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Chapter 1 – Integers

The following Topics and Sub-Topics are covered in this chapter and are available on MSVgo:

Introduction

Class 7th Mathematics chapter ‘Integers‘ is an essential chapter, as it forms the basis of higher-level mathematics. It covers all the critical topics related to integers and numbers. It is also used in successive chapters of class 7th mathematics, so a clear understanding of integers will make understanding other mathematical concepts easier.

The chapter ‘Integers’ covers the following topics:

    • Natural and whole numbers
    • Properties of Integers for addition and subtraction
    • Properties of Integers for multiplication and division
    • Representation of Integers on the number line
    • Additive identity
    • Additive inverse

Natural numbers are a set of positive numbers starting from 1. It does not include 0.

Whole numbers are all positive numbers, along with 0. It is a collection of both 0 and natural numbers.

Integers are all whole numbers along with their negatives. It includes both positive and negative whole numbers.

Following are the integrative properties of addition and subtraction of integers:

    • Closure under Addition: If there are 2 integers x and y, then x+y is also an integer.
    • Closure under Subtraction: If there are 2 integers x and y, then x-y is also an integer.
    • Associative Property of Integers: If there are 3 integers x, y and z, then (x+y)+z = x+(y+z).
    • Commutative Property of Integers: If there are 2 integers x and y, then x+y = y+x.

Additive identity is the number which, when added to any integer, number remains the same. Additive identity for any integer is 0 as x+0 = 0+x = x where x is an integer. For example: 5+0 = 0+5 = 5.

Additive inverse is any number which, when added to an integer, the answer is equal to 0. Additive inverse of any integer is the negative of that integer as x+(-x) = 0, where x is an integer. For example, 2 is the additive inverse of (-2) and -3 is the additive inverse of 3.

The result of the multiplication of two integers is as follows:

    • Multiplication of any two positive integers is a positive integer. For example: (+4) × (+6) = +24
    • Multiplication of any two negative integers is a positive integer. For example: (-4) × (-6) = +24
    • When a positive and a negative integer are multiplied, then the result is a negative integer. For example: (+4) × (-6) = -24

Following are the integrative properties of multiplication:

    • Closure under Multiplication: If there are 2 integers x and y, then x multiplied by y is also an integer.
    • Associative Property of Multiplication: If there are 3 integers a, b and c, then (a×b) ×c = a× (b×c).
    • Commutative Property of Multiplication of Integers: If there are 2 integers a and b, then a×b = b×a.
    • Distributive Property: The distributive property of Integers is used in the case of multiplication and addition to make calculations easier. If there are 3 integers a, b and c, then a×(b+c) = (a×b) + (a×c).
    • Multiplicative Identity: Multiplicative identity is the number that, when multiplied to any integer, remains the same. Multiplicative identity for any integer is 1 as a×1 = 1×a = a where a is an integer. For example: 5×1 = 1×5 = 5.

The result of the division of two integers is as follows:

    • The division of any two positive integers is a positive integer. For example: (+4)÷(+6) = +24
    • The division of any two negative integers is a positive integer. For example: (-4)÷(-6) = +24
    • The division of a positive integer and a negative integer is a negative integer. For example: (+4)÷(-6) = -24 and (-4)÷(+6) = -24.

A number line is a single axis line that has integer markings at an equal interval. Addition and subtraction of the integers are represented on a number line in the following ways:

    • A positive integer is added to any integer by moving to the right on a number line.
    • Any negative integer is added to any other integer by moving to the left on a number line.
    • A positive integer is subtracted from any integer by moving to the left on a number line.
    • A negative integer is subtracted from any integer by moving to the right on a number line.

The chapter ‘Integers’ is an important topic for class 7th mathematics, and an essential concept for advanced and higher-level mathematics. This chapter will smoothen your journey through the upcoming mathematics chapters like algebra, coordinate geometry, statistics, and calculus.

  1. What are Integers in math?
    Integers are all whole numbers along with their negatives. It includes both positive and negative whole numbers.
  2. What is the rule for integers?
    • The addition of any two positive integers is a positive integer.
    • The addition of any two negative integers is a negative integer.
    • The addition of a positive integer and a negative integer is the difference between the integers. The resultant integer bears the sign of the bigger integer.
    • Multiplication of any two positive integers is a positive integer.
    • Multiplication of any two negative integers is a positive integer.
    • When a positive and a negative integer are multiplied, then the result is a negative integer.
  3. What are the types of integers?
    Integersare of three types:

    • Zero
    • Positive integers
    • Negative integers
  4. What is an integer of 4?
    4 is a positive integer and a rational number. The negative integer of 4 is (-4).
  5. Is 0 a positive or a negative integer?
    0 is neither a positive nor a negative integer.

‘Integers‘ is an exciting chapter of mathematics. So, the visual representation of this chapter is really important. The MSVgo app is a video library platform that helps you comprehend topics through exploratory representations and practical models. MSVgo helps you to comprehend the Math & Science behind concepts through interesting visual animations and videos. So, do check out the videos at MSVgo for better understanding.

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Middle School Math

  • Addition
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