Rewriting decimals as fractions: 2.75

right 2.75 as a simplified fraction so once you get some practice here you're going to find it pretty straightforward to do but we're really gonna think through it and get the intuition for why this makes sense so if we were to write this down the two that literally just represents 2/1 so I'll just write it down like that then we have the seven in the MU that in another color we have a seven one place to the right of the decimal it's in the tenths place with a ths at the end at tenth place so it literally represents seven over ten and then finally we have the five in the hundredths place so it represents five over 100 now if I want to write this as a simplified fraction or really as a mixed number I have to merge these fractional parts right here and to add two fractions you have to have a common denominator and to figure out the common denominator you just have to think about the least common multiple of ten and a hundred and that's 100 they 100 is divisible by both 110 so let's get this 10 to be a hundred so we can do that by multiplying it by 10 so when you multiply something by 10 you add a zero at the end of it but you can't just do that to the denominator we also have to do that to the numerator so we multiplied the denominator by 10 let's also multiply the numerator by 10 7 times 10 is 70 or 70 or 100 it's the exact same thing as 7/10 now we can add these two what is 70 plus 5 70 plus 5 is 75 and our denominator is 100 so this can be re-written as 2 + 70 75 hundredths and we saw that in the last video you would read this as 2 and 75 hundredths now we aren't in a completely simplified fraction yet because 75 and a hundred have common factors and the largest number that goes into both if you're familiar with quarters is a twenty five twenty three quarters is 75 cents four quarters is 100 cents or four quarters is a dollar so let's me divide both of them by 25 so 75/25 is three and a hundred divided by 25 is four so as a simplified mixed number this becomes 2 and 3/4 and after you do a lot of practice here and you just see a lot of numbers like this will be almost second nature for you to say Oh 2.75 is the same thing as 2 and 75 hundredths is the same thing as 2 and 3/4