In a class ¼ of the pupils are girls, ⅖ of the girls are boarders and none of the boys are boarder, what fraction of the class are boarders?
Let's assume there are 100 pupils in the class for simplicity.
Since 1/4 of the pupils are girls, there are 100 * 1/4 = 25 girls in the class.
And since 2/5 of the girls are boarders, there are 25 * 2/5 = 10 girl boarders in the class.
Since none of the boys are boarders, the number of boy boarders is 0.
Therefore, the total number of boarders in the class is 10 + 0 = <<10+0=10>>10.
The fraction of the class that are boarders is 10/100 = 1/10. Answer: \boxed{\frac{1}{10}}.
To solve this problem step by step, let's break it down:
Step 1: Determine the fraction of girls in the class.
Given that 1/4 of the pupils are girls, the fraction of girls in the class is 1/4.
Step 2: Determine the fraction of girls who are boarders.
Given that 2/5 of the girls are boarders, we can multiply the fraction of girls by 2/5 to find the fraction of girls who are boarders:
(1/4) * (2/5) = 2/20 = 1/10
Step 3: Determine the fraction of boys who are boarders.
Given that none of the boys are boarders, the fraction of boys who are boarders is 0.
Step 4: Determine the fraction of the class that are boarders.
To find the fraction of the class that are boarders, we add the fraction of girls who are boarders to the fraction of boys who are boarders:
(1/10) + 0 = 1/10
Therefore, the fraction of the class that are boarders is 1/10.
To find the fraction of the class that are boarders, we need to determine the fraction of girls in the class who are boarders.
Let's assume there are 100 pupils in the class (you can choose any number, but 100 makes calculations easier).
Given that ¼ of the pupils are girls, we have:
Number of girls = ¼ * Total number of pupils = ¼ * 100 = 25 girls
Next, we know that ⅖ of the girls are boarders. Let's calculate the number of girls who are boarders:
Number of girls who are boarders = ⅖ * Number of girls = ⅖ * 25 = 10 girls
Now, to find the fraction of the class that are boarders, we'll divide the number of girls who are boarders by the total number of pupils in the class:
Fraction of the class that are boarders = Number of girls who are boarders / Total number of pupils
= 10 / 100
= 1/10
Therefore, 1/10 of the class are boarders.