addin n subtractin fractions
find each difference
3 4/9 - 2 1/8
7 2/7 - 3 5/6
10 3/7 - 5 1/14
2 1/5 -1 4/9
5 5/36 - 4 8/9
6 1/3 - 2 2/5
2 7/18 - 1 3/4
1 5/8 - 1 1/16
2/3 + 1/6 2 - 5/7 1/4 - 1/3 x/3 + x/5 7/12 - 3/12 5/8 - 1/4 1 1/2 -2 4/5 5 7/8 + 3 5/12 3 3/8 +2 1/8 + 1 3/8
I agree with buckaroobill, that's probably the way i'd do it. however, if you have problems converting to improper fractions or you are not confident enough to work with the large numbers that result, you can actually add (or subtract) the whole numbers first, put them aside, and add the small fractons by finding the lcm and what-not and then add back the whole number to the resulting fraction. i will do a few both ways so you get a feel for it. try the rest using whichever method you feel comfortable with or whichever your professor requires and see if you can do them. if you still have problems, tell us. here goes:
3 4/9 - 2 1/8
BuckarooBill's way:
3 4/9 - 2 1/8
= 31/9 - 17/8 ..........the lcm here is 72
= 8(31) - 9(17)
..--------------
.........72
= 248 - 153
..-----------
.........72
= 95
..---
...72
= 1 23/72
note: for the second step, you convert to an improper fraction by the following method. you take the denominator of the fraction and multiply the whole number in front. then add that result to the numerator. then put that result over the original denominator.
example: 3 4/9, i take the 9 and multiply 3 which gives 27. i then add 27 to 4 which gives 31. i then put 31 over the 9 so the resulting fracton is 31/9.
example 2: 2 1/8
8*2 = 16, 16 + 1 = 17, so 2 1/8 = 17/8
example 3: any mixed fracton a b/c
a*c = ac, find ac + b. so a b/c = (ac + b)/c
My way: 3 4/9 - 2 1/8
3 4/9 - 2 1/8
= (3 - 2)..........4.............1
.....................---....-.....--- ........again the lcm here is 72
......................9............8
= 1................8(4)....-....9(1)
....................---------------
.............................72
= 1..................32....-.....9
......................------------
...........................72
= 1 23/72 ..............as we expected.
so you see here, instead of having to calculate 8(31) and 9(17) and then calculate 248 - 153, i just had to calculate 8(4) and 9(1) and then 32 - 9.
why can we do the problem this way?
well think about it. 3 4/9 is the same as 3 + 4/9. similarly 2 1/8 = 2 + 1/8
so
3 4/9 - 2 1/8
= 3 + 4/9 - (2 + 1/8) ..........expansion
= 3 + 4/9 - 2 - 1/8 .............distributive property of multiplication
= 3 - 2 + 4/9 - 1/8 .............commutitive property of addition
= (3 - 2) + (4/9 - 1/8) ........associative property of addition
anyway, that's it for the long explanation, i'll just do one more:
BuckarooBill's way: 7 2/7 - 3 5/6
7 2/7 - 3 5/6
= 51/7 - 23/6 ............the lcm here is 42
= [6(51) - 7(23)]/42
= (306 - 161)/42
= 145/42
= 3 19/42
My Way: 7 2/7 - 3 5/6
7 2/7 - 3 5/6
= (7 - 3) [6(2) - 7(5)]/42
= 4 (12 - 35)/42
= 4 -23/42 .........it seems buckaroobill's way is more efficient here, we ended up having to compute the difference of another set of fractions, o well, its practice
4 - 23/42 ..........lcm here is 42
= [4(42) - 23]/42
= (168 - 23)/42
= 145/42
= 3 19/42
good luck with the rest
Adding and Subtracting fractions is crucial to learning math. I suggest if you cannot compute these in your head it might not be a bad idea to invest in graphing calculator. It would defiantly help you out in regards to completing your homework and most teachers allow their usage on a test.
I disagree. diamond1: You don't have to be able to compute these in your head in order to be successful. And if you can't do them I don't recommend getting a calculator to do them for you. If you weren't able to understand how to do these in time for the test then you need to speak with your teacher and/or look for a tutor. Obviously we here will also be willing to help!
-Dan