How to Multiply a Decimal Number by a Whole Number

Hi, I'm Ellie, and in this video we're going to look at how you can help your pupils to multiply decimal numbers by whole numbers. We're going to look at a few examples to show the different methods that pupils could use. Now, with this first question, 1.34 multiplied by 2, the first thing I'm going to ask my pupils is, do you think we can do this using an informal method or do we need to use a formal written method? Hopefully, they should be able to spot that because we're just multiplying by two, we can easily use our knowledge of doubling to solve this question. I'm going to partition my number to demonstrate this. So I've got 1.34, which I'm going to split up into 1.0.3. Ask your pupils the value of that number. They should be able to tell you it's three tenths and 0.04. Again, they should be able to tell you that's four hundredths. Now, I'm going to double simply each one. So pupils should easily be able to tell you this. 1 times by 2 is 2 3, 10, or 0.3 times by 2 gives me 0.6 and my 400ths multiplied whoopsie, multiplied by 2 gives us 0.08. Now, they just need to add all of that together and that will give them their answer. So two ones, six tenths and eight hundreds gives me 2.68. And you can see that that's double two. Now, the good thing about writing this method out and partitioning it is that it reinforces the steps that pupils take, so eventually they don't have to write these out. They can just quickly do 1.34 multiplied by 2. Let's look at another question. 4.84 multiplied by 4. Now, again, this time, ask your pupils, do you think we need to do this using a formal method or can we use our knowledge of number facts? I would suggest that you can have a go at this using number facts and your knowledge of doubling. Again, when we multiply something by four, it's the same as doubling it and doubling it again. So again, begin by partitioning four ones, eight tenths and four hundredths. And each of those we're going to times by 4. Now, when you times by 4, it's the same as doing times by 2, then times by 2, so you can work out either way. So we could do 4 times by 4, which gives me 16, then 0.8. So that's 8 tenths. I'm going to do times by 2 is 16 tenths times by 2 again is 32 tenths, which is the same as 3.2. And then with my 4 hundreds, if I times that by 2, it would give me 8 hundreds, times by 2 again would give me 16 hundredths, which is the same as 0.16. And again we just add everything up. So we've got 16 plus my three ones here, that would give me 19. Then I've got my two tenths and my 16 hundredths here. So it's 19.36. So there's an informal method they can use again. Now let's move on to an example where you might not be best off using an informal method. So 6.73 multiplied by 7. With this, we're going to go for the written method. You really want to make sure your pupils have a very solid understanding of the place value of decimal numbers for these kind of questions. So if I set this out like this, pupils should know that they always start by multiplying these numbers together here. So we're going to do seven times by three hundredths. Always talk about the value of the digits you're using when you're doing this. So 7 times by 300ths gives me 2100ths. I'm going to put that up here, so I know that my twenty hundredths becomes 2 tenths. So 7 times 7 tenths is 49 tenths. As add my 2 tenths up there, which gives me a total of 51. You must make sure the decimal point is in the same place. We don't want moving that either way. And then six times seven, which is 42, add my five, which gives me 47. So my answer here would be 47.11. And that's how you can use a variety of methods to multiply decimal numbers by a whole number.