Integers Class 7 Notes: Chapter 1

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:

Perimeter and Area Class 7 Notes: Chapter 11

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+band 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.,ab=ba, 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) = ab+ ac, 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,
  1. a ÷ 1 = a
  2. a ÷ 0 is not defined

Problems on Integers for Class 7

  1. Evaluate the following
  1. 13 ÷ [(–2) + 1]
  2. [(– 6) + 5)] ÷ [(–2) + 1]
  3. 13 ÷ [(–2) + 1]
  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?
  1. 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.
  1. Write five pairs of integers (a, b) such that a ÷ b = –3. One such pair is (6, –2)
    because 6 ÷ (–2) = (–3).

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Practise This Question

You are given the measurement of two sides of a right angled triangle such that these sides enclose the right angle. What else do you need in order to draw a triangle?