PROBLEM
What fraction of students received an A or B if 31 got an A and 52 got a B?
STEP 1
Assumptions1. The fraction of students who got an A is 31
. The fraction of students who got a B is 5
3. The fractions represent distinct groups of students, i.e., a student cannot get both an A and a B.
STEP 2
To find the fraction of students who got either an A or a B, we need to add the fraction of students who got an A to the fraction of students who got a B.
FractionofstudentswhogotAorB=FractionofstudentswhogotA+FractionofstudentswhogotB
STEP 3
Now, plug in the given values for the fraction of students who got an A and the fraction of students who got a B.
FractionofstudentswhogotAorB=31+52
STEP 4
To add these fractions, we need to find a common denominator. The least common denominator (LCD) of3 and is15.
STEP 5
Convert the fractions to have the common denominator.
31=3×51×5=15552=5×32×3=15
STEP 6
Now, add the two fractions.
FractionofstudentswhogotAorB=155+156
SOLUTION
Calculate the sum.
FractionofstudentswhogotAorB=155+6=1511So, 1511 of the students got either an A or a B.
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