2-2. Warm Up. Simplify each expression. 1. ( 7)(2.8) ( 9)( 9)

Transcription

1 Warm Up Simplify each expression. 1. ( 7)(2.8) ( 9)( 9)

2 Learning Goals 1. Students will solve and check equations using multiplication 2. Students will solve and check equations using division 3. Students will solve and check equations with fractions by dividing or multiplying by the reciprocal 4. Students will identify important information from an application problem and use that information to set up and solve an equation.

3 Solving an equation that contains multiplication or division is similar to solving an equation that contains addition or subtraction. Use inverse operations to undo the operations on the variable. Inverse Operations Operation Multiplication Division Inverse Operation Division Multiplication

4 Properties of Equality WORDS NUMBERS ALGEBRA Addition Property of Equality You can add the same number to both sides of an equation, and the statement will still be true. 3 = = = 5 a = b a + c = b + c

5 Properties of Equality WORDS NUMBERS ALGEBRA Subtraction Property of Equality You can subtract the same number from both sides of an equation, and the statement will still be true. 7 = = = 2 a = b a c = b c

6 Properties of Equality WORDS NUMBERS ALGEBRA Multiplication Property of Equality You can multiply both sides of an equation by the same number, and the statement will still be true. 6 = 6 6(3) = 6(3) 18 = 18 a = b ac = bc

7 Properties of Equality WORDS ALGEBRA Division Property of Equality You can divide both sides of an equation by the same nonzero number, and the statement will still be true. NUMBERS 8 8 = 8 8 = = 2 a = b (c 0) a = a c c

8 Example 1A: Using Multiplication Solve the equation. Check your answers A. 8 = j 3 B. n = 2.8 C. 6 p 5 = 10 D. 13 = y 3 E. c 8 = 7

9 Example 1a: Using Multiplication Solve the equation. Check your answers a. 9 = j 2 n 4 = 3.1 p 10 = 5 b. c. d. 10 = y 3 e. c 6 = 9

10 Example 2A: Using Division Solve the equation. Check your answer. A. 9y = 108 B. 4.8 = 6v C. 16 = 4c D. 0.5y = 10 E. 15k = 75

11 a. Example 2a: Using Division Solve the equation. Check your answer. 12y = 108 b. 6.4 = 4v c. 49 = 7c 0.4y = 8 25k = 125 d. e.

12 Remember that dividing is the same as multiplying by the reciprocal. When solving equations, you will sometimes find it easier to multiply by a reciprocal instead of dividing. This is often true when an equation contains fractions.

13 Example 3A: Solving Equations That Contain Fractions Solve the equation. Check your answers A. 5 B. C. 6 w = = 1 8 z 1 4 = 1 5 b 4 j 6 = 2 3 D. E. 1 6 w =102

14 Example 3a: Solving Equations That Contain Fractions Solve the equation. Check your answers a. 3 b. c. 4 w = = 1 9 z 1 3 = 1 7 b 5 j 10 = 1 2 d. e. 1 3 w = 54

15 Example 4: Application Ciro puts 1 4 of the money he earns from mowing lawns into a college education fund. This year Ciro added $285 to his college education fund. Write and solve an equation to find how much money Ciro earned mowing lawns this year.

16 Example 4: Application The distance in miles from the airport that a plane should begin descending, divided by 3, equals the plane's height above the ground in thousands of feet. A plane began descending 45 miles from the airport. Use the equation to find how high the plane was flying when the descent began.

17 Lesson Quiz: Part 1 Solve each equation y = = -9q 5. 6.

18 Lesson Quiz: Part A person's weight on Venus is about his or 10 her weight on Earth. Write and solve an equation to find how much a person weighs on Earth if he or she weighs 108 pounds on Venus.