPLE 2 Using the Addition & Multiplication Properties of Equality Solve each equation and check each solution. Add 2 to both sides. (b) 2 3 b =4 – 2 + 2 2 3 b =6 9 =b Multiply both sides by. 3 2 111

13. Ch 4 Sec 7: Slide #13 3 1 Using the Addition & Multiplication Properties of Equality EXAMPLE 2 Using the Addition & Multiplication Properties of Equality Solve each equation and check each solution. Check your solution ( b = 9 ). 4 = 2 3 – 2 9 1 4 6 – 2 = 4 =4Balances (b) 2 3 b =4 – 2

14. Ch 4 Sec 7: Slide #14 Problem Solving: Equations Containing Fractions Chapter 4 Section 7 – Completed Written by John T. Wallace