Question

Whitney says that to add fractions with different denominators, you always have to multiply the denominators to find the common unit; for example:

1/4 + 1/6 = 6/24 + 4/24

Show Whitney how she could have chosen a denominator smaller than 24, and solve the problem.

Answer 1

Explanation:

You need to know what prime factorization is. Basically you split up a number into it's prime factors. Or in other words what prime numbers multiply to get this number. So say you have 36, you can split it into 2*2*3*3. This is the methodology we use.

For the fractions given we want to look at the prime factorization of the denominators. so for 4 = 2*2 and 6 = 2*3. What do we have to do to make them equal. Well, if we multiply 2*2 by 3 and 2*3 by 2 what do we get? 2*2*3 and 2*3*2 which are equal. So there's another way to get common denominators. You also have to multiply the numerators by the same numbers you multiply the denominators by. So in total you do this.

1/4 + 1/6

1/(2*2) + 1/(2*3)

(1*3)/(2*2*3) + (1*2)/(2*3*2)

3/12 + 2/12

5/12