Topics
4. Multiplication and division
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AustraliaNSW
Stage 3

4.04 Short Division

Lesson
Practice
Lesson

Are you ready?

We have learned some  different strategies  to help us divide numbers, like partitioning or using an area model. Try this problem to help you remember.

Examples

Example 1

Find the value of 40\div4.

Worked Solution
Create a strategy

We halve both numbers to make it easier to divide the numbers.

Apply the idea

Divide each number by 2.

40\div 2 = 20

4\div 2 = 2

By the half and half again method we can use these results in our division.

\displaystyle 40\div 4\displaystyle =\displaystyle 20 \div 2Use the results from halving
\displaystyle =\displaystyle 10Divide 20 by 2
Idea summary

To make a division easier, we can divide both numbers by 2.

We can also think of dividing by 4 as dividing by 2 twice.

Short division

This video shows how a short division algorithm can be used to solve division problems, with trading, remainder and a zero in the answer. An estimate also helps to check the reasonableness of the answer.

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Examples

Example 2

Find the value of 856 \div 8.

Worked Solution
Create a strategy

Use the short division algorithm.

Apply the idea
856 divided by 8 using short division. Ask your teacher for more information.

Set up the algorithm.

856 divided by 8 using short division. Ask your teacher for more information.

8 goes into 8 once, so we put a 1 in the hundreds column.

856 divided by 8 using short division. Ask your teacher for more information.

8 goes into 5 zero times with 5 remaining, so we put a 0 in the tens column and carry the 5 to the units column.

856 divided by 8 using short division. Ask your teacher for more information.

8 goes into 56 seven times, so we put a 7 in the units column.

856 \div 8 = 107

Idea summary

When you are dividing, you always start with the digit that is farthest to the left. If you get to a digit that you can't divide into, make sure you put a placeholder zero in the answer, before moving to the next digit.

Outcomes

MA3-6NA

selects and applies appropriate strategies for multiplication and division, and applies the order of operations to calculations involving more than one operation

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