 # 4.04 Short Division

Lesson

## Ideas

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.

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.

### Examples

#### Example 2

Find the value of 856 \div 8.

Worked Solution
Create a strategy

Use the short division algorithm.

Apply the idea

Set up the algorithm.

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

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.

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