Joshua surveys his friends to find out which recreational sport is most liked. He asks each of his friends if they prefer basketball, soccer, baseball, or volleyball. He finds 1/5 of his friends like volleyball and 2/5 prefer soccer. How many of Joshua’s friends prefer volleyball and soccer over the other two sports?
If 1/5 of his friends like volleyball, then Joshua has (1/5)*5= <<1/5*5=1>>1 friend who likes volleyball.
If 2/5 of his friends prefer soccer, then Joshua has (2/5)*5= <<2/5*5=2>>2 friends who like soccer.
Volleyball and soccer fans total to 1+2= <<1+2=3>>3. Answer: \boxed{3}.
To find out how many of Joshua's friends prefer volleyball and soccer, we need to find the common fraction that represents both preferences.
We know that 1/5 of Joshua's friends like volleyball and 2/5 prefer soccer.
To find the fraction that represents both preferences, we need to find the lowest common denominator (LCD) of the two fractions, which is the smallest multiple that both denominators can divide evenly into.
The denominators in this case are 5 and 5.
The LCD of 5 and 5 is also 5.
Now we need to convert the fractions so they have a denominator of 5.
For the first fraction, to get a denominator of 5, we multiply both the numerator and the denominator by (5/1):
1/5 x (5/1) = (1x5)/(5x1) = 5/5
For the second fraction, to get a denominator of 5, we multiply both the numerator and the denominator by (1/1):
2/5 x (1/1) = (2x1)/(5x1) = 2/5
So, 1/5 is equivalent to 1/1, and 2/5 is equivalent to 2/1.
Now we can add these two fractions together:
5/5 + 2/5 = (5+2)/5 = 7/5
But we can't have a fraction greater than 1 for the number of friends who prefer volleyball and soccer, so we need to convert this fraction to a mixed number:
7/5 = 1 2/5
Therefore, 1 and 2/5 is the number of Joshua's friends who prefer volleyball and soccer over the other two sports.
To find out how many of Joshua’s friends prefer volleyball and soccer over the other two sports, we need to calculate the sum of those who prefer volleyball and soccer.
Given that 1/5 of Joshua's friends like volleyball, we can calculate the number of friends who like volleyball by multiplying the total number of friends by 1/5.
To find out how many friends prefer soccer, we need to multiply the total number of friends by 2/5.
To calculate the overlap between those who like volleyball and soccer, we need to multiply the number of friends who like volleyball by 2/5.
Let's assume that Joshua has a total of N friends:
Number of friends who prefer volleyball = N * 1/5
Number of friends who prefer soccer = N * 2/5
Number of friends who prefer both volleyball and soccer = (N * 1/5) * (2/5) = (2N/25)
Therefore, the number of friends who prefer volleyball and soccer over the other two sports is (2N/25).