Class 6 Notes - Integers

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1. Introduction to Integers

Integers are a set of numbers that include all positive numbers, negative numbers, and zero. They do not include fractions or decimals.

  • Examples of integers: ..., -3, -2, -1, 0, 1, 2, 3, ...
  • Zero is neither positive nor negative.

2. Representation of Integers on a Number Line

Integers can be shown on a number line. Numbers to the right of zero are positive, and numbers to the left are negative.

Example: On a number line, -2 is to the left of 0, and 3 is to the right of 0.

3. Comparing Integers

  • On a number line, the number to the right is always greater.
  • Negative numbers are less than zero; positive numbers are greater than zero.
  • -5 < -2, 0 < 4, -3 < 0

4. Addition and Subtraction of Integers

Addition

  • Adding two positive integers gives a positive integer.
  • Adding two negative integers gives a negative integer.
  • Adding a positive and a negative integer: subtract and keep the sign of the bigger number.
Example: (-3) + 5 = 2
Example: 4 + (-7) = -3

Subtraction

  • To subtract an integer, add its opposite.
Example: 5 - 7 = 5 + (-7) = -2
Example: (-4) - (-6) = (-4) + 6 = 2

5. Properties of Addition and Subtraction

  • Addition of integers is commutative: a + b = b + a
  • Addition of integers is associative: (a + b) + c = a + (b + c)
  • Zero is the identity for addition: a + 0 = a
  • Subtraction is not commutative or associative.

6. Word Problems

  1. The temperature was 5°C in the morning. It dropped by 8°C by night. What is the temperature at night?
  2. A submarine is at a depth of -120 m. It rises 30 m. What is its new depth?
  3. Find the sum: (-7) + 12

7. Practice Exercises

  1. Represent -4, 0, and 3 on a number line.
  2. Which is greater: -2 or 1?
  3. Calculate: (-5) + (-8)
  4. Calculate: 9 - (-3)
  5. Fill in the blank: The opposite of -6 is ____.

8. Common Mistakes

  • Forgetting to change the sign when subtracting a negative integer.
  • Thinking that negative numbers are always smaller, even when comparing two negatives.
  • Placing integers incorrectly on the number line.

9. Summary

  • Integers include positive numbers, negative numbers, and zero.
  • They can be represented on a number line.
  • Learn the rules for adding and subtracting integers.
  • Practice helps avoid common mistakes.