SOLUTION: a plus 1 over 4 minus a over 6

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Question 571552: a plus 1 over 4 minus a over 6
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
a + 1%2F4 - a%2F6

Write a as a%2F1

a%2F1 + 1%2F4 - a%2F6

The LCD is 12.

The denominator of a%2F1 needs to be multiplied by 12 to become
the LCD of 12, so multiply the first fraction by red%28%2812%29%2F%2812%29%29

a%2F1red%28%2812%29%2F%2812%29%29 + 1%2F4 - a%2F6

The denominator of 1%2F4 needs to be multiplied by 3 to become
the LCD of 12, so multiply the second fraction by red%28%283%29%2F%283%29%29

a%2F1red%2812%2F12%29 + 1%2F4red%28%283%29%2F%283%29%29 - a%2F6

The denominator of a%2F6 needs to be multiplied by 2 to become
the LCD of 12, so multiply the third fraction by red%28%282%29%2F%282%29%29

a%2F1red%28%2812%29%2F%2812%29%29 + 1%2F4red%28%283%29%2F%283%29%29 - a%2F6red%28%282%29%2F%282%29%29

Multiply the numerators and the denominators in each of the the three
terms:

%2812a%29%2F12 + 3%2F12 - 2a%2F12

Now that all three fractions have the same denominator, we combine
the three numerators and write that over the LCD of 12:

%2812a%2B3-2a%29%2F12


Combine the like terms 12a and -2a and get 10a.

So the final simplification is

%2810a%2B3%29%2F12

Edwin