Addition, Subtraction, Multiplication, and Division Lesson

Lesson Overview

• What Is Addition?
• What Is Subtraction?
• What Is Multiplication?
• What Is Division?
• How to Add, Subtract, Multiply, and Divide Fractions
• Practical Applications of Addition, Subtraction, Multiplication, and Division
• Practice Problems

In mathematics, the four fundamental operations-addition, subtraction, multiplication, and division-are the building blocks for all other mathematical concepts. These operations are essential for solving problems in everyday life, whether you're adding up prices while shopping, subtracting time from a clock, multiplying for group calculations, or dividing a pizza into equal portions. Understanding how to use these operations is crucial for improving your math skills.

In this lesson, we will cover the basics of each operation, explain how they work, and provide examples and practice problems. You will also learn some useful strategies to solve problems quickly and accurately.

What Is Addition?

Addition is the process of combining two or more numbers to find the total or sum. It is one of the simplest and most commonly used operations in mathematics.

How Addition Works:

• When you add two numbers together, you combine their values to get a new total.
  
• For example:
  3 + 5 = 8
  Here, 3 and 5 are added to get a total of 8.
  

Properties of Addition:

• Commutative Property: The order of numbers doesn't matter. For example, 3 + 5 = 5 + 3.
  
• Associative Property: You can add numbers in any grouping. For example, (2 + 3) + 4 = 2 + (3 + 4).
  
• Identity Property: Adding zero to any number doesn't change its value. For example, 5 + 0 = 5.
  

What Is Subtraction?

Subtraction is the process of finding the difference between two numbers. It is the opposite of addition. When you subtract, you are taking one number away from another.

How Subtraction Works:

• To subtract, you take one number away from another to find the difference.
  
• For example:
  8 - 5 = 3
  Here, 5 is subtracted from 8, leaving 3 as the result.
  

Properties of Subtraction:

• Non-Commutative: The order of numbers does matter in subtraction. For example, 8 - 5 ≠ 5 - 8.
  
• Non-Associative: Grouping doesn't work the same as addition. For example, (10 - 3) - 2 ≠ 10 - (3 - 2).
  

What Is Multiplication?

Multiplication is repeated addition. It involves adding a number to itself multiple times. Multiplication helps you find the total when something is repeated several times.

How Multiplication Works:

• For example:
  3 × 4 = 12
  This means 3 is added to itself 4 times: 3 + 3 + 3 + 3 = 12.
  

Properties of Multiplication:

• Commutative Property: The order of numbers doesn't affect the result. For example, 3 × 4 = 4 × 3.
  
• Associative Property: You can multiply numbers in any grouping. For example, (2 × 3) × 4 = 2 × (3 × 4).
  
• Identity Property: Multiplying any number by 1 doesn't change its value. For example, 5 × 1 = 5.
  
• Zero Property: Multiplying any number by 0 results in 0. For example, 5 × 0 = 0.
  

What Is Division?

Division is the process of splitting a number into equal parts. It is the opposite of multiplication. When you divide, you are essentially finding how many times one number is contained within another.

How Division Works:

• For example:
  12 ÷ 4 = 3
  This means 12 is divided into 4 equal parts, and each part is 3.
  

Properties of Division:

• Non-Commutative: The order of numbers matters. For example, 12 ÷ 4 ≠ 4 ÷ 12.
  
• Non-Associative: Grouping doesn't work the same as multiplication. For example, (12 ÷ 4) ÷ 2 ≠ 12 ÷ (4 ÷ 2).
  

Take This Quiz:

Maths quiz on Addition, Subtraction & Multiplication

How to Add, Subtract, Multiply, and Divide Fractions

In this section, we will learn how to apply the basic operations to fractions, which are numbers representing parts of a whole.

Adding and Subtracting Fractions:

• To add or subtract fractions, you must have a common denominator.
  
• Example:
  1/4 + 2/4 = 3/4
  The denominators are the same, so you just add the numerators.
  

Multiplying Fractions:

• To multiply fractions, multiply the numerators and then multiply the denominators.
  
• Example:
  1/2 × 3/4 = 3/8
  Multiply the numerators: 1 × 3 = 3
  Multiply the denominators: 2 × 4 = 8
  So, 1/2 × 3/4 = 3/8.
  

Dividing Fractions:

• To divide fractions, multiply by the reciprocal (flip the second fraction).
  
• Example:
  1/2 ÷ 3/4 = 1/2 × 4/3 = 4/6
  Simplify to 2/3.
  

Practical Applications of Addition, Subtraction, Multiplication, and Division

Solving word problems is an important skill in math. Here are a few examples to practice:

Example 1: Addition

• Problem: Sarah has 5 apples. She buys 3 more apples. How many apples does she have now?
  
• Solution: 5 + 3 = 8. Sarah has 8 apples.
  

Example 2: Subtraction

• Problem: There are 12 cookies. If 4 cookies are eaten, how many are left?
  
• Solution: 12 - 4 = 8. There are 8 cookies left.
  

Example 3: Multiplication

• Problem: A box contains 4 rows of pencils. Each row has 6 pencils. How many pencils are in the box?
  
• Solution: 4 × 6 = 24. There are 24 pencils.
  

Example 4: Division

• Problem: A teacher has 24 students and 4 rows of desks. How many students will sit in each row?
  
• Solution: 24 ÷ 4 = 6. There will be 6 students per row.
  

Take This Quiz:

Basic Addition, Subtraction, Multiplication, and Division

Practice Problems

Let's test your understanding with some practice problems:

1. What is 5 + 3?
   
2. Subtract 8 - 2 and simplify the result.
   
3. Multiply 6 × 7 and give the answer.
   
4. Divide 20 ÷ 5 and provide the result.