Division of Whole Numbers Lesson: Learn Division Techniques

Division is one of the four fundamental arithmetic operations, along with addition, subtraction, and multiplication. It is used to separate a number into equal parts or groups. Understanding division is essential for solving problems involving equal distribution, grouping, and sharing. 

In this lesson, we will focus on the division of whole numbers. We'll explore the basic concepts of division, the relationship between division and multiplication, and the steps involved in performing division calculations manually. By the end of this lesson, you will be able to confidently divide whole numbers and solve division problems using pencil and paper.

What is Division?

Division is the process of splitting a number (called the dividend) into equal parts, based on a number (called the divisor). The result of division is called the quotient.

In the equation:

Dividend÷Divisor=Quotient

• Dividend: The number to be divided.
  
• Divisor: The number by which you divide the dividend.
  
• Quotient: The result of the division.
  

Example:

For 12 ÷ 4 = 3,

• 12 is the dividend,
  
• 4 is the divisor,
  
• and 3 is the quotient.
  

Division is essentially the reverse of multiplication. For example, if 3 × 4 = 12, then 12 ÷ 4 = 3.

Division Terminology

Understanding key division terms is important for solving problems effectively. Here are some important terms you'll need to know:

1. Dividend: The number you want to divide.
   
2. Divisor: The number you are dividing by.
   
3. Quotient: The result of the division.
   
4. Remainder: Sometimes, when dividing, there is a leftover part that cannot be evenly divided. This is called the remainder.
   

Take This Quiz:

Can You Score Well In This Math Division Test?

Division with Remainders

When dividing whole numbers, sometimes the division does not result in an exact quotient. In these cases, the division will leave a remainder. A remainder is the leftover part after performing the division.

For example:

13÷4=3 remainder 1

Here, 13 is the dividend, 4 is the divisor, and 3 is the quotient. The remainder is 1, meaning that when you divide 13 by 4, you get 3 complete groups, and there's 1 left over.

How to Express the Remainder:

• As a fraction: 3 1/4 (the remainder becomes the numerator of a fraction, and the divisor is the denominator).
  
• As a decimal: 3.25 (divide the remainder by the divisor to get the decimal equivalent).
  

Long Division

Long division is a method of dividing large numbers by breaking the process into simpler steps. Here's how you can divide using long division:

Steps for Long Division:

1. Divide: Divide the first digit of the dividend by the divisor.
   
2. Multiply: Multiply the divisor by the quotient from step 1.
   
3. Subtract: Subtract the result from step 2 from the first digit (or group of digits) of the dividend.
   
4. Bring down: Bring down the next digit from the dividend.
   
5. Repeat: Repeat the process until you've used all the digits in the dividend.
   

Let's go through a long division example:

Example:

Divide 864 by 4.

1. Divide the first digit of the dividend (8) by 4:
   8 ÷ 4 = 2.
   The first digit of the quotient is 2.
   
2. Multiply 2 (the quotient) by 4 (the divisor):
   2 × 4 = 8.
   
3. Subtract 8 from 8:
   8 - 8 = 0.
   
4. Bring down the next digit, 6. Now, divide 6 by 4:
   6 ÷ 4 = 1.
   The second digit of the quotient is 1.
   
5. Multiply 1 by 4:
   1 × 4 = 4.
   
6. Subtract 4 from 6:
   6 - 4 = 2.
   
7. Bring down the final digit, 4. Now, divide 24 by 4:
   24 ÷ 4 = 6.
   The final digit of the quotient is 6.
   

The result of 864 ÷ 4 is 216.

Take This Quiz:

Whole Numbers Quiz Questions And Answers

Division Word Problems

Let's apply division to some scenarios using word problems.

Example 1: Division with Equal Groups

• Problem: There are 24 candies, and 6 children want to share them equally. How many candies will each child get?
  
• Solution:
  24 ÷ 6 = 4
  Each child will get 4 candies.
  

Example 2: Division with Remainders

• Problem: You have 50 cookies, and you want to pack them into boxes that each hold 7 cookies. How many full boxes can you pack, and how many cookies will be left over?
  
• Solution:
  50 ÷ 7 = 7 remainder 1
  You can pack 7 full boxes, with 1 cookie left over.
  

Tips for Dividing Whole Numbers

Here are a few tips to make division easier:

1. Know Your Multiplication Facts: Division is the opposite of multiplication. Knowing your times tables will help you divide more quickly and accurately.
   
2. Estimate First: For large numbers, estimate the quotient by rounding the numbers to make division easier.
   
3. Check Your Work: After dividing, multiply the quotient by the divisor to check if the result matches the dividend. If there's a remainder, make sure it matches as well.
   

Take This Quiz:

Division of Whole Numbers

Practice Problems

Let's test your understanding of division with a few practice problems:

1. 18 ÷ 3 = ?
   
2. 81 ÷ 9 = ?
   
3. 100 ÷ 4 = ?
   
4. 56 ÷ 8 = ?
   
5. 75 ÷ 6 = ? (with remainder)
   
6. 144 ÷ 12 = ?