Lesson Objective: I will be able to … Multiply real numbers 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

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

Page 9 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 = 20 –15 ÷ (–3) = 5

Page 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) = –18 –18 ÷ 2 = –9

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

Find the value of each expression. 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

Page 8 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. You can write the reciprocal of a number by switching the numerator and denominator. A whole number has a denominator of 1. Helpful Hint Dividing by a nonzero number is the same as multiplying by the reciprocal of the number. 10 ÷ 5 = 2 10 ∙ = = 2 1 5 10 Multiplicative inverses Dividing by 5 is the same as multiplying by the reciprocal of 5, which is .

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

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

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

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

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

Example 3: Multiplying and Dividing with Zero Page 11 Multiply or divide. 15 A. Zero is divided by a nonzero number. The quotient of zero and any nonzero number is 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. The product of an number and 0 is 0.

Any number divided by 0 is undefined. 0 ÷ 0 is undefined 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

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

Homework Assignment #14 1-3 Homework Worksheet