**What is an Integer? Definition and Examples – Integers Class 7**

**Integer definition**: The term “integer” means intact or whole. Integers are similar to whole numbers, except they can also include negative values.

From the set of negative and positive numbers, including zero, an integer is a number without a decimal or fractional portion.

**Integers examples**

Examples of integers are: -2, 10, 5, 800, and 1470. A set of integers is represented by Z and it consists of:

Integers come in three types:

**Zero (0):**Positive (or negative) integer does not exist for zero. Hence, zero is a neutral number i.e. there is no sign for zero.

**Positive Integers (Natural numbers):**Positive integers are natural numbers (also referred to as counting numbers).*Z*+ is the denotation for these numbers. The right side of 0 is the direction on the number line, where positive integers lie.

Example: 1, 2, 3, 4, 5…….

**Negative Integers (Additive inverse of Natural Numbers):**The negative integers are the negative of natural numbers.*Z*– is the denotation for these numbers. The left side of 0 is the direction on the number line, where negative integers lie.

Example: -1, -2, -3, -4, -5 …….

**Number Line Representation – **Integers can be represented on a number line in the same way that other numbers can.

**Placing Integers on a Number Line**

The following should be kept in mind while arranging integers on a number line:

- The number on the right horizontal side is always higher than the number on the left horizontal side.
- The centre is kept at zero, which is neither positive nor negative.
- Because positive integers are bigger than ‘0’, they are put on the right side of 0.
- Negative numerals are small than 0 and are, therefore, placed to the left of 0

**Integer Operations**

Integers are related to four basic arithmetic operations:

- Addition of Integers
- Subtraction of Integer
- Multiplication of Integers
- Division of Integers

There are some rules for doing these operations.

We need to keep a few things in mind before we start studying these integer operations approaches.

- If a number does not have a sign in front of it, it is a positive number. For instance, the number 5 denotes +5.
- An integer’s absolute value is a positive number. For example, |−3| = 3 and |3| = 3

**Addition of Integers**

The procedure of obtaining the sum of two (or more) integers, where the value may rise or decrease depends on whether the number is positive or negative.

When adding two numbers, either of the 2 cases is possible –

**Both integers have the same signs:**Add the absolute values of the numbers and give the result the same sign as the provided integers. For example, (+3) + (+7) = +10. Here, we just added 3 and 7 and gave the final result i.e. 10 a positive sign before it because 3 and 7 had positive signs. Similarly, (-2) + (-4) = -6. Here, we added 2 and 4 and have the result a negative sign, i.e. -6 because 2 and 4 had negative signs.**One integer is positive while the other is negative:**Calculate the difference between the absolute values of the numbers, then add the sign of the greater of the two numbers to the result. For example, (-5) + (+3) = (-2). Here we subtracted 5 from 3 and gave the result (2) a negative sign (-2) because the greater number (5) had a negative sign (-5).

**Subtraction of Integers**

The process of finding the difference between two or more integers is known as integer subtraction, and the final value varies depending on whether the integer is positive or negative.

For subtracting two numbers, follow these:

- Change the sign of the subtrahend to make the operation become an additional issue.
- Apply the same laws of integer addition to the issue you created in the previous stage and solve it.

For instance,

(-3) – (+2) = (-3) + (-2) = -5

**Multiplication of Integers**

Integer multiplication is similar to repeated addition in that an integer is added a certain number of times.

For multiplication of two numbers, follow these:

- To get the resulting sign, multiply their signs.
- To get the final solution, multiply the numbers and then add the resultant sign.

The below table gives a few examples of multiplications of two signs:

Product of Signs |
Resul |

+ × + | + |

+ × – | – |

– × + | – |

– × – | + |

For example, (+4) * (+3) = (+12) and (+2) * (-4) = (-8)

**Division of Integers**

The rule for dividing integers is quite similar to the rule for multiplying.

- Integers having the same sign, then the result is +ive.
- Integers have different signs, then the result is -ive.

Similarly, (+8) / (+2) = +4 and (-12) / (+4) = -3

Division of Signs |
Resulting sign |

+ ÷ + | + |

+ ÷ – | – |

– ÷ + | – |

– ÷ – | + |

**Rules of Integers**

For integers, rules are as follows

- Two +ive integers sum results in an integer.
- Two -ive integers sum results in an integer.
- Two +ive integers product results in an integer.
- Two -ive integers product results is an integer.
- Addition operation between any integer as well as its negative value, in addition, would result in zero
- Multiplication operation between any integer as well as its reciprocal would result in 1.

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