Topics
4. Multiplication and division
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Australia
Year 6

4.06 Story problems

Lesson
Practice
Lesson

Are you ready?

How do we know if we need to multiply or divide in our problem? The words and the context they're used in tells us whether we are multiplying or dividing.

What words can you think of for division?

Idea summary

Here are some words that we may come across in multiplication and division problems:

Multiplication wordsDivision words
\text{groups of}\text{shared among}
\text{product}\text{distributed between}
\text{altogether} \\\text{quotient}\text{multiplied by} \\\text{shared equally}
\text{product}\text{per}

Story problems with multiplication and division

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Examples

Example 1

This year there are 2627 registered self-driving cars in the world. By the same time next year there are expected to be 9 times as many self-driving cars.

a

Which number sentence correctly describes to total number of self-driving cars registered by next year?

A
9 + 2627
B
9 \times 2627
C
9 \div 2627
D
2627 \div 9
Worked Solution
Create a strategy

The word "times" means multiply.

Apply the idea

We need to multiply 2627 by 9. So the correct answer is option B: 9 \times 2627.

b

Find the total number of self-driving cars registered by next year.

Worked Solution
Create a strategy

Perform the multiplication from part (a).

Apply the idea

We can use a vertical algorithm. The working is shown below:\begin{array}{c} &&&\text{}^5 2&\text{}^2 6&\text{}^6 2&7 \\ &\times &&&&&9 \\ \hline &&2&3&6&4&3\\ \hline \end{array}

There will be 23\,643 self-driving cars registered by next year.

Idea summary

If a story problem uses the word "times" then we need to multiply.

Story problems with larger numbers

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Examples

Example 2

A real estate agency has portfolio of 6 properties that it manages. The total value of the properties is \$3\,518\,400.

If each property is valued equally, what is the cost of one of the properties in the portfolio?

Worked Solution
Create a strategy

We need to divide the total value of the portfolio by the number of properties by using division algorithm.

Apply the idea

The working and steps are shown below:

  • 6 goes into 3 zero times with remainder 3.

  • 6 goes into 35 five times with remainder 5.

  • 6 goes into 51 eight times with remainder 3.

  • 6 goes into 38 six times with remainder 2.

  • 6 goes into 24 four times.

  • 6 goes into 0 zero times.

3,518,400 divided by 6 in a short division algorithm. Ask your teacher for more information.

The cost of one of the properties in the portfolio is \$586\,400.

Idea summary

Sometimes there may be pieces of information that are not relevant to our problem. How do we know which things we need? The best thing to do is to highlight the keywords, and then think about what they are suggesting, these are like the clues to the puzzle.

Identifying the clues helps us work out how to write out our number problem. We can also look for pieces of information that may not be useful, and ignore those.

Outcomes

AC9M6N09

use mathematical modelling to solve practical problems, involving rational numbers and percentages, including in financial contexts; formulate the problems, choosing operations and efficient calculation strategies, and using digital tools where appropriate; interpret and communicate solutions in terms of the situation, justifying the choices made

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