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Properties of Real Numbers. 1-2. Warm Up. Lesson Presentation. Lesson Quiz. Holt Algebra 2. Warm Up Simplify. 1. –5+5 2. 3. 4. Find 10% of $61.70. 5. Find the reciprocal of –4. 0. 1. 1.81. $6.17. Objective. Identify and use properties of real numbers.

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slide1

Properties of Real Numbers

1-2

Warm Up

Lesson Presentation

Lesson Quiz

Holt Algebra 2

slide2

Warm Up

Simplify.

1. –5+5

2.

3.

4. Find 10% of $61.70.

5. Find the reciprocal of –4.

0

1

1.81

$6.17

slide3

Objective

Identify and use properties of real numbers.

slide4
The four basic math operations are addition, subtraction, multiplication, and division. Because subtraction is addition of the opposite and division is multiplication by the reciprocal, the properties of real numbers focus on addition and multiplication.
slide5

Properties Real Numbers

Identities and Inverses

slide6

Properties Real Numbers

Identities and Inverses

slide7

Properties Real Numbers

Identities and Inverses

slide8

Properties Real Numbers

Identities and Inverses

slide9

Recall from previous courses that the opposite of any number a is –a and the reciprocal of any nonzero number a is .

slide10

multiplicative inverse:

The reciprocal of 12 is .

Check

Example 1A: Finding Inverses

Find the additive and multiplicative inverse of each number.

12

additive inverse: –12

The opposite of 12 is –12.

Check –12 + 12 = 0 

The Additive Inverse Property holds.

The Multiplicative Inverse Property holds.

slide11

The opposite of is .

The reciprocal of is

Example 1B: Finding Inverses

Find the additive and multiplicative inverse of each number.

additive inverse:

multiplicative inverse:

slide12

The reciprocal of 500 is .

multiplicative inverse:

Check

Check It Out! Example 1A

Find the additive and multiplicative inverse of each number.

500

additive inverse: –500

The opposite of 500 is –500.

Check 500 + (–500) = 0 

The Additive Inverse Property holds.

The Multiplicative Inverse Property holds.

slide13

Check It Out! Example 1B

Find the additive and multiplicative inverse of each number.

–0.01

additive inverse: 0.01

The opposite of –0.01 is 0.01.

multiplicative inverse: –100

The reciprocal of –0.01 is –100.

slide14

Properties Real Numbers

Addition and Multiplication

slide15

Properties Real Numbers

Addition and Multiplication

slide16

Properties Real Numbers

Addition and Multiplication

slide17

Properties Real Numbers

Addition and Multiplication

slide18

Reading Math

Based on the Closure Property, the real numbers are said to be closed under addition and closed under multiplication.

slide19

Example 2: Identifying Properties of Real Numbers

Identify the property demonstrated by each question.

Numbers are multiplied in any order without changing the results.

A. 2  3.9 = 3.9  2

Commutative Property of Multiplication

The numbers have been regrouped.

B.

Associative Property ofAddition

slide20

Check It Out! Example 2

Identify the property demonstrated by each equation.

2a.

Numbers are multiplied in any order without changing the results.

Commutative Property of Multiplication

The numbers have been regrouped.

2b. 9(12) = (9  12)

Associative Property of Multiplication

slide21

Think:5% = (10%)

Example 3: Consumer Economics Application

Use mental math to find a 5% tax on a $42.40 purchase.

Think:10% of $42.40

Move the decimal point left 1 place.

10%(42.40)

= 4.240 = 4.24

5% is half of 10%, so find half of 4.24.

A 5% tax on a $42.40 is $2.12.

slide22

Check It Out! Example 3

Use mental math to find a 20% discount on a $15.60 shirt.

Think:20% = 10%  2

Move the decimal point left 1 place.

10%(15.60)

= 1.560 = 1.56

1.56  2 = 3.12

20% is double 10%, so multiply 1.56 by 2.

A 20% discount on a $15.60 shirt is $3.12.

slide23

Example 4A: Classifying Statements as Sometimes, Always, or Never True

Classifying each statement as sometimes, always, or never true. Give examples or properties to support your answers.

a b = a, where b = 3

True and false examples exist. The statement is true when a = 0 and false when a ≠ 0.

sometimes true

true example: 0 3 = 0

false example: 1 3 ≠ 1

slide24

Example 4B: Classifying Statements as Sometimes, Always, or Never True

Classifying each statement as sometimes, always, or never true. Give examples or properties to support your answers.

3(a+ 1) = 3a + 3

Always true by the Distributive Property.

always true

slide25

Check It Out! Example 4a

Classify each statement as sometimes, always, or never true. Give examples or properties to support your answer.

a + (–a) = b + (–b)

Always true by the Additive Inverse Property.

slide26

Check It Out! Example 4b

Classify each statement as sometimes, always, or never true. Give examples or properties to support your answer.

a – (b + c) = (a – b) + (a – c)

sometimes true

True and false examples exist. The statement is true when a = 0, b = 1, and c = 2. False when a = 1, b = 2, and c = 3.

true example: 0 – (1 + 2) = (0 – 1) + (0 – 2) –3 = –3

false example:

1 – (2 + 3) = (1 – 2) + (1 – 3) –4 ≠ –3

slide27

15;

;

Lesson Quiz

Find the additive and multiplicative inverse of each number.

1. –15 2.

Identify the property demonstrated by each question.

3.

Commutative Property of Addition

Distributive Property

4.

5. Use mental math to find a 15% tip for a $ 64.20 bill.

$9.63