Common fractions and decimals

what we're going to do in this videos 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 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 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 is a certain number of tenths because if you know how many tenths we know how to represent that as a decimal well they go to from 5th to 10th 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 but 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 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 five tenths which if you want to represent it as s as a decimal is zero point five five ten 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 2000s to be able to immediately recognize hey that's one-fifth or 2500 say that's 1/4 or 1/4 that's 2500 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 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 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 10 is 6 cents 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 is equal to 3 times 2 10 and 2/10 you know is 1/5 so this is going to be equal to 3 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 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 recognize 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 hundred steps 3/4 because 25 hundredths is 1/4 and now let's do let's say we have let's say we have 2.5 and we want to rep present that as a fraction well there's a bunch of ways that you could do this you could say well this is five times zero point five and that's going to be five times one half well that's going to be five halfs 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 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 6 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