Introduction

In this lesson, you will learn about division, which is the opposite of multiplication. The word divide means to split something into parts. In math, dividing is splitting a number into equal parts. This is the opposite of multiplication which is adding a number of equal parts together.

This video illustrates the lesson material below. Watching the video is optional.

• Introduction to Division (05:08 mins) | Transcript

Division

Look at this multiplication table.

Figure 1

In multiplication, a number is added repeatedly. For example, if you have 5 and add it together 4 times, the answer is 20.

• \(5\times4=20\)

Division is the opposite of multiplication. Consider having 20 and wanting to divide it by 4, which means splitting it into 4 equal parts. How many pieces would be in each part? The answer is 5.

• \(20\div4=5\)

To visualize this, here are 20 squares. There are 4 sets of 5 because each one of these groups has 5 pieces in it.

Figure 2

Separating the 20 boxes into 4 groups is the same as saying \(20\div4\), because division is simply separating a group into equal amounts.

Factors

There can be many ways to divide the same number. Instead of dividing the group of 20 into 4 groups of 5, you could divide it into 2 groups of 10. This represents \(10\times2\), which still equals 20.

Figure 3

Similarly, if you want to divide 20 by 10, you can do that by creating 10 groups. Each group would have 2 boxes in it.

Figure 4

The numbers that you use to divide another number are called factors. Factors are different numbers multiplied to get the same value. 2 and 10 are factors of 20.

Look again at the multiplication table in Figure 1. Using the multiplication table, you can see that 16 can be divided by 1, 2, 4, 8, and 16 because \(1\times16=16\), \(2\times8=16\), and \(4\times4=16\). So, 1, 2, 4, 8, and 16 are all factors of 16.

From the example in Figures 3 and 4, you know 2 and 10 are factors of 20. 1, 4, and 5 are also factors of 20 because 20 can be divided into even groups when divided by any of these numbers. So, the factors of 20 are 1, 2, 4, 5, 10, and 20.

Any number has a factor of one and a factor of the original number because anything divided by itself equals one.

Things to Remember

• Division is the opposite of multiplication.
• A number can have multiple factors.
• Every number has at least two factors: one and the original number.

Practice Problems

1. \(3 ÷ 1 = ?\) (
   Solution

   x

   Solution:
   3
   )
2. \(35 ÷ 5 = ?\) (
   Solution

   x

   Solution: 7
   Details:
   Division is the opposite of multiplication. These two operations undo each other.
   \(35 \div 5\)
   
   The problem can be written in terms of multiplication. The missing number will solve this multiplication problem and the original division problem.
   \(5 \times {\boxed{\color{red} ?}} = 35\)
   
   The problem is solved by multiplying by \(5 \times 7\) to get 35.
   \(5 \times {\boxed{\color{red} 7}} = 35\)
   
   The division problem that includes the same numbers as the multiplication problem above, has one of its numbers in the answer.
   \(35 \div 5 = {\color{red} 7}\)
   
   The answer to 35 divided by 5 is 7.
   )
3. \(24 ÷ 4 = ?\) (
   Video Solution

   x

   Solution: 6
   Details:
   

   
   (Division #3 (00:39 mins) | Transcript)
   | Transcript)
4. \(42 ÷ 7 = ?\) (
   Video Solution

   x

   Solution: 6
   Details:
   

   
   (Division #4 (00:52 mins) | Transcript)
   | Transcript)
5. \(81 ÷ 9 = ?\) (
   Solution

   x

   Solution:
   9
   )
6. \(48 ÷ 8 = ?\) (
   Solution

   x

   Solution: 6
   Details:
   Division is the opposite of multiplication. These two operations undo each other.
   \(48 \div 8\)
   
   The problem can be written in terms of multiplication. The missing number will solve this multiplication problem and the original division problem.
   \(8 \times {\boxed{\color{red} ?}} = 48\)
   
   The problem is solved by multiplying by \(8 \times 6\) to get 48.
   \(8 \times {\boxed{\color{red} 6}} = 48\)
   
   The division problem that includes the same numbers as the multiplication problem above, has one of its numbers in the answer.
   \(48 \div 8 = 6\)
   
   The answer to 48 divided by 8 is 6.
   )

Need More Help?

1. Study other Math Lessons in the Resource Center.
2. Visit the Online Tutoring Resources in the Resource Center.
3. Contact your Instructor.
4. If you still need help, Schedule a Tutor.