# 7.06 Multiply decimals by single digit numbers

Lesson

We have looked at  visual models for multiplying whole numbers  in previous lessons. Let's look to an area model as a review.

### Examples

#### Example 1

Let's use the area model to find 38\times7.

a

Fill in the areas of each rectangle.

Worked Solution
Create a strategy

For each rectangle, use the formula \text{Area} = \text{length} \times \text{width}.

Apply the idea

Filling in the rectangle, we get:

b

Find the sums of each column.

Worked Solution
Create a strategy

Add the areas of each column using a place value table.

Apply the idea

We can add the numbers in the first column using a vertical algorithm:

\begin{array}{c} &&{}^11&5&0 \\ &+&&6&0 \\ \hline &&2&1&0 \\ \hline \end{array}

We can add the numbers in the second column using a vertical algorithm:

\begin{array}{c} &&4&0 \\ &+&1&6 \\ \hline &&5&6 \\ \hline \end{array}

c

What is the total area of the rectangles?

Worked Solution
Create a strategy

Add the areas of the two rectangles in a vertical algorithm.

Apply the idea

\begin{array}{c} &&2&1&0 \\ &+&&5&6 \\ \hline &&2&6&6 \\ \hline \end{array}

The total area is 266. So 38\times 7=266.

Idea summary

We can use area models to multiply two-digit numbers.

## Multiply decimals by single digit numbers

This video looks at using visual models for multiplying decimals.

### Examples

#### Example 2

Use the area model to find 4\times1.209.

a

Fill in the areas of each rectangle.

Worked Solution
Create a strategy

For each rectangle, use the formula \text{Area} = \text{length} \times \text{width}.

Apply the idea

For the second rectangle we need to multiply 0.2 by 4. So we can first multiply 2 by 4 then add the decimal point so that the answer has the same decimal places as the question.

We can use the same strategy for the last rectangle:

Filling in the rectangles, we get:

b

What is the total area of all three rectangles, and the answer to 4 \times1.209?

Worked Solution
Create a strategy

Add the areas of each rectangle found in part (a) using a place value table.

Apply the idea

Write each area in a place value table. Use 0s as placeholders.

So the total area is 4.836, which is also the answer to 4 \times1.209=4.836.

Idea summary

We can use area models to multiply a decimal by a whole number.

## Multiply decimals to thousandths by single digit numbers

This video uses the vertical algorithm and a couple of simple methods to check our answers for reasonableness. While this doesn't always tell us our answer is correct, it can definitely help us check our decimal place is in the correct spot.

### Examples

#### Example 3

We want to find 6\times 7.003.

a

First, choose the most reasonable approximation for 6\times 7.003.

A
80
B
42
C
4
Worked Solution
Create a strategy

Round the decimal to the nearest whole number, then find the product.

Apply the idea

7.003 to the nearest whole number is 7.

The product of 6\times7 is 42. So the correct answer is option B.

b

Worked Solution
Create a strategy

Multiply the numbers together as whole numbers first then insert the decimal point.

Apply the idea

Ignore the decimal point and multiply the numbers together as whole numbers in a vertical algorithm.

\begin{array} {c} &&7&0&{}^10&3 \\ \times &&&&&6\\ \hline &4&2&0&1&8& \\ \hline \end {array}

There are 3 decimal places in 7.003. So we will insert the decimal point so that there is 3 decimal places in our answer to get: 6\times7.003=42.018

Idea summary

Whichever method we use to multiply decimals, the most important thing is to remember that we don't need to learn any new processes at all. The value of the digits change, but the way we solve the problem doesn't.

### Outcomes

#### VCMNA215

Multiply decimals by whole numbers and perform divisions by non-zero whole numbers where the results are terminating decimals, with and without digital technologies