**1.) Definition of Integers in Maths**

**2.) Examples of Positive and Negative Integers**

- Integers from 1 to 50
- Integers 1 to 100
- Odd Integers from 1 to 100
- Negative Integer example from 1 to 50

**3.) How to solve Integers**

- Adding Integers rule
- How to add integers with different signs
- Integers subtraction rules
- How to subtract integers with different signs
- Integers multiplication rules
- How to multiply integers with different signs

**4.) Integers FAQs**

## 1.) Definition of Integers in Maths

## 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.

### Integers from 1 to 50

### Integers 1 to 100

### Odd Integers from 1 to 100

### Negative Integers example from 1 to 50

## 3.) How to solve Integers?

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

### 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)

= (-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.*

= (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.)

= (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 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)

= 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.*

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

= __30-1__-__8+3__-9 *(U**nderline showing we will solve it* )

= __29-5__-9

= __24-9__

= 15

*Our answer is 15.*

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

= __30-1__-__8+3__-9 *(U nderline 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)

= __(-9)✕(+8)__✕__4✕(-7)__ *(Underline showing we will solve it)*

= -72✕-28

= 2016

*Our answer is 2016.*

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

= __-16____✕-24__*✕(-5)*

= 384*✕(-5)*

= -1920

*Our answer is -1920*

= __(+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.

Let the first integer = x

So, the second consecutive integer is = x+1

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

### 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.

Let the first integer = x

So, the second consecutive integer is = x+1

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.

What is the smallest positive integer?