# Fractions

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## 7/29 Fractions

Read the following SAT test question and then select the correct answer.

For every math problem, always be sure to follow the Knowsys Method. This will keep you from falling for traps and trick questions! First, read the question carefully.  You have to understand the information that you are given before you can begin working the problem.  The second step is to identify the bottom line, the question that you must answer.  In this case, you are asked to identify the total number of students who study art.  Next, assess your options to find the most efficient way to solve the problem, attack the problem, and loop back to make sure you answered the correct question.

Every student who studies art in a certain school receives exactly one of the grades A, B, C, or D. If $\frac{1}{5}$ of the students receive A’s, $\frac{1}{4}$ receive B’s, $\frac{1}{2}$ receive C’s, and 10 students receive D’s, how many students inthe school study art?

In this problem, you have fractions for the students who receive A’s, B’s, and C’s, but you have an actual number of students who receive D’s. To find the total number of students, you will need to find out what fraction of the whole is represented by the 10 students who receive D’s. Find out what fraction of the whole is represented by the students who receive A’s, B’s and C’s first. To add these fractions together, you need to find the least common denominator. You don't need to worry much about the 2 since it is a factor of 4. Instead, focus on the 5; the least common denominator will be the product of 4 and 5.

$\frac{1}{5}+\frac{1}{4}+\frac{1}{2}$ then becomes $\frac{4}{20}+\frac{5}{20}+\frac{10}{20}=\frac{19}{20}$

If $\frac{19}{20}$ of the students receive A’s, B’s or C’s, then that only leaves $\frac{1}{20}$ of the students who can receive D’s. Remember that there are 10 students who receive D’s. Think about it this way: $\frac{1}{20}$ of the total number of students is 10 students. For math problems the word “of” indicates that you will need to multiply. So $\frac{1}{20}$ times the total number equals ten. Use x to represent the unknown total, and then solve for x.

$\frac{1}{20}x =10$ Multiply each side by 20 to get rid of the fraction.

1x = 200

You solved for x (the total number of students), so check to make sure that you have found the bottom line. Then match your answer to the answer choices you are given.

(A) 30

(B) 60

(C) 100

(D) 200

(E) 500