SOLUTION: i have a problem on my homework math that says Matt split a circle into 12 equal parts and shaded 2 of them. mark split a congruent circle into 3 equal parts and shaded 2 of them.

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Question 297578: i have a problem on my homework math that says
Matt split a circle into 12 equal parts and shaded 2 of them. mark split a congruent circle into 3 equal parts and shaded 2 of them. what is the difference between the fraction that mark's represents and the fraction that Matt's circle represents?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
When you shade 2 parts out of 12 parts in the circle, the shaded part is 2/12 of the circle.

When you shade 2 parts out of 3 parts of the same circle ( or a congruent circle), the shaded part is 2/3 of the circle.

You can compare the fractions if the denominators are the same.

If you multiply the numerator and the denominator of a fraction by the same number, then the value of the fraction remains the same.

1/2 = 2/4 = 3/6 = 4/8 = 5/10 = 6/12

In your problem:

2/3 = 4/6 = 6/9 = 8/12

2/3 is the same fraction as 8/12.

Matt split his circle into 12 equal parts and shaded 2 of them.

Matt's fraction is 2/12.

Mark split his circle into 3 equal parts and shaded 2 of them.

Mark's fraction is 2/3 which is the same as 8/12.

Mark's fraction is 4 times the size of Matt's fraction.

8%2F12+=+%284%2A2%29%2F12+=+4+%2A+%282%2F12%29

To compare fractions, it helps to get the fractions to have the same denominator.

In order to change the denominator of a fraction, you would multiply the numerator and the denominator by the same factor (the number 4 in this example).

2%2F3+%2A+4%2F4+=+8%2F12

In order to change it back, you would divide the numerator and the denominator by the same factor that you multiplied them by (the number 4 in this example).

%288%2F4%29%2F%2812%2F4%29+=+2%2F3

If you wish to visualize this, then the following diagram might help.


***** picture not found *****

Just pretend this is a circle rather than a dodecagon (12 sided regular polygon).

Matt shaded 2/12 of his circle. That's represented by the 2 dots in the left hand sided figure.

Mark shaded 2/3 of his circle. That's represented by the 8 dots in the right hand sided figure.

2/3 is the same as 8/12.

Each dot is 1/12.

4 dots make up 1/3 because (4*1)/(4*3) = 4/12.

8 dots make up 2/3 because (2*4*1)/(4*3) = 8/12.