In the class 7 Maths Chapter 1 Integers, various properties and operations carried out on integers are discussed. Before we delve deeper into the chapter let us look at a few points studied about integers in our previous classes.

## What are Integers?

Integers are a collection of numbers formed by whole numbers and their negatives. Integers can be represented on a number line as follows:

In the given number line, the ascending order of the listed numbers is -16, -9, -4, 0, 3, 8, 14.

The descending order is 14, 8, 3, 0, -4, -9, -16.

### Properties of Integers Under Addition And Subtraction

- The addition and subtraction of two integers give an integer. In other words,
*a+b*and a-b are again integers, where*a*and*b*are integers - For all integers, Addition is commutative which means that
*a+b=b+a* - For all integers, addition is associative, i.e., (
*a+b*)*+c=a+*(*b+c*) - The additive identity in integers is
*0*, for every integer*a*,*a*+*0*=*0*+*a*=*a*.

### Properties of Integers Under Multiplication

- The product of two integers is always an integer.
- Multiplication is commutative for integers, i.e.,
*a**b=b**a*, where*a*and*b*are integers. - The multiplicative identity for integers is 1, For any integer
*a*, 1 x*a*=*a*x 1. - For integers, multiplication is associative, i.e., (ab)c=a(bc), where
*a*and*b*are integers.

The distributive property is exhibited under addition and multiplication of integers, i.e.,*a**(b+c) = a**b+ a**c**, *for any three integers *a*, *b* and *c*.

Integers manifest the following properties under division:

- The quotient obtained when a positive integer divided by a negative integer is negative.
- When a negative integer is divided by another negative integer, the obtained quotient is positive.
- For any integer
*a*,

*a*÷ 1*= a**a*÷ 0 is not defined

## Problems on Integers for Class 7

- Evaluate the following

- 13 ÷ [(–2) + 1]
- [(– 6) + 5)] ÷ [(–2) + 1]
- 13 ÷ [(–2) + 1]

- The temperature at 12 noon was 10°C above zero. If it decreases at the rate of 2°C

per hour until midnight, at what time would the temperature be 8°C below zero?

What would be the temperature at midnight?

- An elevator descends into a mine shaft at the rate of 6 m/min. If the descent starts

from 10 m above the ground level, how long will it take to reach – 350 m.

- Write five pairs of integers (a, b) such that a ÷ b = –3. One such pair is (6, –2)

because 6 ÷ (–2) = (–3).

Learn more about Integers and other related topics including class 7 maths notes, at BYJU’S.

**Also, Read**