Common fractions and decimals

- [Instructor] What we're going to do in this video is give ourselves practice representing fractions that you're gonna 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. So 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 five into one. You could say that this is equal to one divided by five 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 'cause 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 two. So let's multiply the numerator by two as well. So 1/5, one times two 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 2/10. Now, let's do 1/4. Same idea. How could 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 four so let's see if we can do it in terms of hundredths 'cause 100 is a multiple of four. Well, to go from four to 100, you have to multiply by 25. So let's multiply the numerator by 25 to get an equivalent fraction. So one times 25 is 25. So 1/4 is equal to 25/100 and we can represent that in decimal notation as 25/100 which we could also consider 2/10 and 5/100. Now, let's do 1/2. Same exact idea. Well, 10 is a multiple of two so we can think about this in terms of tenths. So to go from two to 10, we multiply by five. So let's multiply the numerator by five as well. So 1/2 is equal to 5/10 which if you wanna represent as a decimal is 0.5, 5/10. Now, why is this useful? Well, one, you're gonna see these fractions show up a lot in life and you're gonna go both ways. If you see 2/10 or 20/100 to be able to immediately recognize, hey, that's 1/5 or 25/100, hey, that's 1/4 or 1/4, that's 25/100. 1/2 is 0.5 or 0.5 is 1/2 and it's not just useful for these three fractions. It's useful for things that are multiple 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, well, 3/5, that's just going to be three times 1/5 and I know that 1/5 is 2/10 so that's gonna be three times 2/10 which is, well, three times two is six so three times 2/10 is 6/10. So really quick, you're able to say, hey, that's 3/5 is 6/10 and you could have gone the other way around. You could have said 6/10 is equal to two times, is equal to three times 2/10 and 2/10 is 1/5. So this is gonna be equal to three times 1/5 and 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, let's say you wanted to represent, let me do it another way. 0.75 as a fraction. Pause the video, try to do it yourself. Well, you might immediately recognize that 75 is three times 25 so 75/100 is equal to three times 25/100 and 25/100 we already know is 1/4 so this is equal to three 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 75/100, that's 3/4 because 25/100 is 1/4 and now let's do, let's say we have, let's say we have 2.5 and we wanna 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 5/2. It's an improper fraction but it's a fraction. And so once again, the whole point here and you might already be familiar with the 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'd be a little bit more work. If I said, let me convert 3/5 to a decimal, well, then you would have to divide five into three. Five into three and you'd say, okay, five goes into three zero times so let's put a decimal here. Now, let's go to 30. Five goes into 30 six times. Six times five 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.