Question

In Washington County,1/16 of the adults polled said they enjoyed gardening. In Webster County, 5 out of 76 adults polled said they liked to garden. Which county has a greater fraction of adults who enjoy gardening?

Answer 1

Explanation:

1/16 for Washington County.

5/76 for Webster County.

so, let's bring both to the same denominator (bottom part of the fractions).

this is usual the LCM of both denominators.

since 16 = 2×2×2×2

76 = 2×2×19

the least common multiple (LCM) is the combination of the longest sequence per prime factor involved :

2×2×2×2×19 = 16×19 = 304

1/16 = 19/304

5/76 = 5× 1/76 = 5× 4/304 = 20/304

so, now we know, 20/304 > 19/304, and therefore Webster County has the greater fraction of adults, who enjoy gardening.