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Mathematics Class 6 - Integers Notes

Comprehensive study notes for Class 6 - Integers olympiad preparation

Integers

Welcome to the chapter on Integers for Class 6. In this chapter, you will learn about positive and negative numbers, how to compare and order them, and how to add, subtract, multiply, and divide integers. By the end of this chapter, you will be able to solve problems using integers confidently!

Introduction

Integers are numbers that include all whole numbers and their negatives. Integers do not have fractions or decimals. Examples of integers are -3, 0, 7, -12, 25.

Types of Integers

  • Positive Integers: Numbers greater than zero (1, 2, 3, ...).
  • Negative Integers: Numbers less than zero (-1, -2, -3, ...).
  • Zero: Zero is neither positive nor negative.

Representing Integers on a Number Line

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

  • ... -3, -2, -1, 0, 1, 2, 3 ...

Comparing and Ordering Integers

The greater the number, the farther right it is on the number line. Negative numbers are always less than positive numbers.

  • -5 < -2
  • 3 > -1

Operations with Integers

  • Addition: Add positive and negative numbers using rules.
  • Subtraction: Subtract integers by changing the sign and adding.
  • Multiplication: Multiply integers using sign rules.
  • Division: Divide integers using sign rules.

Rules:
- Adding two positives gives a positive.
- Adding two negatives gives a negative.
- Adding a positive and a negative: subtract and keep the sign of the bigger number.
- Multiplying or dividing two numbers with the same sign gives a positive.
- Multiplying or dividing two numbers with different signs gives a negative.

  • (-4) + 3 = -1
  • (-5) × (-2) = 10
  • 6 ÷ (-3) = -2

Word Problems with Integers

Integers are used in real life to show temperature, bank balances, elevations, and more.

  • Example: If the temperature drops from 5°C to -3°C, what is the change? (5 - (-3) = 8°C)

Fun Activity: Integer Game!

Draw a number line and use counters to move left and right for positive and negative numbers. Play with friends to see who reaches zero first!

Summary

  • Integers include positive numbers, negative numbers, and zero.
  • Use rules to add, subtract, multiply, and divide integers.
  • Integers are used in real life for temperature, money, and more.

Practice Questions

  1. Write all integers between -4 and 3.
  2. Add: (-7) + 5
  3. Subtract: 6 - (-2)
  4. Multiply: (-3) × 4
  5. Divide: 12 ÷ (-3)

Challenge Yourself

  • Solve: (-8) + (-5) - 3
  • If the bank balance is -250 and you deposit 100, what is the new balance?

Did You Know?

  • Negative numbers were first used in ancient China!
  • Zero is the only integer that is neither positive nor negative.

Glossary

  • Integer: A whole number that can be positive, negative, or zero.
  • Number Line: A line to show numbers in order.
  • Positive: Greater than zero.
  • Negative: Less than zero.

Answers to Practice Questions

  1. -3, -2, -1, 0, 1, 2
  2. -2
  3. 8
  4. -12
  5. -4

Practice working with integers to become a math expert!

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