How To Add Mixed Fractions With Same Denominators

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 Mixed Fractions With Same Denominators, 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!