Video: FP2P1-Q22



Video Transcript

Calculate 24.7 multiplied by 5.9.

There are a number of ways to approach this problem. However, most of them begin by imagining there are no decimal points in the question. Instead, we want to calculate 247 multiplied by 59. Let’s consider two such methods.

The first is the column method. To start, we’re going to multiply each of the digits from the number 247 by this nine. Seven multiplied by nine is 63. So we put a three in the units column and carry the six. Four multiplied by nine is 36. Then, when we add that six, we get 42. So we put a two in the tens column and carry the four. Then, two multiplied by nine is 18. When we add that four, we get 22.

Next, we’re going to multiply each of the digits from the number 247 by this five. This isn’t really five though; it’s 50. So we put a zero in the units column to show that every answer is gonna be 10 times bigger than we expect. Seven multiplied by five is 35. So we put a five in the tens column and carry the three. Four multiplied by five is 20. And then, when we add that three, we get 23. And two multiplied by five is 10. 10 plus two is 12.

Next, we’re going to add these two numbers. Three plus zero is three, two plus five is seven, two plus three is five, two plus two is four, and one by itself is just one. So we’ve worked out that 247 multiplied by 59 is 14573. We need to use this to work out 24.7 multiplied by 5.9.

Now, in fact, 24.7 is 10 times smaller than 247 and 5.9 is 10 times smaller than 59. So to work out the answer, we can divide our answer of 14573 by 10 and then by 10 again. This is actually the same as dividing by 100. And when we divide by 100, we move all of the digits two spaces to the right. This means that 24.7 multiplied by 5.9 is 145.73.

Now, there is a shortcut for this final step. It involves counting the number of digits in our question that are after the decimal point. We have a total of one, two digits in the question that are after the decimal point. We need to, therefore, make sure that there are two digits after the decimal point in our answer; that’s 145.73.

Let’s see what this would have looked like had we used the grid method. For the grid method, we split the numbers into their component parts: their one hundreds, their tens, and their units. We then multiply each bit: 50 multiplied by 200. Well, five multiplied by two is 10. So 50 multiplied by 200 is 10000.

Next, we’ll do 50 multiplied by 40. Five multiplied by four is 20. So 50 multiplied by 40 is 2000. Five multiplied by seven is 35. So 50 multiplied by seven is 350. Nine multiplied by two is 18. So nine multiplied by 200 is 1800. Nine multiplied by four is 36. So nine multiplied by 40 is 360. And of course, nine multiplied by seven is 63.

We can then use a standard column method to add these numbers together. By doing so, once again, we can see that 247 multiplied by 59 is 14573. And using the same reasoning from earlier, that means that 24.7 multiplied by 5.9 is 145.73.

Now, it’s worth mentioning at this point that we can check the suitability of our answers by estimating. When we estimate, we round each part of the calculation to one significant figure; that’s the first number that’s not zero. The first number in 24.7 that’s not zero is two. So 24.7 rounded to one significant figure is 20. 5.9 rounds to six. 20 multiplied by six is 120.

120 is pretty close to 145.73. So it’s very likely that we’ve done our calculation correctly. If we got an estimation of say 1200, we could have assumed that our place value could have been incorrect.

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