1-3 Multiplying and Dividing Real Numbers

Transcription

1 Multiplying and Dividing 1-3 Multiplying and Dividing Real Numbers Real Numbers Warm Up Lesson Presentation Lesson Quiz 1

2 2 pts Bell Quiz 1-3 Add or Subtract pts pts 3. 4 (-4) 2 pts 2 pts 4. x (-6) for x = (-12) 10 pts possible 2

3 Questions on 0-6/0-14 3

4 Multiply real numbers. Divide real numbers. Objectives 4

5 reciprocal Vocabulary multiplicative inverse 5

6 Question? You are buying a car by paying $300 per month for 48 months. How much will you pay in all? What operation did you use? Suppose you pay a total of $15,000 for a car by making equal payments for 60 months. What is the monthly payment? What operation did you use? 6

7 When you multiply two numbers, the signs of the numbers you are multiplying determine whether the product is positive or negative. Factors 3(5) Both positive 3( 5) One negative 3( 5) Both negative Product 15 Positive 15 Negative 15 Positive This is true for division also. 7

8 Multiplying and Dividing Signed Numbers WORDS Multiplying and Dividing Numbers with the Same Sign If two numbers have the same sign, their product or quotient is positive. NUMBERS 4 5 = ( 3) = 5 8

9 Multiplying and Dividing Signed Numbers WORDS Multiplying and Dividing Numbers with Different Signs If two numbers have different signs, their product or quotient is negative. NUMBERS 6( 3) = = 9 9

10 Example 1: Multiplying and Dividing Signed Numbers Find the value of each expression. A. The product of two numbers with different signs is negative. B. The quotient of two numbers with the same sign is positive. 10

11 Example 1C: Multiplying and Dividing Signed Numbers Find the value of the expression. First substitute for x. The quotient of two numbers with different signs is negative. 11

12 Check It Out! Example 1 Find the value of each expression. 1a. 35 ( 5) The quotient of two numbers with different signs is negative. 1b. 11( 4) The product of two numbers with the same sign is positive. 1c. 6x for x = 7 The product of two numbers with different signs is negative. 12

13 Two numbers are reciprocals if their product is 1. A number and its reciprocal are called multiplicative inverses. To divide by a number, you can multiply by its multiplicative inverse. Dividing by a nonzero number is the same as Multiplying by the reciprocal of the number. 13

14 Multiplicative inverses = = 5 = 2 Dividing by 5 is the same as multiplying by the reciprocal of 5. 14

15 Helpful Hint You can write the reciprocal of a number by switching the numerator and denominator. A whole number has a denominator of 1. 15

16 Divide. Example 2A: Dividing by Fractions Example 2 Dividing by Fractions To divide by, multiply by. Multiply the numerators and multiply the denominators. and have the same sign, so the quotient is positive. 16

17 Divide. Example 2B: Dividing by Fractions Write as an improper fraction. To divide by, multiply by. and have different signs, so the quotient is negative. 17

18 Check It Out! Example 2 Divide. a) b) c) 18

19 No number can be multiplied by 0 to give a product of 1, so 0 has no reciprocal. Because 0 has no reciprocal, division by 0 is not possible. We say that division by zero is undefined. 19

20 Properties of Zero WORDS Multiplication by Zero The product of any number and 0 is 0. NUMBERS = 0 0( 17) = 0 ALGEBRA a 0 = 0 0 a = 0 20

21 Properties of Zero WORDS Zero Divided by a Number The quotient of 0 and any nonzero number is 0. NUMBERS 0 6 = = 0 ALGEBRA 0 a = 0 0 a = 0 21

22 Properties of Zero Division by Zero WORDS Division by 0 is undefined. NUMBERS 12 0 Undefined 5 0 ALGEBRA a 0 Undefined a 0 22

23 Example 3: Multiplying and Dividing with Zero Multiply or divide. 0 A. 15 Zero is divided by a nonzero number. The quotient of zero and any nonzero number is 0. B C. 8.45(0) A number is divided by zero. Division by zero is undefined. A number is multiplied by zero. The product of an number and 0 is 0. 23

24 Check It Out! Example 3 Multiply or divide: a) b) 0 0 c) ( )(0) 24

25 HOMEWORK Sec 1-3: (Pg 23) 1, 2, 5, 6, 9, 10, 14, 16-18, 21-24, 26-28, 30, 35-38, 95, 96 Ex Cr:

26 HOMEWORK 26