At a parade 1/4 of the participants have red hair, 1/6 of them have brown hair, and the rest of the participants have black hair. What fraction of the participants have black hair?
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To find the fraction of participants with black hair, we first need to determine the fractions of participants with red and brown hair.
Given that 1/4 of the participants have red hair, it means that if we divide the total number of participants by 4, we would get the number of participants with red hair. Similarly, if we divide the total number of participants by 6, we would get the number of participants with brown hair.
Let's assume that the total number of participants in the parade is x.
So, the number of participants with red hair would be x/4, and the number of participants with brown hair would be x/6.
Now, we can add the fractions for red and brown hair. The sum of these fractions represents the total number of participants with either red or brown hair.
(x/4) + (x/6)
To add fractions, we need a common denominator, which in this case is 12.
[x * (6/6)]/4 + [x * (4/4)]/6
(6x/24) + (4x/24)
Now, we can simplify the sum of these fractions:
(6x + 4x)/24
10x/24
Finally, since the remaining participants have black hair, the fraction of participants with black hair is the complement of the fractions with red and brown hair:
1 - (10x/24)
So, the fraction of participants with black hair is (24 - 10x)/24.