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Video: Calculating Percentages in Word Problems

Tim Burnham

If a team won 0.564 of the games it played, determine the percent of the games they lost or drew.

03:45

Video Transcript

If a team won nought point five six four of the games it played, determine the percent of the games they lost or drew.

Well in this question, nought point five six four is the proportion, out of one, of the games that the team won. Now if you don’t win a game, you either lose it or draw it. So the lost or draw must be the rest of the games. And given that one represents the proportion of all of the games that they’ve played, the proportion they lost or drew must be one minus nought point five six four. Let’s look at two different ways of calculating one take away nought point five six four.

First, let’s think about one point zero zero zero minus nought point five six four. Okay, let’s look at the first column on the right there, zero take away four. Well I can’t do that, so I’m gonna need to borrow one from the next column. Ah, but that’s a zero so I can’t borrow one from there, so I borrow one form the next column. And I can’t borrow one from there cause that’s a zero, so I’ll have to borrow one from the next column. So that makes that a zero, and I’ve borrowed one from here. Now I’ve got ten in the tenths column. So what I can do is borrow one from there, which leaves me with nine in the tenths column and ten in the hundredths column. Now I can borrow one from there, from those ten hundredths for my thousandths column. Right, now we’re in business. Ten minus four is six. Nine minus six is three, and nine minus five is four. And then I’m gonna put my decimal point, and zero minus zero is nothing. So the answer is: Zero point four three six.

Now let’s take an alternate approach. Let’s consider these two numbers on the number line. What’s the difference between nought point five six four and one? Well if I add nought point nought nought six, then I’m gonna get four plus six in this column, which is gonna round me up to nought point five seven. And if I now add nought point nought three, then I’m going to add one to this seven hundredths to make it nought point six. And then lastly, to get from nought point six all the way up to one, I need to add nought point four. So to go from nought point five six four up to one, I needed three steps. Nought point nought nought six, which took me up to nought point five seven. Another nought point nought three, which took me up to nought point six. And then another nought point four, which took me up to one. So if I add those three steps together, nought point four plus nought point nought three plus nought point nought s- nought six is nought point four three six. So I get the same answer, but I’ve looked at it in an entirely different way.

So if all of this carrying business over here confuses you and you can visualise these steps towards one a bit more easily, then use that method. But if you’re happy with the carrying method, then maybe not having to do the drawings might be easier. That first method might be quicker for you.

Either way, the proportion of games that they lost or drew is nought point four three six. But we need to determine this as a percent of the games they lost, not just as a proportion out of one. Now percent means out of a hundred, so nought point four three six is out of one and we want to get the answer out of a hundred. We need to multiply this by a hundred in order to get our answer. Now nought point four three six times a hundred is forty-three point six.

So our answer is: Forty-three point six percent of games were lost or drawn.