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Video: Solving Word Problems by Multiplying a Decimal Number by Another

Tim Burnham

A grizzly bear can run up to 46.93 feet per second. Determine how far it can run in 3.1 seconds.

05:33

Video Transcript

A grizzly bear can run up to forty-six point nine three feet per second. Determine how far it can run in three point one seconds.

Well if it can run forty-six point nine three feet in every one second, if it’s doing that for three point one seconds, then it’s going to be three point one times forty-six point nine three feet that it covers in that time.

So the calculation I’m doing is forty-six point nine three times three point one or three point one times forty-six point nine three, doesn’t matter which way round you do it. But look all these decimal points are a little bit worrying, so I’m gonna rewrite that calculation slightly differently.

Forty-six point nine three is four thousand six hundred and ninety-three divided by a hundred, and three point one is thirty-one divided by ten. So look, the calculation I’m gonna do is four thousand six hundred and ninety-three times thirty-one, and I’m gonna take that answer and divide it by a hundred times ten or a thousand.

So let’s write this calculation out here, four six nine three times thirty-one. So I’ve just written in the place value of each of those digits. That might help us when we’re talking about this calculation. And I also want us to think about thirty-one. Thirty-one is thirty plus one so four thousand six hundred and ninety-three times thirty-one is the same as four thousand six hundred and ninety-three times thirty plus four thousand six hundred and ninety-three times one. So that’s how I’m gonna do this calculation.

Let’s start off with one times four thousand six hundred and ninety-three. One times three is three; one times nine is nine; one times six is six; and one times four is four. So I’ve done one time four thousand six hundred and ninety-three. Now I need to do thirty times four thousand six hundred and ninety-three. Now that’s the same as three times four thousand six hundred and ninety-three, but I’d need to multiply the answer by ten to make it thirty times. So when I multiply numbers by ten, I move all of my digits to the left one and I’m ending it up with a zero on the end. So let’s do the calculation now: three times three is nine; three times nine is twenty-seven.

That means I can write as seven in the next column and carry two over to the next column. Next, I’m doing three times six. Well three times six is eighteen plus this two that I’ve got here makes twenty, which means I can write a zero in this column and carry two over to the next column, which will be my ten thousands column.

Now we’ve got to do three times four. Well three times four is twelve plus the two we’ve got here makes fourteen. So that’s a four in this column and I carry one over to my next column, but there’s no more notification to do so in fact I can carry this straight up here, no worries.

And that one is gonna appear in the hundred thousands column. So thirty times four thousand six hundred and ninety-three turns out to be one hundred and forty thousand seven hundred and ninety. Now I need to add these two things together.

But before I do that I’m just gonna roll another line under there just so that all my carrying that went on down here isn’t confused as part of my next calculation. So what I’m gonna do is add three and zero to make three. Nine and nine is eighteen, so I’m gonna put eight in this column and I’m gonna carry ten over to the next column. Six and seven is thirteen plus the one that I carried over makes fourteen, so that’s a four in this column and carry the ten over to the next column. Four and zero is four plus the one I carried over makes five. Now I’ve just got a four and a one, so thirty-one times four thousand six hundred and ninety-three is a hundred and forty-five thousand four hundred and eighty-three.

So I’ve done that part of the calculation, but now I need to divide my answer by a thousand in order to get the answer to the actual question. And a hundred and forty-five thousand four hundred and eighty-three divided by a thousand is a hundred and forty-five point four eight three.

And remember that our units were feet; it’s feet per second that he was running, and he was running for or she was running for three point one seconds. So the answer is a hundred and forty-five point four eight three feet.

And when you’re doing these questions, it’s always worth just quickly checking your answer roughly by guessing the kind of scale of the answer you were expecting. So in case you divided by a thousand when you meant a hundred or you divided by ten when you meant a thousand and so on. So roughly speaking, forty-six point nine three feet well if we round that to one significant figure, that’s just fifty feet.

And three point one seconds to one significant figure is just three seconds, so we were thinking that the answer’s gonna to be roughly fifty times three. So we were expecting our answer to be around about a hundred and fifty, maybe a little bit more maybe a little bit less. And in fact that’s what it is, around about a hundred and fifty. So we think we’ve probably got the right answer.