# 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:

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

For Division:

1. 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.
2. 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.

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

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

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

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

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

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

• $$\color{blue}{7.2}$$
• $$\color{blue}{76.23}$$
• $$\color{blue}{3.9}$$
• $$\color{blue}{4}$$
• $$\color{blue}{8}$$
• $$\color{blue}{5.2}$$ 