**Introduction**

In this lesson, you will learn how to divide by a decimal. Previously, you have worked with the dividend as a decimal, and now you will work with the divisor as a decimal. Dividing by a decimal can look difficult, but there’s actually only one simple step you need to do before you can divide by a decimal number.

### Ways to Show Division

The division symbol (**÷**) is not the only way to show division. As learned previously in the lesson about how to use Excel as a calculator, division can be symbolized with a slash (**/**) too. You may see this on some calculators as well. This course will often use the **/ **symbol to represent division.

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

**Dividing by a Decimal**

When the divisor (the number you are dividing by) has a decimal, follow these steps:

- Count the decimal places in the divisor.
- Move the decimal in the dividend as many places as you counted in the divisor. If the divisor does not have a decimal, add an extra place to the end of the number and fill it with 0. Place the decimal for your answer directly above the decimal place you counted in the dividend.
- Divide, ignoring the decimals.

**Example 1**

\(12\div1.5\)

The dividend is the original amount that you start with, in this case, 12. The divisor in this example is a decimal: 1.5. Start by counting the decimal places in the divisor.

In this example, the decimal would be moved over one space, turning 1.5 into 15. Since you had to move the decimal over one place in the divisor, you must move the decimal over one space in the dividend as well, turning 12 into 120.

\begin{align*} 12&\div 1\underrightarrow{.5} &\color{red}\small\text{Count decimal places in the divisor}\\\\ 12\underrightarrow{.0}&\div 15 &\color{red}\small\text{Move the decimal in the dividend}\\\\ 120&\div 15 &\color{red}\small\text{Divide}\end{align*}

The answer is 8.

\(12\div 1.5\) will give you the same answer as \(120\div15\). Why does this work?

**Example 2**

\(6\div2\)

\(6\div2\) is represented with the following squares.

Figure 1

If you divide the six squares into two groups, or two sets, how many would be in each set?

Figure 2

Each set has three inside of it because \(6\div2=3\).

What if you multiply both the dividend and divisor by ten? \(6\times10=60\) and \(2\times10=20\). Now, instead of \(6\div2\), you have \(60\div20\). What is the answer?

\(60\div20\) is represented with sixty squares. To divide them into twenty different sets, you want to find out how many would be in each set.

Figure 3

Notice there are 20 rows of squares. To divide by 20, you can simply select each row, making 20 sets. There are 3 squares in each set, which means \(60\div20=3\).

Figure 4

This demonstrates that as long as you multiply both dividend and divisor by the same number, in this case 10, the answer will still be the same.

Remember Example 1: \(12\div1.5\). You moved both numbers one decimal place over, making \(120\div15\). In other words, you multiplied both dividend and divisor by 10.

\begin{align*} \frac{12}{1.5} = \frac{12 \color{red}\times 10}{1.5 \color{red}\times 10} & = \frac{120}{15}\\ \end{align*}

**Example 3**

\(8.52 \div 2.13\)

- Count the decimal places in the divisor. In this case, there are two decimal places.
- Count the decimal in the dividend two places to the right. Put the decimal for the answer directly above where you stopped counting.

Figure 5

Divide as if there are no decimals

Figure 6

Thus, \(8.52 \div 2.13=4\)

**Example 4**

\(43.875 \div 2.1\)

- Count the decimal places in the divisor. In this case, there is one decimal place.
- Count the decimal in the dividend one place to the right, then put the decimal for the answer directly above where you stopped counting.

Figure 7

Divide as if there are no decimals.

Figure 8

Figure 9

Figure 10

Figure 11

Thus, \(438.75 \div 21\), rounding to the nearest hundredth, is 20.89.

**Things to Remember**

- When doing the division algorithm with a decimal in the divisor:
- Count the decimal places in the divisor.
- Move the decimal in the dividend as many times as you counted in the divisor. Move the decimal up to your answer.
- Divide.

### Practice Problems

Evaluate the following expressions:- \(54 \div 1.2 = \text{?}\) (Solution
- \(69 \div 2.4 = \text{?}\) (Solution
- \(8.4 \div 6.5 = \text{?}\) (Round your answer to the nearest hundredth.) (Video Solution
- \(24.7 \div 3.9 =\text{?}\) (Round your answer to the nearest hundredth.) (Video Solution
- \(62.5 \div 1.75 =\text{?}\) (Round your answer to the nearest hundredth.) (Solution
- \(25 \div 4.35 = \text{?}\) (Round your answer to the nearest hundredth.) (Solution

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