1-31-3 multiplying and dividing real numbers warm...

1-3 Multiplying and Dividing Real Numbers1-3Multiplying and Dividing

Real Numbers

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Lesson PresentationLesson Presentation

Holt Algebra 1

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Holt Algebra 1

Lesson PresentationLesson Presentation

Lesson QuizLesson Quiz

1-3 Multiplying and Dividing Real Numbers

Bell Quiz 1-3

Add or Subtract

1. 3 – 8

2. - 8 + 12

2 pts

2 pts

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3. 4 – (-4)

4. x – (-6) for x = 3

5. 6 + (-12)

10 pts

possible

2 pts

2 pts

2 pts


Questions on 1-2

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Multiply real numbers.

Divide real numbers.

Objectives

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reciprocal

multiplicative inverse

Vocabulary

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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?

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– 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?


When you multiply two numbers, the signs of the

numbers you are multiplying determine whether

the product is positive or negative.

Factors Product

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3(5) Both positive

3(–5) One negative

–3(–5) Both negative

15 Positive

–15 Negative

15 Positive

This is true for division also.


WORDS

Multiplying and Dividing Numbers with the Same Sign

If two numbers have the same sign,

Multiplying and Dividing Signed Numbers

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If two numbers have the same sign, their product or quotient is positive.

NUMBERS

4 •••• 5 = 20

–15 ÷ (–3) = 5


WORDS

Multiplying and Dividing Numbers with Different Signs

If two numbers have different signs,

Multiplying and Dividing Signed Numbers

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If two numbers have different signs, their product or quotient is negative.

NUMBERS

6(–3) = –18

–18 ÷ 2 = –9


Find the value of each expression.

The product of two numbers

Example 1: Multiplying and Dividing Signed Numbers

A.

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The product of two numberswith different signs is negative.

The quotient of two numberswith the same sign is positive.

B.


Find the value of the expression.

Example 1C: Multiplying and Dividing Signed Numbers

First substitute for x.

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The quotient of two numberswith different signs is negative.

First substitute for x.


Find the value of each expression.

The quotient of two numberswith different signs is negative.

Check It Out! Example 1

1a. 35 ÷÷÷÷ (–5)

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The product of two numberswith the same sign is positive.

1b. –11(–4)

1c. –6x for x = 7 The product of two numbers with

different signs is negative.


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

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Dividing by a nonzero number is the same as

Multiplying by the reciprocal of the number.


10 ÷ 5 = 2 10 · = = 21

5

10

5

Multiplicative inverses

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10 ÷ 5 = 2 10 · = = 25 5

Dividing by 5 is the same as multiplying by the

reciprocal of 5.


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

Helpful Hint

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whole number has a denominator of 1.


Example 2 Dividing by FractionsExample 2A: Dividing by Fractions

Divide.

To divide by , multiply by .

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Multiply the numerators and

multiply the denominators.

and have the same sign,

so the quotient is positive.


Example 2B: Dividing by Fractions

Divide.

Write as an improper fraction.

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Write as an improper fraction.


and have different signs,

so the quotient is negative.



Divide.

a)

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b)

c)


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.

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undefined.


Properties of Zero

WORDS

Multiplication by Zero

The product of any number

and 0 is 0.

1

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NUMBERS

ALGEBRA

13· 0 = 0 0(–17) = 0

a · 0 = 0 0 · a = 0


Properties of Zero

WORDS

Zero Divided by a Number

The quotient of 0 and any nonzero number is 0.

0 2

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NUMBERS

ALGEBRA

06= 0

0 ÷ a = 0

0 ÷23= 0

0a= 0


Properties of Zero

WORDS

Division by Zero

Division by 0 is undefined.

–5

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NUMBERS

ALGEBRA a ÷ 0 a

0

12 ÷ 0

Undefined

–50

Undefined


Example 3: Multiplying and Dividing with Zero

Multiply or divide.

A.15 Zero is divided by a nonzero number.

The quotient of zero and any nonzero

0

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B. –22 ÷ 0

C. –8.45(0)

The quotient of zero and any nonzeronumber is 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.



Multiply or divide:

a)

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b) 0 ÷ 0

c) (–12.350)(0)


HOMEWORKSec 1-3: (Pg 23)

1, 2, 5, 6, 9, 10, 14, 16-18,

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10, 14, 16-18, 21-24, 26-28, 30, 35-38, 95, 96

Ex Cr: 39-46

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