Answer: 1/10
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Step-by-step explanation
Method 1
Let's say the class has 20 students. I picked this value because the denominators multiply to 20.
1/4 of the class are girls, so (1/4)*20 = 5 students are girls.
2/5 of those girls are boarders, so there must be 2 boarders out of those 5 girls. Overall there are 2 boarders out of the class of 20 students.
2/20 = 1/10 is the answer
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Method 2
Multiply the fractions and reduce
(1/4)*(2/5) = (1*2)/(4*5) = 2/20 = 1/10 is the answer
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Method 3
Draw four boxes. Label 3 of them B for boys. The fourth box is labeled G for girls. This represents the idea 1/4 of the students are girls.
Split each of those boxes into 5 equal pieces. Since we have 4 boxes, 5 pieces per box, it gives 4*5 = 20 pieces total.
Shade 2 pieces inside box G to represent 2/5 of the girls being boarders. None of the boxes for the boys will get shaded because none of the boys are boarders.
We have 2 shaded pieces out of 20 pieces total.
2/20 = 1/10 is the answer
See the diagram below.