Question

Darcy is trying to add together 2/5 and 3/8. Her first step is to rewrite the fractions using their lowest common denominator. What is the lowest common denominator of 2/5 and 3/8?

1) 5
2) 8
3) 10
4) 15

Answer 1

The lowest common denominator of 2/5 and 3/8 is 40 as it is the smallest number that both denominators divide into without a remainder. Hence the provided answer choices are incorrect as they do not include 40.

Step-by-step explanation:

The lowest common denominator (LCD) of 2/5 and 3/8 is the smallest number that both denominators divide into without leaving a remainder. To find the LCD, we can list the multiples of the denominators 5 and 8 to see where they first coincide. The multiples of 5 are 5, 10, 15, 20, 25, and so on, while the multiples of 8 are 8, 16, 24, 32, and so on. The first common multiple that we encounter in both lists is 40. So the lowest common denominator of 2/5 and 3/8 is indeed 40, which is not one of the options provided in the question. In order to add these fractions with different denominators, Darcy must rewrite both fractions as equivalent fractions with the denominator of 40. This would involve multiplying the numerator and denominator of 2/5 by 8 to get 16/40 and multiplying the numerator and denominator of 3/8 by 5 to get 15/40.