Multiplying and Dividing Real Numbers

1. Page 9 • Lesson Objective:I will be able to … • Multiply real numbers • Divide real numbers • Language Objective: I will be able to … • Read, write, and listen about vocabulary, key • concepts, and examples

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

3. Page 9 Multiplying and Dividing Signed Numbers

4. Page 9 Multiplying and Dividing Signed Numbers –18 ÷ 2 = –9

5. B. C. First substitute for x. Example 1: Multiplying and Dividing Signed Numbers Page 10 Find the value of each expression. The product of two numbers with different signs is negative. A. = –5 The quotient of two numbers with the same sign is positive. = 12 The quotient of two numbers with different signs is negative.

6. Your Turn 1 Page 10 Find the value of each expression. A. 35  (–5) The quotient of two numbers with different signs is negative. = –7 B. –6x for x = 7 = –6(7) First substitute 7 for x. The product of two numbers with different signs is negative. = –42

7. Helpful Hint You can write the reciprocal of a number by switching the numerator and denominator. A whole number has a denominator of 1. Multiplicative inverses 1 10 10 ÷ 5 = 2 10 ∙ = = 2 5 5 Dividing by 5 is the same as multiplying by the reciprocal of 5, which is . Page 8 Two numbers are reciprocals if their product is 1. A number and its reciprocal are called multiplicativeinverses. 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.

8. To divide by , multiply by . and have the same sign, so the quotient is B. positive. Write as an improper fraction. To divide by , multiply by . and have different signs, so the quotient is negative. Example 2: Dividing by Fractions Page 11 Example 2 Dividing by Fractions Divide. A. Multiply the numerators and multiply the denominators.

9. Write as an improper fraction. To divide by , multiply by . and have the same signs, so the quotient is positive. Your Turn 2 Page 11 Divide:

10. 1 3 · 0 = 0 Page 10 Properties of Zero Multiplication by Zero The product of any number and 0 is 0. WORDS 0(–17) = 0 NUMBERS ALGEBRA a · 0 = 0 0 · a = 0

11. 2 3 0 6 = 0 0 ÷ = 0 0 a = 0 Page 10 Properties of Zero Zero Divided by a Number The quotient of 0 and any nonzero number is 0. WORDS NUMBERS ALGEBRA 0 ÷ a = 0

12. –5 0 a 0 Page 10 Properties of Zero Division by Zero WORDS Division by 0 is undefined. 12 ÷ 0 NUMBERS Undefined ALGEBRA a ÷ 0 Undefined

13. Example 3: Multiplying and Dividing with Zero Page 11 Multiply or divide. 0 15 A. Zero is divided by a nonzero number. The quotient of zero and any nonzero number is 0. 0 B. –22  0 A number is divided by zero. undefined Division by zero is undefined. C. –8.45(0) A number is multiplied by zero. 0 The product of an number and 0 is 0.

14. Your Turn 3 Page 12 Multiply or Divide: A. 0 ÷ 0 Any number divided by 0 is undefined. 0 ÷ 0 is undefined B. (–12.350)(0) The product of any number and 0 is 0. (–12.350)(0) = 0

15. Cornell Notes • Fill in the Essential Question: • “How do I multiply and divide with real • numbers?” • Write two or three main ideas from this lesson • in the Notes section. • Write a Question for each main idea. • (The answer to the question should be the • main idea.) • Summarize the answers to your questions in • the Summary section. Page 13

16. Homework • Assignment #14 • 1-3 Homework Worksheet