# arithmetics

ok i have a few more questions. this question. If a barrel has a capacity of 100 gallons, how many gallons will it contain when it is two-fifths full? I know its 40 gallons but how and why? this one also. the number of half-pound packages of tea that can be made up from a box that holds 10 1/4 pound of tea is 20 1/2 pound. But how and why? one more five girls each ate 3 cookies from a box containing two dozen. What part of a dozen was left?
5 times 3 right? equals 15 two dozen is 24 so so 24 minus 15 is 9 but how does 9 equal 3/4?

If you take 40/100 and then simplify, it should be obvious why that fraction = 2/5. Let me know if it isn't obvious.

I think you need to re-think that second one. Ten 1/4-pound packages would equal five 1/2-pound packages, not twenty. Do you see why?

One dozen = 12. 9/12 = 3/4 after you have simplified it. Do you see it?

??

http://mathforum.org/library/drmath/sets/elem_fractions.html

http://www.themathpage.com/ARITH/arithmetic.htm
Scroll down to lessons 19 and onward.

ok i get it now. Thanks alot. But i still don't get the second question. In my book it says the answer is 20 1/2.
this is how it figures it but i don't understand. 10 1/4 lbs. divided by 1/2=41/4*2/1=20 1/2

Why are you dividing by 1/2?

Use blocks, and let each block represent one 1/4-pound package.

You have ten of them, right?

Re-arrange the blocks so you have them in pairs (2 x 1/4 = 1/2), and you'll have five pairs ... or five 1/2-pound units of tea.

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