Common fractions and decimals | Math | 4th Grade | Khan Academy

What we're going to do in this video is give ourselves practice representing fractions that you're going to see a lot in life in different ways.

So the first fraction we're going to explore is 1/5. Then we're going to explore 1/4. Then we are going to explore 1/2. So let's start with 1/5. I encourage you to pause the video and say and think about how would you represent 1/5 as a decimal.

Well, there's a bunch of ways that you could think about it. You could divide 5 into 1. You could say that this is equal to 1/5, and if you did that, you actually would get the right answer. But there's a simpler way of thinking about this. Even in your head, you could say, "Well, let me see if I can represent this as a certain number of tenths."

Because if you know how many tenths, we know how to represent that as a decimal. Well, to go from fifths to tenths, you have to multiply the denominator by 2. So let's multiply the numerator by 2 as well. So 1/5, 1 times 2 is the same thing as 2/10.

And we know how to represent that in decimal notation. That's going to be 0.2. This is the tenths place, so we have exactly two tenths. Now let's do 1/4. Same idea: how can I represent this as a decimal?

Well, at first, you might say, "Well, can I represent this as a certain number of tenths?" And you could do it this way, but 10 isn't a multiple of 4. So let's see if we can do it in terms of hundreds because 100 is a multiple of 4.

Well, to go from 4 to 100, you have to multiply by 25. So let's multiply the numerator by 25 to get an equivalent fraction. So 1 times 25 is 25. So 1/4 is equal to 25 hundredths, and we can represent that in decimal notation as 25 hundredths, which we could also consider two tenths and five hundredths.

Now let's do 1/2. Same exact idea. Well, 10 is a multiple of 2, so we can think about this in terms of tenths. So to go from 2 to 10, we multiply by 5. So let's multiply the numerator by 5 as well.

So 1/2 is equal to five tenths, which, if you want to represent it as a decimal, is 0.5. Now why is this useful? Well, one, you're going to see these fractions show up a lot in life, and you're going to go both ways.

If you see two tenths or 25 hundredths, to be able to immediately recognize, "Hey, that's one-fifth," or "25 hundredths, say that's 1/4," or "1/4, that's 25 hundredths," "1/2 is 0.5," or "0.5 is 1/2." It's not just useful for these three fractions; it's useful for things that are multiples of these three fractions.

For example, if someone said, "Quick, what is 3/5 represented as a decimal?" Well, in your brain, you could say, "What? 3/5? That's just going to be 3 times 1/5." And I know that 1/5 is 2/10, so that's going to be 3 times 2 tenths, which is, well, 3 times 2 is 6.

So 3 times 2 tenths is 6 tenths. So really quick, you were able to say, "Hey, that's 3/5 is 6/10." You could have gone the other way around. You could have said 6/10 is equal to 2 times, it's equal to 3 times 2 tenths, and 2 tenths, you know, is 1/5.

So this is going to be equal to 3 times 1/5. Once again, these are just things that you'll get comfortable with the more that you get practice. Let's do another one. Let's say you wanted to represent, what's it, you want to represent.

So let me do it another way: 0.75 as a fraction. Pause the video, try to do it yourself. Well, you might have immediately recognized that 75 is 3 times 25. So 75 hundredths is equal to 3 times 25 hundredths.

And 25 hundredths we already know is 1/4, so this is equal to 3 times 1/4, which is equal to 3/4. And over time, you won't have to do all of this in your head; you'll just recognize 75 hundredths as 3/4 because 25 hundredths is 1/4.

Now let's do, let's say we have 2.5, and we want to represent that as a fraction. Well, there's a bunch of ways that you could do this. You could say, "Well, this is five times 0.5," and that's going to be five times 1/2.

Well, that's going to be five halves. It's an improper fraction, but it's a fraction. And so once again, the whole point here is that you might already be familiar with different ways of converting between fractions and decimals.

But if you recognize 1/5, 1/4, 1/2, it's going to be a lot easier. Notice if you did it the other way around, it would be a little bit more work. If I said, "Let me convert 3/5 to a decimal," well then you would have to divide 5 into 3.

5 into 3? Okay, 5 goes into 3 zero times, so let's put a decimal here. Now let's go to 30. 5 goes into 30 six times. 6 times 5 is 30. You subtract, and then you get no remainder.

So this wasn't a ton of work, but this one, the reason why I like this one not only is it faster, but it gives you a better intuition for what actually is going on.