SOLUTION: In a group of 15 students, 7 can speak Spanish, 8 can speak French, and 3 can speak neither of the two languages. What fraction of the group can speak both French and Spanish? *

Question 243081: In a group of 15 students, 7 can speak Spanish, 8 can speak French, and 3 can speak neither of the two languages. What fraction of the group can speak both French and Spanish?
**I don't understand where "3 can speak neither of the two languages." Its says 15 students in a group, doesn't 7+8=15...what does it mean by the other 3?? Not sure how to go about solving this one.
And also what does it mean by asking "What fraction of..." Make a whole number a fraction? Does that mean the same as "a part of"??
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
In a group of 15 students, 7 can speak Spanish, 8 can speak French, and 3 can speak neither of the two languages. What fraction of the group can speak both French and Spanish?
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Draw a Venn diagram: a rectangle with two intersecting circles inside.
Label the rectangle with 15 (the number of students in the group).
Label one circle as "spanish" = 7, the other as "french" = 8
Put a 3 in the rectangle but not in either circle.
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Find the number that speak both languages:
12 of the students must be in the two circles
#(span OR french) = #(span)+ #(french) - #(span AND french)
12 = 8 + 7 - #(span AND french)
#(span AND french) = 15-12 = 3
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What fraction of the group can speak both French and Spanish?
Ans: 3/15 = 1/5
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Cheers,
Stan H.
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**I don't understand where "3 can speak neither of the two languages." Its says 15 students in a group, doesn't 7+8=15...what does it mean by the other 3?? Not sure how to go about solving this one.
And also what does it mean by asking "What fraction of..." Make a whole number a fraction? Does that mean the same as "a part of"??

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