For your fractions above you need a common denominator then you add the two fractions together to get the total weight lost over two weeks. Once you get that amount you need to subtract that weight from 10 pounds. There two schools of thought on this
I think this is the current thinking
3 1/2 is 7/2 as an improper fraction
2 2/3 is 8/3 as an improper fraction
The least common denominator for 2 and 3 is 6
Raise the improper fractions above to equivalent fractions with 6 as the denominator
7/2 = (7*3)/(2*3) or 21/6
8/3 = (8*2)/(3*2) or 16/6
Add these two together to get the total weight lost over 2 weeks
(21 + 16)/6 = 37/6
Now subtract this from 10 but first express 10 as an improper fraction with a denominator of 6
60/6
Finally we have
(60 - 37)/6 = 23/6
Reduce the improper fraction to a mixed number by dividing 6 into 23.
3 5/6
Old School (as far as I know)
Use a common denominator of 6 to first add 3 1/2 and 2 2/3 by raising the fractions to equivalent fractions with a denominator of 6
3 1/2 = 3 3/6
2 2/3 = 2 4/6
Add these together to give the total weight lost over 2 weeks
5 7/6 reduce this to lowest terms
5 7/6 = 6 1/6
Subtract 6 1/6 from 10 by borrowing 1 as 6/6 from 10, then 10 drops to 9 and you have
9 6/6
-6 1/6
3 5/6
3 5/6 lbs still need to be lost
I don't know if both methods are still taught but they can certainly be used to check on each other. If you have any questions please send me a message.
The problem with wear on the tire tread only needs a least common denominator, its already there, only one of the fractions needs to be raised to an equivalent fraction over this least common denominator and subtracted to give the answer. Just give it a try.
