Joshua surveys his friends to find out which recreational sport is most like he has each of his friends if they prefer basketball soccer baseball or volleyball he finds 1/5 of his friends like volleyball and prefer 2/5 of soccer how many of Joshua's friends prefer volleyball and soccer over the other two sports
To solve this problem, we need to find the common fraction between the two preferences (volleyball and soccer).
Let's start by determining what fraction of Joshua's friends prefer volleyball:
1/5 of Joshua's friends prefer volleyball.
So, if we have the total number of friends as x, then the number of friends who prefer volleyball is (1/5) * x.
Next, we need to find the fraction of friends who prefer soccer:
2/5 of Joshua's friends prefer soccer.
So, the number of friends who prefer soccer is (2/5) * x.
To find the common fraction between the two preferences (volleyball and soccer), we'll look for the least common multiple (LCM) of the denominators 5 and 5, which is 5.
To make the denominators the same, we need to multiply the numerator and denominator of (1/5) by 5, and the numerator and denominator of (2/5) by 1, respectively. This gives us:
Volleyball preference: (1/5) * 5 = 1
Soccer preference: (2/5) * 1 = 2/5
Therefore, Joshua has 1 friend that prefers volleyball and soccer over the other two sports.