Fill in the missing symbol using greater than, less than, or equal to: two-fifths of an hour is greater than less than or equal to 24 minutes.
We can’t really compare two-fifths of an hour with 24 minutes because they have different units. In order to compare, we’ll need to convert two-fifths of an hour into minutes and then we can compare minutes to minutes. We’ll start with our two-fifths. And when we see the word “of” in math, it almost always means multiplication. We can represent two-fifths of an hour by saying two-fifths times that hour.
However, we don’t really want to use an hour. We need to convert this hour into minutes. So we say how many minutes are in an hour. Instead of multiplying two-fifths times an hour, we can multiply two-fifths by 60 minutes, because there are 60 minutes in an hour.
We’ll multiply two-fifths times 60 over one. When we multiply fractions, we multiply their numerator: two times 60 equals 120. After that we multiply the denominators together: five times one equals five. So two-fifths times 60 minutes equals one hundred and twenty fifths minutes.
But that’s not very helpful. Let’s see if we can simplify 120 over five. To do that, I’m going to divide 120 by five. How many times does five go into 12? Two times. Two times five equals 10. 12 minus 10 equals two.
From there, we bring down the next digit. And then we say how many times does five go into 20. Five goes into 20 four times. Four times five is 20. When we subtract 20 minus 20, we have a remainder of zero. 120 divided by five equals 24.
So instead of saying one hundred and twenty fifths minutes, we can say 24 minutes. Two-fifths of an hour is 24 minutes. And how then does 24 minutes compared to 24 minutes? They are equal. That means two-fifths of an hour is equal to 24 minutes.