# Multiplying and Dividing Decimals Learn how to easily multiply and divide decimals in a few simple steps.

## Step by step guide to multiply and divide decimals

For Multiplication:

• Ignore the decimal point and set up and multiply the numbers as you do with whole numbers.
• Count the total number of decimal places in both of the factors.
• Place the decimal point in the product.

For Division:

• If the divisor is not a whole number, move the decimal point to the right to make it a whole number. Do the same for the dividend.
• Divide similar to whole numbers.

### Example 1:

Find the product. $$0.60 \ \times \ 0.20=$$

Solution:

Set up and multiply the numbers as you do with whole numbers. Line up the numbers: $$\begin{array}{r} &60\\ \times \!\!\!\!\!\!&20\\ \hline \end{array}$$ , Start with the ones place $$→ 60 \ \times \ 0=0$$, $$\begin{array}{r} &60\\ \times \!\!\!\!\!\!&20\\ \hline \end{array} \\ \ \ \ \ \ \ \ 0$$ Continue with other digits $$→ 60 \ \times \ 2=120$$, $$\begin{array}{r} &60\\ \times \!\!\!\!\!\!&20\\ \hline \end{array} \\ \ \ \ 1,200$$ , Count the total number of decimal places in both of the factors. $$(4)$$. Then Place the decimal point in the product. Then: $$\begin{array}{r} &0.60\\ \times \!\!\!\!\!\!&0.20\\ \hline \end{array} \\ \ \ \ 0.1200$$ $$→ 0.60 \ \times \ 0.20=0.1200=0.12$$

### Example 2:

Find the quotient. $$1.40 \ \div \ 0.2=$$

Solution:

The divisor is not a whole number. Multiply it by $$10$$ to get $$2$$. Do the same for the dividend to get $$14$$.
Now, divide: $$14 \ \div \ 2=7$$. The answer is $$7$$.

### Example 3:

Find the product. $$0.50 \ \times \ 0.20=$$

Solution:

Set up and multiply the numbers as you do with whole numbers. Line up the numbers: $$\begin{array}{r} &50\\ \times \!\!\!\!\!\!&20\\ \hline \end{array}$$ , Start with the ones place $$→ 50 \ \times \ 0=0$$, $$\begin{array}{r} &50\\ \times \!\!\!\!\!\!&20\\ \hline \end{array} \\ \ \ \ \ \ \ \ 0$$ Continue with other digits $$→ 50 \ \times \ 2=100$$, $$\begin{array}{r} &50\\ \times \!\!\!\!\!\!&20\\ \hline \end{array} \\ \ \ \ 1,000$$ , Count the total number of decimal places in both of the factors. $$(4)$$. Then Place the decimal point in the product. Then: $$\begin{array}{r} &0.50\\ \times \!\!\!\!\!\!&0.20\\ \hline \end{array} \\ \ \ \ 0.1000$$ $$→ 0.50 \ \times \ 0.20=0.1000=0.1$$

### Example 4:

Find the quotient. $$1.20 \ \div \ 0.2=$$

Solution:

The divisor is not a whole number. Multiply it by $$10$$ to get $$2$$. Do the same for the dividend to get $$12$$.
Now, divide: $$12 \ \div \ 2=6$$. The answer is $$6$$.

## Exercises

### Find each Product and Quotient.

1. $$\color{blue}{\begin{array}{r} &4.5\\ \times \!\!\!\!\!\!&1.6\\ \hline \end{array}}$$

2. $$\color{blue}{\begin{array}{r} &7.7\\ \times \!\!\!\!\!\!&9.9\\ \hline \end{array}}$$

3. $$\color{blue}{\begin{array}{r} &2.6\\ \times \!\!\!\!\!\!&1.5\\ \hline \end{array}}$$

4. $$\color{blue}{14.4\div 3.6}$$

5. $$\color{blue}{30.4\div 3.8}$$

6. $$\color{blue}{24.44\div 4.7}$$

1. $$\color{blue}{7.2}$$
2. $$\color{blue}{76.23}$$
3. $$\color{blue}{3.9}$$
4. $$\color{blue}{4}$$
5. $$\color{blue}{8}$$
6. $$\color{blue}{5.2}$$ 27% OFF

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