Understanding decimal multiplication
About this video
The video uses a known whole-number product to solve decimal multiplication. Since 427 x 23 = 9,821 and both 42.7 and 2.3 are 1/10 of 427 and 23, the product 42.7 x 2.3 is 9,821 divided by 10 twice, or 98.21; estimating 40 x 2 = 80 confirms it. A second example uses 527 x 63 = 33,201 and estimation (50 x 60 = 3,000) to find that 52.7 x 63 = 3,320.1.
You'll be able to
- use a known whole-number product to find a decimal product.
- explain that dividing a factor by 10 divides the product by 10.
- estimate to check where the decimal point goes.
Key words
- product
- The answer when you multiply numbers.
- factor
- One of the numbers being multiplied.
- estimate
- A quick, rounded calculation to get close to the answer.
- divide by 10
- Make a number 1/10 as big, which moves the decimal point one place to the left.
Transcript
- [Lecturer] We're told that Sydney knows that 427 times 23 is equal to 9,821. Use this understanding to help Sydney solve 42.7 times 2.3. So pause this video and think about what you think it's going to be. Alright, now let's do this together. So you might realize that 42.7 is just 427 with a decimal between the two and the seven.
Or another way to think about it is if you were to take 427 and move the decimal one to the left, you are essentially dividing by 10 to get to 42.7. And similarly, to get from 23 to 2.3, you are dividing by 10. So you're taking the product of two things. Each of them is 1/10 of each of the things in that original product.
So let's just keep that in mind for a second. But another way to think about what this would be is it's going to be the same product. We're just going to have to divide by 10 a few times, or we're going to have to move the decimal. And one way to think about it is we can estimate what, say, 40 times two is, and think about which of these is close to that.
If I were to say 40 times two, 40 times two is equal to 80. So which of these are even remotely close to 80? Well, this is 9,800-something. This is 980-something. This is 98. This one is the one that is closest to 80. Now how do we really feel good about this?
Well, as I just said, when I took 427 times 23, it equals 9,821. But to go from that to 42.7 times 2.3, you have to divide by 10 twice. So if you start with 9,821, this product over here, and if we were to divide by 10 twice, you would get two, you'd move the decimal two to the left, you'd get 98.21, which is exactly what we chose.
Let's do another example here. So we are told that Dom knows that 527 times 63 is equal to 33,201. Use this understanding to help Dom find which equation gives a product of 3,320.1. Pause this video and think about that. Well, there's a couple of ways that you can approach this.
One way to think about it is if you just estimate these products here, which of these would get you around 3000-ish? So if I were to take five times six, and once again I'm just rounding, I'm approximating it. So this is approximately five times six, which is equal to 30.
Well, 30 is nowhere close to 3,300 and something. All right, if I were to say this is approximately 50 times six, that's equal to 300. 300 is still off by more than a factor of 10. So if I were to say this is approximately equal to 50 times 60, five times 60 is 300.
So 50 times 60 is 3000. Well, this is pretty close. 3000 is not off by a factor of 10 from 3320.1. So I already like this choice. Now you can also think about it this way. To go from 527 to 52.7, you are dividing by 10. To go from 63 to 63, you aren't doing anything.
So if you're taking this product and you're getting 33,201 and you want to go to this product, well, one of these needs to get divided by 10 or the product has to get divided by 10. If you took 33,201 and divide it by 10, you are going to move the decimal one to the left, you're going to get 3,320.1.
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