7.10 Story problems with multiplication or division

Lesson

Let's review how to  multiply  and  divide  with decimals.

Examples

Example 1

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

Example 2

Find the value of 92.4\div6.

Worked Solution
Create a strategy

Use short division.

Apply the idea

6 goes into 9 once with 3 remaining, so we put a 1 in the tens column at the top and carry 3 to the units column.

6 goes into 32 five times with 2 remaining, so we put a 5 in the units column at the top and carry 2 to the tenths column.

6 goes into 24 four times with 0 remaining, so we put a decimal point and a 4 in the tenths column at the top.

92.4\div6=15.4

Idea summary

We can use the vertical algorithm to multiply a decimal by a whole number. First we multiply the numbers without the decimal point. Then we include the decimal point so that the answer has the same number of decimal places as the question.

We can divide a decimal by a whole number using short division.

Decimal story problems: multiplication

This video looks at how to interpret the story problem and identify the mathematics for a problem requiring multiplication.

Examples

Example 3

A landscaper is paving a garden path with tiles that each have a mass of 7.18 kg. If he uses 7 tiles, what is the total mass?

Worked Solution
Create a strategy

Multiply the mass of the tile by the number of tiles.

Apply the idea

Ignore the decimal point and multiply the numbers togetherin a vertical algorithm.

\begin{array} {c} &&{}^17&{}^51&8 \\ \times &&&&7\\ \hline &5&0&2&6& \\ \hline \end {array}

7.18\times 7 has two decimal places, so we insert the decimal point in our answer so that it has two decimal places.

\text{Total mass} =50.26 \text{ kg}

Idea summary

If we need to work out groups of something, it means we will need to use multiplication.

Solve decimal problems: division

This video looks at how to interpret the story problem and identify the mathematics for a problem requiring division.

Examples

Example 4

A TV series goes for a total duration of 13 hours. If there are 4 episodes in the series, all of equal length, how long is each episode? Give your answer in hours.

Worked Solution
Create a strategy

Divide the number of hours by the number of episodes.

Apply the idea

4 goes into 13 three times since 4\times 3=12. So there a remainder of 1.

So each episode is 3\dfrac{1}{4} hours long. \dfrac{1}{4} as a decimal is 0.25.

So each episode is 3.25 hours long.

Idea summary

If we are sharing and amount, then we will need to use division.

Decimal problems with multiple operations

This video works through a story problem that involves division and subtraction.

Examples

Example 5

Adam was buying supplies for the new school year. He bought 5 books at \$14.82 each and a pencil case for \$6.36. How much did he spend in total?

Worked Solution
Create a strategy

Multiply the cost of each to book by the number of books bought then add the cost of the pencil case.

Apply the idea

We will first multiply the cost of each book by the number of books ignoring the decimal point.

\begin{array} {c} &{}^21&{}^44&{}^18&2 \\ \times &&&&5\\ \hline &7&4&1&0& \\ \hline \end {array}

14.82 \times 5 has 2 decimal places, so we will place a decimal point in our answer so there are 2 decimal places. This gives us: 74.10.

\begin {array} {c} &{}^17&4&.&1&0 \\ + &&6&.&3&6 \\ \hline &8&0&.&4&6\\ \hline \end {array}

Idea summary

When we have a story problem, there can be things that are not useful, so we need to make sure we find the right information.

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