Class 6 Maths Integers Notes

Class 6 Maths Integers Notes

Introduction:
In the chapter “Integers”, students are introduced to the world of positive and negative numbers, which are collectively known as integers. Integers are a crucial part of mathematics, used in various real-life situations such as temperatures, bank balances, and elevations. Understanding integers helps students grasp basic concepts of number lines, addition, subtraction, and comparisons of numbers.

Key Concepts Covered:

  1. What are Integers?
    • Integers include all positive whole numbers, their negative counterparts, and zero.
    • Example: … -3, -2, -1, 0, 1, 2, 3 …
    • Integers are the set of numbers that are not fractions or decimals.
  2. Representation of Integers on the Number Line:
    • Integers are represented on a number line where:
      • Positive integers are to the right of 0.
      • Negative integers are to the left of 0.
    • The farther you move to the right, the larger the positive number, and the farther you move to the left, the smaller the negative number.
  3. Addition and Subtraction of Integers:
    • Addition of Integers:
      • Adding two positive integers gives a positive result.
      • Adding two negative integers gives a negative result.
      • Adding a positive and a negative integer depends on their absolute values.
    • Subtraction of Integers:
      • Subtracting a positive integer is like moving left on the number line.
      • Subtracting a negative integer is like moving right on the number line.
  4. Multiplication and Division of Integers:
    • Multiplication of Integers:
      • A positive integer multiplied by a positive integer gives a positive result.
      • A positive integer multiplied by a negative integer gives a negative result.
      • A negative integer multiplied by a negative integer gives a positive result.
    • Division of Integers:
      • The same rules as multiplication apply to division.
  5. Properties of Integers:
    • Commutative Property: Addition and multiplication of integers are commutative.
    • Associative Property: Addition and multiplication of integers are associative.
    • Distributive Property: Multiplication distributes over addition and subtraction.
  6. Order of Integers:
    • Understanding how to compare integers:
      • Negative integers are always less than positive integers.
      • The farther a negative integer is from 0, the smaller it is.
      • The farther a positive integer is from 0, the larger it is.

Important Questions with Answers:

  1. What is an integer?
    • Answer: An integer is any whole number, either positive, negative, or zero, that does not include fractions or decimals.
  2. Which is greater: -5 or -8?
    • Answer: -5 is greater because it is closer to zero on the number line.
  3. Add: -4 + 6
    • Answer: 2 (since the positive number is larger, the result is positive).
  4. Subtract: 3 – 7
    • Answer: -4 (since we are subtracting a larger number from a smaller one).
  5. Multiply: -3 × 5
    • Answer: -15 (a negative number multiplied by a positive number is negative).
  6. Divide: -12 ÷ 4
    • Answer: -3 (a negative divided by a positive is negative).