LESSON: Multiplying Decimals

INTRODUCTION

READ: Multiplying Decimals by Whole Numbers

Multiplying Decimals by Whole Numbers

Multiplication is a short-cut for repeated addition. We think about multiplication and we think about groups of numbers.

Example

4 3 12

With this example, we are saying that we have four groups of three that we are counting or we have three groups of four. It doesn’t matter which way we say it, because we still end up with twelve.

When we multiply decimals and whole numbers, we need to think of it as groups too.

Example

2(.25) = _____

With this example, we are multiplying two times twenty-five hundredths. Remember that when we see a number outside of the parentheses that the operation is multiplication.

We can think of this as two groups of twenty-five hundredths. Let’s look at what a picture of this would look like.

Our answer is .50.

This is one way to multiply decimals and whole numbers; however we can’t always use a drawing. It just isn’t practical.

How can we multiply decimals and whole numbers without using a drawing?

We can multiply a decimal and a whole number just like we would two whole numbers. First, we ignore the decimal point and just multiply. Then, we put the decimal point in the product by counting the correct number of places.

Example

4(1.25) = _____

Let’s start by multiplying just like we would if this was two whole numbers. We take the four and multiply it with each digit in the top number.

Our work isn’t finished yet. We need to add the decimal point into the product. There were two decimal places in our original problem. There needs to be two decimal places in our product.

This is our final answer.

WATCH: Multiplying Decimals by Whole Numbers

WATCH: Multiplying Decimals Example

READ: Multiplying Decimals Using Area Models

Multiply Decimals by Decimals Using Area Models (hundredths grid)

Let’s start by thinking of a decimal in terms of a picture. We can use a hundreds grid to represent the hundredths of a decimal.

0.3 = 0.30 = 30 hundredths

Shade 30 squares green because we are looking at 30 out of 100 or 30 hundredths.

Let’s say that that is our first decimal. We are going to multiply it with another decimal. Let’s say that we are going to multiply .30 .40.

Here is a visual picture of what .40 or 40 hundredths looks like.

0.4 = 0.40 = 40 hundredths

Shade 40 squares yellow.

Now we have two visuals of the decimals that we are multiplying. If we put them both together, then we can see what it would look like to multiply these two decimals together.

Notice that the overlapping part is the product of this problem. Our answer is .12 or 12 hundredths.

How can we multiply two decimals without using a hundreds grid? One of the ways that we can do it is to work on it just like we did when we multiplied decimals and whole numbers together.

• First, we ignored the decimal point and multiplied just like it was two whole numbers that we were multiplying.
• Second, we counted our decimal places and inserted the decimal into the product when we had finished multiplying.

We can approach two decimal multiplication in the same way.

Example

1.3 .24 = ______

To work on this problem, let’s start by writing it vertically instead of horizontally. Then we multiply.

Example

Now that we have finished the other steps, our final step is to put the decimal point in the correct spot. To do this, we need to count the decimal places in each number from right to left. The first number has one decimal place.

1.3

The second number has two decimal places.

.24

This is a total of three decimal places that need to be placed into the product. Our final answer is .312.

WATCH: Model Multiplying Decimals by Decimals

WATCH: Multiplying Decimals by Decimals

EXAMPLE 1

EXAMPLE 2

EXAMPLE 3

CHECK Yourself! Multiplying Decimals