1. Lesson Objective: I will be able to … Multiply real numbers
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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. 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
– Negative
–3(–5) Both negative
Positive
This is true for division also.

3. 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

4. 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

5. Example 1: Multiplying and Dividing Signed Numbers
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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.

6. Find the value of each expression.
Your Turn 1
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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. 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 .

8. Example 2: Dividing by Fractions
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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.

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

10. Properties of Zero Multiplication by Zero The product of any number
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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

11. Properties of Zero Zero Divided by a Number The quotient of 0 and any
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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

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

13. Example 3: Multiplying and Dividing with Zero
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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.

14. Any number divided by 0 is undefined. 0 ÷ 0 is undefined
Your Turn 3
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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