# 7.07 Multiply decimals by whole numbers

Lesson

Let's review a strategy for  multiplying whole numbers  .

### Examples

#### Example 1

Calculate 26\times39 by completing an area model.

a

Firstly, complete the missing values in the area model.

Worked Solution
Create a strategy

Multiply the number at the top of the column by the number on the left of the row.

Apply the idea

For the top left square:

20\times30=600

For the top right square:

6\times30=180

For the bottom left square:

20\times9=180

For the bottom right square:

6\times9=54

Filling in the squares, we get:

b

Now add the values you found in part a to calculate 26\times39.

Worked Solution
Create a strategy

Add all the values found in part (a).

Apply the idea

26 \times 39=1014

Idea summary

We can use area models to multiply two digit numbers.

## Multiply decimals by two digit numbers

This video looks at how to use the area model to multiply numbers with decimals.

### Examples

#### Example 2

Use the area model to find 47 \times 5.4.

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 top right rectangle we need to multiply 0.4 by 40. So we can first multiply 4 by 40 then add the decimal point so that the answer has the same decimal places as the question.

For the bottom right rectangle we need to multiply 0.4 by 7. So we can first multiply 4 by 7 then add the decimal point so that the answer has the same decimal places as the question.

Filling in the rectangles, we get:

b

What is the total area of the four rectangles, and the answer to 47\times5.4?

Worked Solution
Create a strategy

Add the areas of the four rectangles found in part (a).

Apply the idea

Put the numbers in a place value table using 0s as placeholders and add them, regrouping where necessary.

So the total area and the product of 47\times5.4 is equal to 253.8.

Idea summary

We can use area models to multiply decimals.

## Multiply decimals by numbers with more than one digit

This video shows how to multiply a decimal number in the hundredths by a 2 digit number, using the same processes as for whole numbers, while thinking about the placement of the decimal point.

### Examples

#### Example 3

We want to find 43\times 1.06.

a

First, choose the most reasonable estimate for 43\times1.06.

A
91
B
23
C
43
Worked Solution
Create a strategy

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

Apply the idea

1.06 rounded to the nearest whole number is 1.

The product of 43 \times 1 is 43. The best estimate is option C.

b

Worked Solution
Create a strategy

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

Apply the idea

Ignore the decimal point multiply the numbers together as whole numbers in a vertical algorithm. We first multiply 106 by 3 and then by the 4 in the tens column, and then add the results.

\begin{array} {c} &&1&0&6 \\ \times &&&4&3\\ \hline &&3&1&8& \\ + &4&2&4&0 \\ \hline &4&5&5&8 \end {array}

In 43\times 1.06 there are 2 decimal places. So we need to insert the decimal point so that there are 2 decimal places in our answer.

43\times1.06=45.58

Idea summary

When we work with decimals, we can use all of the strategies we used with whole numbers, including the area model and vertical algorithm. The important difference is the value of the digits. Digits to the right of the decimal point are fractions, so they are worth less.

### 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