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Multiplying decimals: problems with tricks

In section four we caution against relying on ‘tricks’ when multiplying decimals.
7.4
MICHAEL ANDERSON: When multiplying with decimals, you might have noticed a pattern or been told about a little trick, so we’re going to explore that now. So for example, if you’re asked to multiply 0.2 by 0.3, what you could do is count the number of digits we have to the right-hand side of the decimal place in our question. So here we’ve got one digit here, the 2, and another digit here, the 3, to the right of the decimal places. What we can now do is multiply 2 and 3 together to give us 6.
37
And the trick is to remember how many decimal places were in our question, because that’s going to be the same number that’s going to be in our answer. So I’m going to put 0.06 in as my answer, because this has two values, two digits, to the right of the decimal place.
52
PAULA KELLY: OK, seems very easy. Will that always be the case?
55.1
MICHAEL ANDERSON: Well, you’ve got to be a little bit careful with this one. If we look at that example that we did in the previous step, 0.4 multiplied by 0.15, we found that the solution to this is 0.06– the same answer. But in this case, if we look at the digits to the right of the decimal place, we have one there in the 4, and then two, three there for the 1 and the 5. In our answer, we’ve only got two. So it doesn’t seem to work. But actually, what we’ve got to consider is originally we did 4 multiplied by 15.
89
Now, 4 times 15 is 60, so if we put 0 in here to make 60, that kind of rights it. It makes the trick work. So you’ve got to be really careful with this trick. If your multiplication leaves you with a multiple of 10 as a solution, then there’s always going to be that 0 there just to balance it out to make the trick work.
107.6
PAULA KELLY: OK.
One ‘trick’ which is often used when multiplying decimals is to count the number of decimals places in the question.

Example

To calculate \(0.3 \times 0.2\), start by performing the simple calculation \(3 \times 2 = 6\).
Then count the number of decimal places in the question, which is two: one in 0.2 and one in 0.3, so the answer must also have two decimal places hence the answer is 0.06.
In this case, the trick works. But if we apply the trick to \(0.4 \times 0.15\) the trick does not appear to work. The question has three decimal places but the answer only has two decimal places. In the video, Michael explains why.

Teaching resources

If you enjoy deconstructing calculation ‘tricks’ in mathematics, you might want to read ‘Nix the Tricks’ by Tina Cordone. The book looks at tricks and short cuts used in maths, explains why they are so damaging, and then provides an alternative method that teaches for understanding.

Problem worksheet

Complete questions 1 and 2 from this week’s worksheet.
As a reminder, the worksheet is found in the first unit of this week.
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Maths Subject Knowledge: Fractions, Decimals, and Percentages

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