IntegersIntegers

Chapter TwoChapter Two

Introduction to Integers

Section 2.1

Numbers greater than 0 are called positive numbers. Numbers less than 0 are called negative numbers.

negative numbers zero

positive numbers

6543210-1-2-3-4-5-6

3Martin-Gay, Prealgebra, 5ed

- 3 indicates “negative three.”3 and + 3 both indicate “positive three.”The number 0 is neither positive nor negative.

negative numbers zero

positive numbers

6543210-1-2-3-4-5-6

4Martin-Gay, Prealgebra, 5ed

Some signed numbers are integers. Integers consist of the numbers labeled on the number line below.

negative numbers zero

positive numbers

6543210-1-2-3-4-5-6

The integers are{ …, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, …}

Martin-Gay, Prealgebra, 5ed

We compare integers just as we compare whole numbers. For any two numbers graphed on a number line, the number to the right is the greater number and the number to the left is the smaller number.

<means

“is less than”

>means

“is greater than”

6Martin-Gay, Prealgebra, 5ed

6543210-1-2-3-4-5-6

The graph of - 5 is to the left of - 3, so- 5 is less than - 3,

written as -5 < - 3 .

We can also write - 3 > - 5.

Since - 3 is to the right of - 5,- 3 is greater than - 5.

6543210-1-2-3-4-5-6

7Martin-Gay, Prealgebra, 5ed

The absolute value of a number is the number’s distance from 0 on the number line. The symbol for absolute value is .

2 is 2 because 2 is 2 units from 0.

6543210-1-2-3-4-5-6

is 2 because - 2 is 2 units from 0.2

6543210-1-2-3-4-5-6

-

8Martin-Gay, Prealgebra, 5ed

Since the absolute value of a number is that number’s distance from 0, the absolute value of a number is always 0 or positive. It is never negative.

Helpful Hint

0 0 6 6

zerozero a positive numbera positive number

-

9Martin-Gay, Prealgebra, 5ed

Two numbers that are the same distance from 0 on the number line but are on the opposite sides of 0 are called opposites.

5 units 5 units

5 and - 5 are opposites

6543210-1-2-3-4-5-6

10Martin-Gay, Prealgebra, 5ed

5 is the opposite of - 5and

- 5 is the opposite of 5.

The opposite of 4 is - 4 is written as

- (4) = - 4

The opposite of - 4 is 4 is written as

- (- 4) = 4

- (- 4) = 4

If a is a number, then - (- a) = a.11

Martin-Gay, Prealgebra, 5ed

Remember that 0 is neither positive nor negative. Therefore, the opposite of 0 is 0.

Helpful Hint

12Martin-Gay, Prealgebra, 5ed