 # 7.08 Division where answers are decimals

Lesson

We've previously learned  how to use a division algorithm with short division  . Let's practice this concept.

### Examples

#### Example 1

Find the value of 856\div8.

Worked Solution
Create a strategy

Use short division.

Apply the idea

Set up the short division.

8 goes into 8 once, so we put a 1 in the hundreds place at the top.

8 goes into 5 zero times with 5 remaining, so we put a 0 in the tens place at the top 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

We can use short division to divide one number by another. We start dividing at the highest place value and carry any remainders to the next place value.

## Divide a 3 digit number by a 1 digit number

Sometimes when we divide whole numbers there is a remainder, this remainder can be expressed as a decimal. This video will show us how.

### Examples

#### Example 2

Find the value of 460\div8.

Worked Solution
Create a strategy

Use short division.

Apply the idea

Set up the short division.

8 can fit into 4 zero times with 4 remaining, so we put 0 on the hundreds place at the top and carry the 4 to the tens column.

8 can fit into 46 five times with 6 remaining, so we put 5 in the tens place at the top and carry the 6 to the units column.

8 can fit into 60 seven times with 4 remaining, so we put 7 in the units place at the top.

We have run our of digits to carry the remainder to, so we need to a decimal point and a 0 in the tenths place. Now we can carry the 4 to the tenths column.

8 can fit into 40 five times with 0 remaining, so we put 5 in the tenths place at the top.

There are no more digits to divide by 8, so we know that we are finished.

460\div8=57.5

Idea summary

When dividing a whole number using short division, if we have a remainder after dividing the units place we will end up with a decimal answer.

## Short division

This video looks at short division and how to use short division when there is a remainder.

### Examples

#### Example 3

Find the value of 3653\div4.

Worked Solution
Create a strategy

Use short division.

Apply the idea

Set up the short division.

4 fits into 36 nine times with 0 remaining, so we put 9 in the hundreds place at the top.

4 fits into 5 once with 1 remaining, so we put 1 in the tens place at the top and carry 1 to the units column.

4 fits into 13 three times with 1 remaining, so we put 3 in the units place at the top.

Since we have a remainder, we add a decimal point and a 0 in the tenths place and carry 1 to the tenths column.

4 fits into 10 two times with 2 remaining, so we put 2 in the tenths place at the top.

We add a 0 in the hundredths place and carry the 2 to the hundredths column.

4 fits into 20 five times with 0 remaining, so we put 5 in the hundredths place at the top.

There are no more digits to divide by 4, so we know that we are finished.

3653\div4=913.25

Idea summary

When dividing a whole number using short division, if we have a remainder, we can add a decimal point and add 0s after the decimal point to carry the remainders to until there are no more remainders.

## Divide a 4 digit number by a 2 digit number

This video looks at how to divide by a two digit number using short division. By remembering place value, we can divide each digit, working from left to right. We move from units to tenths and so on if necessary.

### Examples

#### Example 4

Find the value of 460\div25.

Worked Solution
Create a strategy

Use short division.

Apply the idea

Set up the short division.

25 fits into 4 zero times so we put a 0 above the 4. \,\, 25 fits into 46 once, so we put 1 in the tens place at the top.

25\times 1=25 and 46-25=21 so we have a remainder of 21 which we carry to the units column.

25 fits into 210 eight times since 25\times 8 =200. So we put 8 in the units place at the top and carry 10 to the tenths column by adding a decimal point and a 0.

25 fits into 100 four times, so we put 4 in the units place at the top.

There are no more digits to divide by 25, so we know that we are finished.

460\div25=18.4

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

#### 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