Whole Numbers and Basic Operations

Week 1: Whole Numbers and Basic Operations

Class: JSS1 | Subject: Mathematics | Term: First Term

Learning Objectives

By the end of this lesson, students should be able to:

• Define whole numbers and identify them on a number line
• Read and write whole numbers up to billions
• Perform the four basic operations: addition, subtraction, multiplication, and division
• Apply the order of operations (BODMAS) to solve problems
• Solve real-life word problems involving whole numbers

Introduction to Whole Numbers

Whole numbers are the set of counting numbers together with zero. They include 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and so on, extending to infinity. Whole numbers do not include fractions, decimals, or negative numbers. They are the most fundamental type of numbers used in everyday life for counting objects, measuring quantities, and performing basic calculations.

The set of whole numbers is represented as W = {0, 1, 2, 3, 4, 5, ...}. Every whole number has a unique position on the number line, starting from zero and moving to the right. The number line is a visual representation that helps us understand the order and magnitude of numbers.

Place Value System

The place value system is the foundation of our number system. It tells us the value of each digit in a number based on its position. In the Hindu-Arabic numeral system, we work with base 10, meaning each place is worth ten times the place to its right.

Consider the number 5,347,268. Each digit has a specific place value:

• 5 is in the millions place = 5,000,000
• 3 is in the hundred thousands place = 300,000
• 4 is in the ten thousands place = 40,000
• 7 is in the thousands place = 7,000
• 2 is in the hundreds place = 200
• 6 is in the tens place = 60
• 8 is in the units place = 8

Therefore, 5,347,268 = 5,000,000 + 300,000 + 40,000 + 7,000 + 200 + 60 + 8. This is called the expanded form of the number.

Addition of Whole Numbers

Addition is the process of combining two or more numbers to find their total or sum. The numbers being added are called addends, and the result is called the sum.

Properties of Addition:

• Commutative Property: 5 + 3 = 3 + 5 = 8
• Associative Property: (2 + 3) + 4 = 2 + (3 + 4) = 9
• Identity Property: 7 + 0 = 7

Example: Add 4,567 + 2,835

Step 1: Add units: 7 + 5 = 12. Write 2, carry 1.
Step 2: Add tens: 6 + 3 + 1 = 10. Write 0, carry 1.
Step 3: Add hundreds: 5 + 8 + 1 = 14. Write 4, carry 1.
Step 4: Add thousands: 4 + 2 + 1 = 7.
Answer: 4,567 + 2,835 = 7,402

Subtraction of Whole Numbers

Subtraction is the inverse of addition. It involves finding the difference between two numbers.

Example: Subtract 3,478 from 8,125

8,125 - 3,478:
Units: 5 - 8, borrow. 15 - 8 = 7.
Tens: 1 - 7, borrow. 11 - 7 = 4.
Hundreds: 0 - 4, borrow. 10 - 4 = 6.
Thousands: 7 - 3 = 4.
Answer: 8,125 - 3,478 = 4,647

Multiplication of Whole Numbers

Multiplication is repeated addition. When we multiply 4 x 3, it means 4 + 4 + 4 = 12.

Properties of Multiplication:

• Commutative: 6 x 4 = 4 x 6 = 24
• Associative: (2 x 3) x 4 = 2 x (3 x 4) = 24
• Distributive: 3 x (4 + 5) = 3x4 + 3x5 = 27
• Identity: 9 x 1 = 9
• Zero Property: 7 x 0 = 0

Example: Calculate 256 x 34

256 x 4 = 1,024
256 x 30 = 7,680
1,024 + 7,680 = 8,704

Division of Whole Numbers

Division is the inverse of multiplication. It involves sharing a number into equal parts.

Example: Divide 845 by 5

8 / 5 = 1 remainder 3. Bring down 4: 34 / 5 = 6 remainder 4. Bring down 5: 45 / 5 = 9.
Answer: 845 / 5 = 169

Order of Operations (BODMAS)

When an expression contains more than one operation, we follow the BODMAS rule:

• B - Brackets
• O - Orders (powers, roots)
• D - Division
• M - Multiplication
• A - Addition
• S - Subtraction

Example: Evaluate 12 + 3 x (8 - 2) / 6

Brackets: 8 - 2 = 6
Multiplication: 3 x 6 = 18
Division: 18 / 6 = 3
Addition: 12 + 3 = 15

Word Problems

Problem 1: A school has 1,245 boys and 1,378 girls. Total = 1,245 + 1,378 = 2,623 students.

Problem 2: A trader bought 48 bags of rice at N35,000 each. Total cost = 48 x 35,000 = N1,680,000.

Problem 3: A farmer harvested 7,560 oranges into 36 baskets. Each basket = 7,560 / 36 = 210 oranges.

Evaluation Questions

• 1. Write 8,045,321 in words and in expanded form.
• 2. Calculate: 45,678 + 23,456 + 8,907
• 3. Subtract: 100,000 - 67,893
• 4. Multiply: 345 x 27
• 5. Evaluate using BODMAS: 24 / 6 + 3 x (10 - 5)

Summary

In this lesson, we have learned about whole numbers, their place values, and the four basic operations: addition, subtraction, multiplication, and division. We also learned the BODMAS rule for solving expressions with multiple operations. Practice is essential for mastering these fundamental skills, as they form the foundation for all other topics in mathematics.