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Mathematics Class 7 - Integers Notes

Comprehensive study notes for Class 7 - Integers olympiad preparation

Integers

Welcome to the chapter on Integers for Class 7. In this chapter, you will learn about positive and negative numbers, how to add, subtract, multiply, and divide integers, and how to use them in real-life situations. By the end of this chapter, you will be able to solve problems involving integers confidently!

Introduction

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

  • Examples of integers: ... -3, -2, -1, 0, 1, 2, 3 ...
  • Positive integers: 1, 2, 3, ...
  • Negative integers: -1, -2, -3, ...
  • Zero is also an integer.

Representation of Integers

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

Addition and Subtraction of Integers

  • To add two positive integers, add their values.
  • To add two negative integers, add their values and put a minus sign.
  • To add a positive and a negative integer, subtract the smaller from the larger and use the sign of the larger number.
  • Subtraction is like adding the opposite.

Example:
5 + (-3) = 2
-7 + 4 = -3
6 - (-2) = 6 + 2 = 8

Multiplication and Division of Integers

  • Multiplying two integers with the same sign gives a positive answer.
  • Multiplying two integers with different signs gives a negative answer.
  • Division follows the same rules as multiplication.

Example:
(-4) × (-3) = 12
(-5) × 2 = -10
12 ÷ (-3) = -4

Properties of Integers

  • Closure: Integers are closed under addition, subtraction, and multiplication.
  • Commutative: Addition and multiplication of integers are commutative.
  • Associative: Addition and multiplication of integers are associative.
  • Distributive: Multiplication is distributive over addition.

Using Integers in Real Life

  • Temperature (above and below zero)
  • Bank balance (credit and debit)
  • Elevations (above and below sea level)

Fun Activity: Integer Number Line Game

Draw a number line and use counters to show addition and subtraction of integers. Practice moving left and right for negative and positive numbers!

Summary

  • Integers include positive numbers, negative numbers, and zero.
  • Learn to add, subtract, multiply, and divide integers using rules for signs.
  • Integers are used in many real-life situations.

Practice Questions

  1. Add: 7 + (-5)
  2. Subtract: -8 - 3
  3. Multiply: (-6) × 4
  4. Divide: 20 ÷ (-5)
  5. Solve: (-3) + (-7) - 2

Challenge Yourself

  • Write a word problem using integers and solve it.
  • Find the value: (-5) × (-2) + 8

Did You Know?

  • The word "integer" comes from Latin and means "whole".
  • Negative numbers were used in ancient China for bookkeeping!

Glossary

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

Answers to Practice Questions

  1. 2
  2. -11
  3. -24
  4. -4
  5. -12

Practice with integers every day to become confident in math!

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