integers

MATH 6

Lesson 6: Integers

Integers

are whole counting numbers
(positive) and their opposite

(negative), including zero which
is neither positive nor negative

Number Line

2 example of number line

Counting numbers

The natural numbers are those
numbers used for counting and

ordering. Counting number is also

known as positive numbers.

Whole numbers

A number without fractions; an integers

Integers are

Additive Inverse

● Additive inverse is a property of

integers where if opposite

numbers are added, then their

sum will be zero.

Examples

-4 + 4 = 0
5 + (-5) = 0
8 + (-8) = 0

Multiple Choice

What is the additive inverse of 6

• 6

• -6

Multiple Choice

What is the additive inverse of -12

• 12

• -12

Opposites are integers on opposite

sides of a number line which have the

same distance from zero.

How to read the numbers?

1. +5 - Positive Five

2. -5 - Negative Five

3. 5 - Five or Positive Five

Examples

We can use integers to represent real-
life situations. We usually denote what
is good, above or to right as positive
and those are bad, below or to the left

as negative

Example

● Deposit of Php 1500
● Withdrawal of Php 850

●Profit of Php769

●3 Kilometers downstream

●Decrease of 56 students in enrollment

A.Provide the opposite of the
following integers.

1.-7

6. 18

2.20

7. -2

3.-16

8. 31

4.-100

9. 3

5.0

10. -1

B. Represent the following situations
using integers (positive or negative).

Multiple Choice

Deposit of Php 100

• Positive

• Negative

Multiple Choice

2▫C decrease in temperature

• Positive

• Negative

Multiple Choice

loss in 7 games

• Positive

• Negative

Multiple Choice

payment of Php 40

• Positive

• Negative

Multiple Choice

Decline of altitude by 4000 feet

• Positive

• Negative

Compare

to examine the differences between

numbers, quantities or values to

decide if it is greater than, smaller than

or equal to another quantity.

Number Line

Multiple Choice

-5 ____ 5

• >

• <

• =

Multiple Choice

0 ____ -2

• >

• <

• =

Multiple Choice

6 ____ -1

• >

• <

• =

Multiple Choice

-4 ____ -7

• >

• <

• =

Multiple Choice

-8 ____ 0

• >

• <

• =

Arranging

In arranging the integers on
the number line, makes sure

that you follow the right
position of the integers in

the number line.

Ascending

ascending order means the process of
arranging numbers from smallest to
largest from left to right.

Example

Descending

descending order means to arrange

them from largest to smallest.
Example

-54, 65, 32, 0, -101
Descending order
65, 32, 0, -54, -101

Addition of Integers

Multiple Choice

$$4+8=$$

• 12

• -12

Multiple Choice

$$(−6)+(−3)=$$

• 9

• -9

Multiple Choice

$$12+(−7)=$$

• 5

• -5

Multiple Choice

$$13+\left(-16\right)=$$

• 3

• -3

Subtraction of Integers

Change the equation to addition.

Example:

2

−

4

=

2

+

−

4

=

−

2

2

−

−

4

=

2

+

4

=

6

Multiple Choice

$$8−3=$$

• 5

• -5

Multiple Choice

$$(−2)−2=$$

• 4

• -4

Multiplying Integers

Multiple Choice

$$(−1)\times(−9)=$$

• 9

• -9

Examples

1.

4 + 8 =

2.

(−6) + −3 =

3.

12 + −7 =

4.

−13 + 16 =

5.

8 − 3 =

6.

−2 − 2 =

7.

−3 − −5 =

8.

8 × 0 =

9.

−2 × 6 =

10. 5 × −5 =
11. −1 × −9 =
12. 12 ÷ 2 =
13. 36 ÷ −4 =
14. −81 ÷ 9 =
15. −6 ÷ −6 =

Multiple Choice

$$5\times(−5)=$$

• 25

• -25

Dividing Integers

Multiple Choice

$$36\div(−4)=$$

• 9

• -9

Multiple Choice

$$(−6)\div(−6)=$$

• 1

• -1