Mathematics Class 6 - Whole Numbers Notes

Whole Numbers

Welcome to the chapter on Whole Numbers for Class 6. In this chapter, you will learn what whole numbers are, their properties, and how to use them in math problems. By the end of this chapter, you will be able to identify whole numbers, use them in operations, and solve related questions confidently!

Introduction

Whole numbers are the numbers we use for counting and ordering, starting from zero. They do not include fractions or decimals.

What are Whole Numbers?

• Whole numbers are: 0, 1, 2, 3, 4, 5, ... and so on.
• They do not include negative numbers, fractions, or decimals.

Properties of Whole Numbers

• Closure: If you add or multiply any two whole numbers, the result is also a whole number.
• Commutative Property: Addition and multiplication of whole numbers can be done in any order.
  Example: 3 + 5 = 5 + 3
• Associative Property: Grouping does not affect the sum or product.
  Example: (2 + 3) + 4 = 2 + (3 + 4)
• Identity: 0 is the identity for addition (a + 0 = a). 1 is the identity for multiplication (a × 1 = a).
• Distributive Property: Multiplication distributes over addition.
  Example: a × (b + c) = a × b + a × c

Number Line

Whole numbers can be shown on a number line. The line starts at 0 and goes to the right: 0, 1, 2, 3, ...

Operations on Whole Numbers

• Addition: Example: 7 + 5 = 12
• Subtraction: Example: 10 - 4 = 6 (Note: Subtraction may not always give a whole number if the first number is smaller.)
• Multiplication: Example: 6 × 3 = 18
• Division: Example: 12 ÷ 3 = 4 (Division may not always give a whole number.)

Fun Activity: Draw a Number Line!

Draw a number line from 0 to 10. Mark each whole number and try adding or subtracting by moving left or right on the line.

Summary

• Whole numbers start from 0 and go on forever.
• They have special properties like closure, commutative, associative, and distributive.
• We use whole numbers in daily life for counting and calculations.

Practice Questions

1. Write the first five whole numbers.
2. Is 0 a whole number?
3. Add: 8 + 7
4. Multiply: 5 × 6
5. Show 0, 1, 2, 3, 4 on a number line.

Challenge Yourself

• Find two whole numbers whose sum is 20.
• Is 2.5 a whole number? Why or why not?

Did You Know?

• Zero was first used in India!
• Whole numbers are used in counting objects, days, and money.

Glossary

• Whole Number: A number without fractions or decimals, starting from 0.
• Number Line: A line that shows numbers in order.
• Operation: An action like addition, subtraction, multiplication, or division.

Answers to Practice Questions

1. 0, 1, 2, 3, 4
2. Yes
3. 15
4. 30
5. Draw a line and mark 0, 1, 2, 3, 4 in order.

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Practice using whole numbers every day to become confident in math!