## How to divide fractions

Before we explain how to divide fractions, we will explain how to divide by powers of ten. If you already know how to do it then go straight to how to divide fractions.

How to Divide by powers of ten

It is easier to explain the concept of dividing by ten, once we understand how to multiply by ten. Please, if you are unsure how to do this then check out the page on how to multiply by tens before moving on. It's an absolute must.

Assuming you have read the page on multiplying numbers by 10, we can carry on with explaining how to divide by 10's.

You know that multiplying by 10 increases the number by however many zeros we are multiplying by, 10, 100, 1000 etc. Or rather its to do with the decimal places moving to the right according to however many ten's we are multiplying by.

In the same way dividing by ten's does exactly the same thing, only the decimal place moves to the left.

For example

60÷10=6

Or rather, thinking about where the decimal place is, if we write 60.0 instead of 60. Remember 60 is just the same as 60.0

60.0÷10=6.0

Dividing by 10 means the decimal place has moved 1 place to the left.

Do we need the .0 at the end?

How to divide by 100

What do we do when we divide by 100? How many places to the left does the decimal move?

60÷10=0.6

Its moved 2 places to the left.

After we put the dot in at the front, we can add the zero that comes before it.

We don't need the zero's at the end, so we can rub them out.

There is no better way to see how this works than with some more examples.

Examples

a. 60÷1000=

b. 60÷100=

c. 60÷10=

d. 60÷1=

Answers are at the bottom of the page. Can you spot the pattern? The decimal place moves according to how many zeros there are.

How to Divide Fractions

This part now explains how we divide fractions. Remember 0.1 is a decimal, but as a fraction its written as 1/10.

Forgot how to do that? Then to find out more on how to convert fractions into decimals, go to this link (will be uploaded soon).

e. 60÷0.1=600 (decimal place moves 1 place to the right)

f. 60÷0.01=6000 (decimal place moves 2 place to the right)

g. 60÷0.001=60000 (decimal place moves 3 place to the right)

You can choose to understand how to divide fractions by spotting the pattern above using decimal places, or there are 2 other ways to explain this.

Method 1

Take 60÷0.1=600 for example. What does 0.1 mean as a fraction? 1 tenth or written as a fraction 1/10.

So we have 60 divided by 1 tenths, or 60÷1/10=600. If we imagine 60 blocks. We want to divide each piece into tenths.

To get our answer we count how many little pieces we have. We would end up counting 600 little pieces.

No disrespect, if you did not know how to do this, but this is a fairly easy example (dividing by a tenth). What happens when we divide by 1/2 or 3/4 or 15/65?

This is where method 2 come in. This is the more mature mathematical explanation.

Method 2

Example 1

4÷1/2=8

Just looking at the above example, I am sure you can work out how to do that. But just incase you can't, we have explained it using pictures.

To divide by a fraction we change the divide sign into a multiplication sign and turn the fraction upside down (switch the numbers).

4÷1/2=? ⇒ 4×2/1=8

Example 2

4÷2/3=? ⇒ 4×3/2=6

Or if you want to do the math for this

4×3=12

12÷2=6

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Answers:a. 0.06 (decimal place moves 3 place to the left)

b. 0.6 (decimal place moves 2 place to the left)

c. 6 (decimal place moves 1 place to the left)

d. 60 (decimal place moves 0 places)

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