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3 4. – is between –1 and 0. Use a calculator to find that 7 2.65. Properties of Real Numbers. ALGEBRA 2 LESSON 1-1. 3 4. Graph the numbers – , 7 , and 3.6 on a number line. 1-1. 9 = 3, so – 9 = –3. –9 < – 9. Properties of Real Numbers.

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properties of real numbers

3

4

– is between –1 and 0.

Use a calculator to find that 7 2.65.

Properties of Real Numbers

ALGEBRA 2 LESSON 1-1

3

4

Graph the numbers – , 7 , and 3.6 on a

number line.

1-1

properties of real numbers1

9 = 3, so – 9 = –3.

–9 < – 9.

Properties of Real Numbers

ALGEBRA 2 LESSON 1-1

Compare –9 and – 9. Use the symbols < and >.

Since –9 < –3, it follows that

1-1

properties of real numbers2

Opposite: –(–3 ) = 3

1

7

1

7

1

1

7

22

Reciprocal: = = –

1

7

22

7

–3

1

4

Reciprocal:

Properties of Real Numbers

ALGEBRA 2 LESSON 1-1

Find the opposite and the reciprocal of each number.

1

7

a. –3

b. 4

Opposite: –4

1-1

properties of real numbers3
Properties of Real Numbers

ALGEBRA 2 LESSON 1-1

Which property is illustrated?

a. (–7)(2 • 5) = (–7)(5 • 2) b. 3 • (8 + 0) = 3 • 8

The given equation is true because 2 • 5 = 5 • 2.

The given equation is true because 8 + 0 = 8.

So, the equation uses the Commutative Property

of Multiplication.

This is an instance of the Identity Property of Addition.

1-1

properties of real numbers4

1

3

1

3

1

3

1

3

4 is 4 units from 0, so | 4 | = 4 .

Properties of Real Numbers

ALGEBRA 2 LESSON 1-1

1

3

Simplify | 4 |, |–9.2|, and |3 – 8|.

–9.2 is 9.2 units from 0, so |–9.2| = 9.2.

|3 – 8| = |–5| and –5 is 5 units from 0. So, |–5| = 5, and hence |3 – 8| = 5.

1-1