Definition of Integers in Maths | How to solve Integers | TIRLA ACADEMY

Mathematics is a vast subject. In maths, we study different shapes, numbers, formulas, etc.

In this article, we are going to learn integers in detail. The following points we will cover on it.

1.) Definition of Integers in Maths

2.) Examples of Positive and Negative Integers

1. Integers from 1 to 50
2. Integers 1 to 100
3. Odd Integers from 1 to 100
4. Negative Integer example from 1 to 50

3.) How to solve Integers

1. Adding Integers rule
2. How to add integers with different signs
3. Integers subtraction rules
4. How to subtract integers with different signs
5. Integers multiplication rules
6. How to multiply integers with different signs

4.) Integers FAQs

Let's start with the definition of an Integer.

1.) Definition of Integers in Maths

An integer is a whole number that may be positive or negative in nature.

or

An integer is a number that may be positive, negative or zero in nature.

2.) Examples of Positive and Negative Integers

There are infinite positive and negative integers and some examples of integers are 3, 4, 6, 10, 222, -56, -80, -44, -91, 0, -400, etc.

For better understanding, we are providing the list of integer examples.

Integers from 1 to 50

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50.

Integers 1 to 100

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100.

Odd Integers from 1 to 100

1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99.

Negative Integers example from 1 to 50

-1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15, -16, -17, -18, -19, -20, -21, -22, -23, -24, -25, -26, -27, -28, -29, -30, -31, -32, -33, -34, -35, -36, -37, -38, -39, -40, -41, -42, -43, -44, -45, -46, -47, -48, -49, -50.

3.) How to solve Integers?

To solve the integers we should know the sign rules of integers for addition, subtraction, multiplication, and division.

Here we are discussing the sign rules of integers step by step with their uses-

Adding Integers Rule

(+) + (+) = (Add and put positive sign)

(-) + (-) = (Add and put negative sign)

(+) + (-) = (Subt. & put sign of large no.)

(-) + (+) = (Subt. & put sign of large no.)

How to add integers with different signs?

Solve : (-1)+2+(-4)+8+(-7)

= (-1)+2+(-4)+8+(-7)  (First, we multiply the signs)

= -1+2-4+8-7  (Underline showing we will solve it)

= 1+4-7 

= 5-7 

= -2

Our answer is -2.

Solve : (34)+(-41)+(-11)+22+(-17)+(-61)

= (34)+(-41)+(-11)+22+(-17)+(-61)  (First, we multiply the signs)

= 34-41-11+22-17-61  (Underline showing we will solve it)

= -7+11-78

= 4-78

= -74

Our answer is -74.

Integers Subtraction Rules

(+) - (+) = (Subt. and put positive sign)
(-) - (-) = (Subt. and put negative sign)
(+) - (-) = (Add & put sign of large no.)
(-) - (+) = (Add & put sign of large no.)

How to subtract integers with different signs

Solve : 3-(-7)-(+4)-5-9

= 3-(-7)-(+4)-5-9  (First, we multiply the signs)

= 3+7-4-5-9  (Underline showing we will solve it)

= 10-9-9

= 1-9

= -8

Our answer is -8.

Solve : 30-(+1)-8-(-3)-(+9)

= 30-(+1)-8-(-3)-(+9)  (First, we multiply the signs)

= 30-1-8+3-9  (Underline showing we will solve it )

= 29-5-9 

= 24-9

= 15

Our answer is 15.

Integers multiplication rules

(+) ✕ (+) = (Do Multiply and put + sign)

(-) ✕ (-) = (Do Multiply and put + sign)

(+) ✕ (-) = (Do Multiply and put - sign)

(-) ✕ (+) = (Do Multiply and put - sign)

How to multiply integers with different signs

Solve (-9)✕(+8)✕4✕(-7)

= (-9)✕(+8)✕4✕(-7)  (Underline showing we will solve it)

= -72✕-28

= 2016

Our answer is 2016.

Solve : (+8)✕(-2)✕(-4)✕(+6)✕(-5)

= (+8)✕(-2)✕(-4)✕(+6)✕(-5)  (Underline showing we will solve it)

= -16✕-24✕(-5)

= 384✕(-5)

= -1920

Our answer is -1920

The product of two consecutive positive integers is 812. What is the value of the lesser integer?

Solution:

Let the first integer = x

So, the second consecutive integer is = x+1

According to the Question, the product of two consecutive positive integers is 812.

So,

x(x+1) = 812

x2 + x = 812

x2 + x - 812 = 0

x2 + 29x - 28x - 812 = 0  {splitting the middle term}

x(x + 29) -28(x + 29) = 0  {taking common}

(x + 29) (x - 28) = 0

(x + 29) = 0, (x - 28) = 0

x = -29, x = 28

So the value of the lesser positive integer is 28.

The product of two consecutive negative integers is 600. what is the value of the lesser integer?

Solution:

Let the first integer = x

So, the second consecutive integer is = x+1

According to the Question, the product of two consecutive negative integers is 600.

So,

x(x+1) = 600

x2 + x = 600

x2 + x - 600 = 0

x2 + 25x - 24x - 600 = 0  {splitting the middle term}

x(x + 25) -24(x + 25) = 0  {taking common}

(x + 25) (x - 24) = 0

(x + 25) = 0, (x - 24) = 0

x = -25, x = 24

So the value of the lesser integer is -25.

4.) Integers FAQs

Is an integer a whole number?

Yes, all positive integers are whole numbers.

Is 0 a positive integer?

0 has no sign, but it may be positive or negative.

What is the smallest positive integer?

The smallest positive integer is 1.

What is the greatest negative integer?

-1 is the greatest negative integer.

What is the average of integers from 25 to 41?

The average of integers from 25 to 41 is 33.

Is 0 an Integer?

Yes, 0 is an Integer.