How do you do these fractions?

Question

I can't comprehend them.
i understand i need to find the common denominator and my teacher told us we're only going to use 2,4,6,8,16. no longer than that but i still don't understand since some are mixed and others aren't.

Here's an example of a few I'm working out.. rephrase.. stressing on..

http://i19.tinypic.com/625yt1j.jpg

Answer 1

2 1/8 - 5/8.
As the second fraction (5/8) is bigger than the first (1/8), change 2 1/8 to 1 9/8.
Subtract the integers, and then the fractions.
Both fractions have the same denominator (8), and so you simply subtract the 5 from the 9.
1 9/8 - 0 5/8
= (1 - 0) + (9 - 5) / 8
= 1 4/8
Now reduce 4/8 by dividing the 4 into the 8, giving 1/2.
Answer: 1 1/2.

9 1/2 - 3 1/4.
= (9 - 3) + (1/2 - 1/4)
= 6 + (1/2 - 1/4).
As the factors of 4 are 2 * 2, and that contains a 2, the LCD is 4.
1/2 becomes 2/4
1/2 - 1/4 = (2 - 1)/4
= 1/4.
Answer 6 1/4.

7 7/16 - 1 5/8.
16 = 2*8, and so is the LCD.
7 7/16 - 1 5/8
= ( 7 - 1 ) + (7 - 10) /16
As the numerator of the fraction is negative, change 7 7/16 to 6 23/16.
That gives:
(6 - 1) + (23 - 10)/16
= 5 13/16.

Answer 2

17/8 - 5/8 = 17 - 5 / 8 = 12 / 8 = 3/2

For the first example, what I did was multiply 8 by 2 then add the 1 which gives 17. You have the same number on the bottomn, 8. So you can just subtract what's on the top from each other 17 - 5 = 12

then just divide twelve and 8 by four. these can be done on a calculator

Answer 3

Fractions were big news about 2,200 years ago when Ptolemy was the main astronomer. The fact that they are still around should give you a clue to the slow evolution of understanding.
I will show you the first two and you work out the others.
2&1/8=2(8)eighths+1eighth=17eights or 17/8
17/8-5/8=12/8=3/2 That's as far as you can reduce it.

9&1/2-3&1/4=(9(2)halves+1half)-(3(4)fouths +1fourth)
(18/2+1/2)-(12/4+1/4)=19/2-13/4
since 1/2=2(1/4)
38/4-13/4=25/4 That's as far as you can reduce it.

Answer 4

to get a mix to a straigh fraction (top-heavy), multiply the number by the denominator and add to the numerator:

in your example:
2 1/8 = ((2*8)+1)/8 = 17/8

then do it as normal:
17/8 - 5/8 = (17-5)/8 = 12/8 = 1 4/8 = 1 1/2

Answer 5

2 1/8 + 5/8

i give you a general receipt.

1) make denominators equal.

2 1/8 = 2 * 8/8 + 1/8 = 17 /8
5 / 8 = 5/8

so : 2 1/8 + 5/8 = 17 / 8 + 5/8 = (17+5) / 8 = 22/8

22/8 = 2 6/8 = 2 3/4