Converting units of time
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How many hours are in 549 minutes? And we can write it as a decimal or a fraction. So essentially, we're going to take 549 minutes and divide them into groups of 60. Why 60? Because we know that one hour is equal to 60 minutes. So it's essentially saying, how many groups of 60 minutes can we divide 549 into. Or another way of thinking about that is, well, what is 549 divided into groups of 60. This is how many hours we're going to have. So let's do that. Let's take 549 and divide it by 60. So let's see, 6 goes into 54 9 times. So 60 is going to go into 540 9 times. We're going to have a little bit left over. So we have 9 times 60 is 540. We subtract. We have 9 left over. And now let's see, we have a little left over, so we're going to get a decimal. So let's put a decimal place right over here and let's throw some 0's over there. Let's bring down a 0. So we bring down a 0. 60 goes into 90 1 time. 1 times 60 is 60. And we subtract. We get 30. Let's bring down another 0. And so we get to 300. 60 goes into 300 5 times. 5 times 60, 6 times 6 is 30, so 5 times 60 is 300. Subtract and we are done. So you divide 549 into groups of 60. You can divide it into 9.15 groups of 60 minutes. A group of 60 minutes is an hour. So this 549 minutes is 9.15 hours. I want to make sure that we can visualize that properly. So let's actually construct what 9.15 hours looks like. So let me draw a little line here, and on the top I'll label Hours, and on the bottom I'll label Minutes. So this is 0 hours, 0 minutes. And now we have 1 hour, which is 60 minutes. Now we have 2 hours, which is 120 minutes. Then you have 3 hours, which is 180 minutes. Then you have 4 hours, which is 240 minutes. 5 hours is 300 minutes. 6 hours is 360 minutes. 7 hours, I might be running out of space, is for 420 minutes. Let me copy and paste this someplace where I have more real estate. So let me clear that. And then let me paste that someplace where I don't run into my other math that I did. All right. So then you have 8 hours is 480 minutes. And then you have 9 hours. Notice, I'm just adding 60 minutes every time. 9 hours is 540 minutes. Or another way you could think about it is, well, if each hour is 60, 9 times 60 is 540. And we don't want to go to just 540. We have another 9 left. So then we have to go another 9 minutes to go to 549. So you have 9 minutes left over. So another way of thinking about this, is that 549 is 9 hours. And then you have 9 minutes left over. And 9 minutes is what fraction of an hour? Well, 60 minutes is a whole hour. So 9 minutes is 9/60 of an hour. So you could write it this way. It's 9 and 9/60 hours. Or we could write this as an equivalent fraction. 9/60 is the same thing if we divide the numerator and the denominator by 3, is the same thing as 3/20. So we could write this as 9 and 3/20. And 3/20, well we could figure out what that is going to be. Let's see, 20 divided by 3. It's definitely going to be smaller than 1, because 3 is smaller than 20. So let's throw some 0's on here. 20 doesn't go into 3, but it does go into 30 1 time. 1 times 20 is 20. Subtract, we get a 10. Bring down a 0. 20 goes into 100 5 times. 5 times 20 is 100. And we are done. So notice, 3 over 20 is the exact same thing. So 9 and 3/20 is the exact same thing as 9 and 15/100. These are all equivalent answers.