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?

??

Here are some links to sites that will help you with fractions and simplifying:

(Broken Link Removed)

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.

Does that make sense?

In the second question, you have a box that holds 10 1/4-pound packages of tea. To find out how many half-pound packages can be made up from this box, you need to divide the total weight of the tea in the box (10 1/4 pounds) by the weight of each half-pound package (1/2 pound).

So, you divide 10 1/4 pounds by 1/2 pound:

10 1/4 ÷ 1/2 = (10 + 1/4) ÷ (1/2)

To simplify this division, you need to change the division into multiplication by taking the reciprocal of the divisor:

= (10 + 1/4) * (2/1)

Remember that 1 whole divided by a fraction is the same as multiplying by the reciprocal of the fraction.

Now, multiply the whole number by the numerators and then divide by the denominator:

= 20 + (1/4) * 2

= 20 + 2/4

Since 2/4 simplifies to 1/2, the final answer is:

= 20 1/2

So, you can make up 20 1/2-pound packages of tea from the box that holds 10 1/4 pounds of tea.

In the second question, you are given a box that holds 10 1/4-pound packages of tea. To determine how many half-pound packages can be made from this box, you need to divide the total weight of the tea by the weight of each half-pound package.

To do this, you can convert the 10 1/4-pound packages into a fraction with a common denominator of 4. It becomes 41/4, which is equivalent to 10 1/4.

Now, you divide this fraction by 1/2, which represents the weight of each half-pound package. Dividing fractions requires flipping the second fraction (1/2) and multiplying. So, you have (41/4) * (2/1).

Multiplying the numerators together gives you 82, and multiplying the denominators together gives you 4. So, the result of the multiplication is 82/4.

To simplify this fraction, you can divide both the numerator and the denominator by their greatest common divisor, which in this case is 2. Dividing 82 by 2 gives you 41, and dividing 4 by 2 gives you 2. Simplifying the fraction 41/2 gives you 20 1/2.

Therefore, the answer is 20 1/2 half-pound packages of tea that can be made from the box that holds 10 1/4-pound of tea.