At a parade, 1/4 of the participants have red hair, 1/6 of them have brown hair, and the rest have black hair. What fraction of the participants have black hair

First we need to make the fractions have the same denominator. the smallest common multiple of 4 and 6 is 12, and 1x3 = 3, and 4x3 = 12, so 3/12 of the participants have red hair. 1x2 = 2, and 6x2=12, so 2/12 of the participants have brown hair. 3+2=5, so 5/12 of the participants have red OR brown hair, and there's 7 left. therefore 7/12 of the participants have black hair.

Ok so first we need to find out how many have either red or brown hair, which is 1/4+1/6. here, we need to find a common denominator, which is 12. so we are going to multiply 1/4 by 3/3 and 1/6 by 2/2. this yields, 3/12+2/12=5/12. since the rest have black hair, we do 1-5/12 which is 7/12