pls help...fraction...: How many twelfths are equal to 5/3?

Here's another way to solve this, since you've posted this in the "Arithmetic" sub-forum and thus probably don't know any algebra yet. Take a piece of paper and cut into twelve equal parts. Now take a different piece of paper and cut it into three equal parts. How many of the "twelfths" can you glue to one of the "thirds" without any overlap? Do you fully cover the "third"? How does this physical reality relate to how many twelfths equal one third? If that many twelfths equal one third, how many twelfths equal five thirds?
 
Another way

ksdhart2 said:
Here's another way to solve this, since you've posted this in the "Arithmetic" sub-forum and thus probably don't know any algebra yet. Take a piece of paper and cut into twelve equal parts. Now take a different piece of paper and cut it into three equal parts. How many of the "twelfths" can you glue to one of the "thirds" without any overlap? Do you fully cover the "third"? How does this physical reality relate to how many twelfths equal one third? If that many twelfths equal one third, how many twelfths equal five thirds?
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Good suggestion!

Here's something that you can do quickly.
1) Make a pile of 12 pennies. Notice that each penny is one 12th of the pile.
2) Call each penny "one twelfth" instead of "one penny"
3) Separate the pile into three equal piles. Call each of these piles "one third" instead of "a pile"
4) How many "one twelfth"s are in a "one third"?
5) If I made 5 "one third" piles how many "one penny"s would I have?
6) If I made 5 "one third" piles how many "one twelfth"s would I have? (use step 2)
 
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Denis said:
n/12 = 5/3 ; solve for n
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This proportion method is used in some arithmetic classes, but, usually, I see a question mark used for the unknown number, instead of a variable. Also, the language of "solving" is not generally used, even though that's the end result.

5/3 = ?/12

To find the unknown number, students are taught about proportion and methods like "the product of the means equals the product of the extremes" (commonly known as "cross-multiplication") or "multiply on the diagonal and divide by the number not yet used".

Using the latter instruction, we get (5×12)÷3 = 20


Another method taught involves multiplying the original fraction by a rational form of 1, where we choose a specific rational form of 1, to achieve the desired, new denominator. (When the numbers involved are small and appear in the Multiplication Table, this is the method I use most often.)

53×  ??\displaystyle \dfrac{5}{3} \times \; \dfrac{?}{?}

When we multiply the denominators, we want to get 12. By inspection, we see that 3 needs to be multiplied by 4, in order to get 12. Therefore, the rational form of 1 that we need is 4/4.

53×44=2012\displaystyle \dfrac{5}{3} \times \dfrac{4}{4} = \dfrac{20}{12} :cool:
 
And, when you feel like you understand this topic, you could try this new exercise:

How many twelfths are equal to 3/5 ? :cool:
 
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