To find the fraction of the group that can speak both French and Spanish, you can use the principle of inclusion-exclusion.

Given:

• Total number in the group (n) = 15
• Number who can speak Spanish (S) = 7
• Number who can speak French (F) = 8
• Number who can speak neither (N) = 3

You want to find the fraction who can speak both French and Spanish (denoted as FS).

First, find the fraction who can speak either French or Spanish or both: Fraction who can speak French or Spanish = (S + F - FS) / n

Now, you know that 3 people can speak neither, so: Fraction who can speak French or Spanish = (S + F - FS) / n = (7 + 8 - FS) / 15 = (15 - FS) / 15

Since you want to find the fraction who can speak both French and Spanish, you need to subtract the fraction who can speak either French or Spanish from 1 (because everyone falls into one of these categories, so the sum of their fractions should equal 1):

1 - Fraction who can speak either French or Spanish = 1 - [(15 - FS) / 15] = (15/15) - (15 - FS) / 15 = (15 - 15 + FS) / 15 = FS / 15

So, the fraction of the group that can speak both French and Spanish (FS) is FS / 15.

Now, you're given that this fraction is equal to 1/5:

FS / 15 = 1/5

To find FS, multiply both sides by 15:

FS = (1/5) * 15 = 3

So, the fraction of the group that can speak both French and Spanish is 3/15, which simplifies to 1/5.