INTEGERS

What Are Integers ?

Integers are the numbers that comprise of both negative numbers and positive numbers. Example - -5 , -4 -3 , -2 , -1 , 0 , 1 , 2 , 3 , 4 , 5 , etc. We can do all the four operations – addition, subtraction, multiplication, and division on it. We can also represent them on the number line and perform BODMAS with them. Positive Integers are always greater than negative integers.

How do we represent integers on number line?To represent positive integers on a

number line. Example – Represent 3 on a number line

-4 -3 -2 -1 0 1 2 3 4

To represent negative integers on a number line.Example – Represent -3 on number line.

-3 -2 -1 0 1 2 3

Absolute Value of an integer

To find the absolute value of integers , look at the following examples:

Q. Find the absolute value of the following integers.

a. 3 The absolute value of 3 = 3b. -3 The absolute value of -3 = 3c. -10 The absolute value of -10 = 10

Comparison Between Integers

To compare between two integers , look at the following examples:

Q. Compare the following integers.a. 3 and 5 As, 5 lies on the right of 3 and the value of integers increase on going to the right . So, 3<5.b. -3 and -5 As, -5 lies on the left of -3 and the value of integers increase on going to the right . So, -5 < -3 .

Additive Inverse

To find the additive inverse of integers, look at the following examples.

Q. Find the additive inverse of the following integers.

a. -3 The additive inverse of -3 = 3

b. 5The additive inverse of 5 = -5

c. -10The additive inverse of -10 = 10

Operations on integersThe operations which can be done on integers are:

Addition

Subtraction

Multiplication

Division

Addition on Integers Rule 1 : To add integers with same sign , we

simply add them irrespective of the sign . After adding , we put the common sign before the integer.

Q. Add the following :a. (+3)+(+5)

= +8b. (-3) + (-5)

= -8 Rule 2 : To add integers with different signs , we simply subtract them irrespective of their sign . After adding we will take out the absolute value of the integers which were to be added and the sign with greater integer will be put before the answer. Q. Add the following :

c. 8+(-3)=5

b. 7+(-2)=5

Subtraction of integers

Rule 1: To subtract an integer , add the additive inverse of the subtrahend to the minuend. And then normally, add the addends.Example – Subtract the following :a. (-4) – 5(-4) + (-5) = -9b. (-4) – (-5)(-4) + 5 = 1c. 4 – (-5)4 + 5 = 9

vMultiplication Of Integers

Rule 1: Multiply the integers irrespective of their sign. Look at the following table to know how to put the sign in the product.First Integer Second

IntegerProduct

+ + +- - ++ - -- + -

follDivision Of Integers

Rule 1: Divide the integers irrespective of their sign. Look at the following table to know how to put the sign in the quotient.

First Integer Second Integer

Quotient

+ + +

- - -

+ - -

- + -

-10

Q – 1. Solve the following . a.(–3) + (-5) b. (-3) – (-6)c. (-7) – 8d. (-5) x (-8)e. (-9) x 12f. (-45) ÷ 15g. (-72) ÷ (-12)

Q – 2. Represent -10 on a number line. Q – 3. Do as directed.h.Find absolute value . b. Find the additive

inverse. c. Compare the following .i. -10 i. 10

i. -10 , -70ii. -5 ii. -1000

ii. 10, 80iii.75 iii. -5

iii. -50 , 25

Answers

Q – 1. a. -8 b.-2 c. 3 d. -15e. 40 f. -108g. -3 h. 6

Q – 2. -4 -3 -2 -1 0 1 2 3 4Q – 3. a.i. 20 ii. 5

iii. 75

b.ii. -10 ii. 1000

iii. 5

c. i. -10 > -70 ii. 10 < 80 iii. -50<25