Multiply and Divide Fractions

How to Multiply Decimals

Just follow these steps:

• Multiply normally, ignoring the decimal points.
• Then put the decimal point in the answer - it will have as many decimal places as the two original numbers combined.

In other words, just count up how many numbers are after the decimal point in both numbers you are multiplying, then the answer should have that many numbers after its decimal point.

Example: Multiply 0.03 by 1.1

start with:		0.03 × 1.1
multiply without decimal points:		3 × 11 = 33
0.03 has 2 decimal places, and 1.1 has 1 decimal place, so the answer has 3 decimal places:		0.033

See the Multiplying Decimals Animations

How Does It Work?

Because when you multiply without the decimal point, you are really shifting the decimal point to the right to get it out of the way:

Original:		1 Move:		2 Moves:		3 Moves:
0.03 × 1.1		0.3 × 1.1		3. × 1.1		3. × 11.

Then we do the (now easy) multiplication:

3. × 11. = 33.

But remember, we did 3 Moves of the decimal point, so we need to undo that:

3 Moves:		2 Moves:		1 Move:		Correct
33.		3.3		0.33		0.033

Here are some more examples:

Example: Multiply 0.25 by 0.2

	start with:		0.25 × 0.2
	multiply without decimal points:		25 × 2 = 50
	0.25 has 2 decimal places, and 0.2 has 1 decimal place, so the answer has 3 decimal places:		0.050

Example: Multiply 102 by 0.22

	start with:		102 × 0.22
	multiply without decimal points:		102 × 22 = 2,244
	102 has 0 decimal places, and 0.22 has 2 decimal place, so the answer has 2 decimal places:		22.44

Common Sense

As a final check you can put your "common sense" hat on and think "is that the right size?", because you don't want to pay ten times too much for anything, nor get only one-tenth of what you need!
And that's all.

Just remember: the answer should have the same number of decimal places as are in both the numbers you are multiplying.

Dividing Decimals

Quick method: use Long Division without the decimal point,
then re-insert the decimal point in the answer.

Dividing a Decimal Number by a Whole Number

To divide a decimal number by a whole number:

• Use Division or Long Division (ignoring the decimal point)
• Then put the decimal point in the same spot as the dividend (the number being divided)
  

Example: Divide 9.1 by 7

Ignore the decimal point and use Long Division:

13 7 )91    9    7    21    21     0

Put the decimal point in the answer directly above the decimal point in the dividend:

1.3 7 )9.1

The answer is 1.3

Dividing by a Decimal Number

But what if you want to divide by a Decimal Number?
The trick is to convert the number you are dividing by to a whole number first, by shifting the decimal point of both numbers to the right:

Now you are dividing by a whole number, and can continue as normal.
It is safe to do this if you remember to shift the decimal point of both numbers the same number of places.

Example: Divide 6.4 by 0.4

You are not dividing by a whole number, so you need to move the decimal point so that you are dividing by a whole number:

move 1
6.4		64
0.4		4
move 1

6.4/0.4 is exactly the same as 64/4,
as you moved the decimal point of both numbers.

And the answer is:

64 / 4 = 16

(Note: we didn't have to reinsert the decimal point in the answer, as 64 is a whole number.)

You can see for yourself how many 0.4s make 6.4:

Example: Divide 5.39 by 1.1

Move the decimal point so that you are dividing by a whole number:

move 1
5.39		53.9
1.1		11
move 1

You are now dividing by a whole number, so you can proceed:
Ignore the decimal point and use Long Division:

049 11 )539     5     0     53     44      99      99       0

Put the decimal point in the answer directly above the decimal point in the dividend:

04.9 11 )53.9

The answer is 4.9

Animations

Have a look at these Decimal Division Animations for further help.

Lastly ...

As a final check you can put your "common sense" hat on and think "is that the right size?", because you don't want to pay ten times too much for anything, nor do you want to get only one-tenth of what you need!