LESSON: Multiplying Decimals

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 $\times$ .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 $\times$ .24 = ______

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

Example

$1.3 \\ \underline{\times \quad .24} \\ 52 \\ \underline{+ \ \ 260} \\ 312$

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.