How To Add Large Fractions

divide. simplify the answer and writeas a mixed number. and we have 2 and 1/4 dividedby 1 and 3/4. so the first thing we want todo since both of these are mixed numbers is toconvert them both

How To Add Large Fractions, into improper fractions. so let's start with 2 and 1/4. so we're still going to have4 in the denominator, but instead of 2 and 1/4,remember, 2 is the

same thing as 8/4. so we have 8/4, and thenwe have another 1/4. that gives us 9/4. or another way to come up withthis 9, you take 4 times 2, which is 8, plus 1. that gives you 9. and then the 1 and 3/4,same process. you're going to have 4 in thedenominator, and then the numerator is going to be 4 times1, which is 4, plus 3,

which is 7. so this is the exactsame problem here. 2 and 1/4 divided by 1 and 3/4is the same thing as 9/4 divided by 7/4. and we saw in several videosalready that dividing by a fraction is the same thing asmultiplying by its reciprocal. so this is equivalent to-- sothese are all equivalent. this is equivalent to 9/4 timesthe reciprocal of this. we're changing the divisionoperation to a multiplication,

and we're taking the reciprocalof the 7/4. for the reciprocal of 7/4, youswap the numerator and denominator, or the topnumber and the bottom number, and you get 4/7. now, we could justmultiply these. we could just say this is 9times 4, which would be 36, over 4 times 7, which is 28,and then try to put it in lowest terms, or we could do itright now because it would be simpler.

we have a 4 in the numerator. we have a 4 in the denominator,that'll eventually be in thedenominator, so let's divide our eventual numeratorsand our eventual denominators both by 4. so you divide this 4by 4, you get 1. this 4 by 4, you get 1. so now when you multiply it, youget 9 times 1, which is 9, over 1 times 7, which is 7.

so we have our answer,but right now, it's an improper fraction. they want us to write itas a mixed number. and to figure it out as a mixednumber, we can do it in our heads now. i think we've seen thisenough times. we say how many timesdoes 7 go into 9? well, it goes into it exactlyone time, but when you take 7 into 9 one time, what doyou have left over?

well, you're going to have2 left over, right? 7 times 1 is 7, and you're goingto have 2 left over. you need 2 more to get to 9. so you're going to have 2 leftover, so this is 1 and 2/7. and we're done!