Video: Comparing Quantities of Time Involving Fractions

Complete 2/3 of an hour _ 41 minutes using <, = or >.


Video Transcript

Complete two-thirds of an hour what 41 minutes using the symbol for is less than, is equal to, or is greater than.

In the middle of this question, we have a statement two-thirds of an hour what 41 minutes. Now, we need to complete the gap in between these two measurements, two-thirds of an hour and 41 minutes using one of the symbols that we’re given. Is two-thirds of an hour less than 41 minutes, is it equal to 41 minutes, or is it greater than 41 minutes? At the moment, both of our measurements of time are written in different units. We have hours on the left, two-thirds of an hour, and we have minutes on the right, 41 minutes. Now, in order for us to compare these, we’re going to have to convert one of them into the same unit as the other.

Now, if we were going to convert minutes into hours, we’d have to think of a fraction of an hour. It might be quite difficult to compare those fractions. So instead, let’s try to think about how to convert two-thirds of an hour into minutes. How many minutes is two-thirds of an hour worth? Let’s use this bar to represent one hour. Now, what fact do we know about the number of minutes in an hour? We know that one hour is 60 minutes. So let’s label our bar model showing the number of minutes. It still represents the same amount, but we’ve converted hours into minutes.

Now, the expression on the left-hand side of the space says two-thirds of an hour. How can we find two-thirds of 60 minutes? Well, first, we can find what one-third of an hour is worth. And we can do this by dividing 60 by three. We know that six divided by three equals two. And so, 60 which is 10 times greater divided by three will give us an answer that’s 10 times greater than two. 60 divided by three equals 20. So now, we know one-third of an hour is worth 20 minutes.

It’s now only a simple step for us to realize that two-thirds of an hour is going to be worth two lots of 20 minutes. Two-thirds of an hour equals 40 minutes. We can prove this using a clock face. All the way around the clock is 60 minutes. That’s one hour. There’s our one-third of an hour, which is worth 20 minutes. And so, two-thirds of the clock face equals 40 minutes. Now that we know that two-thirds of an hour is worth 40 minutes, we can compare the two expressions using the correct symbol.

40 minutes is less than 41 minutes. So we need to use the symbol is less than in between the two expressions. We solved the problem by converting two-thirds of an hour into minutes. And then because both expressions were in the same unit of measurement, it was easy to compare them. Two-thirds of an hour or 40 minutes is less than 41 minutes.

The correct symbol is is less than.

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