11 Plus Exams Forum

Hi.

Just wondering if anyone can explain to me please how to multiply decimals.

have seen lots of questions in Bond Assessment papers where it says e.g What's 0.1 x 0.1 or what's 0.2 x 0.1 or similar

Can anyone help please?

thanks

pp1 wrote:Hi.

Just wondering if anyone can explain to me please how to multiply decimals.

have seen lots of questions in Bond Assessment papers where it says e.g What's 0.1 x 0.1 or what's 0.2 x 0.1 or similar

Can anyone help please?

thanks

Not sure if this is the "official" way taught in schools, but the way I think of multiplying decimals in my head is as follows.

Firstly remember that the actual numbers in the answer will be the same as for an equivalent non-decimal multiplication (e.g. 2 x 1). Its just the decimal point that you have to make sure is in the right place.

Take your example 0.1 x 0.1.

0.1 x 1 = 0.1 (obviously)

So 0.1 x 0.1 will be 10 times smaller = 0.01.

Similarly 0.2 x 0.1 = 0.02.

Or for a slightly harder example, 0.7 x 0.005.

0.7 x 5 = 3.5
so,
0.7 x 0.005 = 0.0035

thank you so much!

Let's say the question is 0.5 x 0.3

I always went about it this way - first ignore the decimals. Concentrate on 5x3 = 15. Then, look to see how many digits are to the right of the decimal in the question. The same number need to be to the right of the decimal in the solution. In the example, there are two digits to the right of decimal (0.5 is one, 0.3 is another). This means the solution must have two digits to the right - 15 becomes 0.15, which is the solution.

Sometimes you need to add zeroes: think of 0.05 x 0.03. This time there are four digits to the right of decimals. 15 then becomes 0.0015 - four digits to the right.

0.5 x 0.04 -> 5x4 = 20. Three digits to the right, so 20 becomes 0.020, which would be written as 0.02.

1.5 x 0.5 -> 15x5 = 75. Two digits to the right, so 75 becomes 0.75.

I don't know if this is the "official" way, but it is the way I figured it out and taught my son!

Ditto, again same frowned upon way as above, but we count the zeros in the given question numbers and move the decimal the same number of places left in our non decimal answer.
He does know about tenths and hundredths too, just make sure they are completely competent at place value before taking short cuts.

For simple decimals like 0.5, 0.1 etc it is also worth them understanding that multiplying by 0.5 just means "a half" or multiplying by 0.1 means "a tenth" etc.

So if you had say 0.5 x 0.04, the quickest and easiest way is to just think of it as a half of 0.04, which they should immediately be able to see is 0.02, rather than going round the houses multiplying 5 x 4 and then counting the number of decimal places or zeroes to put back in.

Use the knowledge of place value.

Start by asking simple questions, such as how many 0.2 in 1.2?

then use the reverse 0.2 x 6 = 1.2

Then, use a whole number multiplied by a decimal first to enable DC to see that the numbers get smaller. Count these out if necessary.

Once the concept of multiplying decimals make a number smaller is understood, it is a simple step to understanding that each decimal makes a number even smaller.

Convert decimals to whole
Cancel out zeros
Multiply the whole
Move the decimal places (based on zeros left)

This way helps even for solving slightly complex decimal questions where it may involve decimal fraction.

For example

0.05 x 0.36 / 0.006

0.09/0.003

0.008/0.49 x 7

Hope that helps.

I taught the same method to my dd as 'JustADadHere', ignoring decimals and then adding at the end. Now that she has practiced fraction to decimals and vice versa she says she find it easy to convert them into fractions do the multiplications and then count the zeros in the denominator and add the decimal according to it e.g. two zeros meaning two numbers after the decimal.
Why she find it easier that way is beyond my understanding but whatever floats her boat.

Please do NOT teach moving decimal points - the digits move not the decimal point.

An estimate helps too to recognise the magnitude of the answer.