SAT Math : How to add fractions

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #1 : How To Add Fractions

Jesse has a large movie collection containing X movies. 1/3 of his movies are action movies, 3/5 of the remainder are comedies, and the rest are historical movies. How many historical movies does Jesse own?

Possible Answers:

(3/9)*X

(11/15)*X

(7/12)*X

(4/15)*X

(2/5)*X

Correct answer:

(4/15)*X

Explanation:

1/3 of the movies are action movies. 3/5 of 2/3 of the movies are comedies, or (3/5)*(2/3), or 6/15. Combining the comedies and the action movies (1/3 or 5/15), we get 11/15 of the movies being either action or comedy. Thus, 4/15 of the movies remain and all of them have to be historical.

Example Question #2 : How To Add Fractions

If x = 1/3 and y = 1/2, find the value of 2x + 3y.

Possible Answers:

2

13/6

1

6/5

5/6

Correct answer:

13/6

Explanation:

Substitute the values of x and y into the given expression:

2(1/3) + 3(1/2)

= 2/3 + 3/2

= 4/6 + 9/6

= 13/6

Example Question #2 : How To Add Fractions

Alternating1

Possible Answers:

\dpi{100} \frac{43}{60}

\dpi{100} -\frac{47}{60}

\dpi{100} -\frac{43}{60}

\dpi{100} \frac{17}{60}

\dpi{100} \frac{47}{60}

Correct answer:

\dpi{100} \frac{47}{60}

Explanation:

Alternating2

Alternating3

Example Question #2 : How To Add Fractions

Solve \frac{3}{7}+\frac{5}{8}-\frac{1}{2}.

Possible Answers:

\frac{31}{56}

\frac{5}{7}

\frac{39}{56}

\frac{7}{8}

\frac{33}{56}

Correct answer:

\frac{31}{56}

Explanation:

Finding the common denominator yields \frac{24}{56}+\frac{35}{56}-\frac{28}{56}. We can then evaluate leaving \frac{31}{56}.

Example Question #5 : How To Add Fractions

What is the solution, reduced to its simplest form, for x = \frac{7}{9}+\frac{3}{5}+\frac{2}{15}+\frac{7}{45}} ?

Possible Answers:

x = \frac{115}{45}

x = \frac{5}{3}

x =2

x = \frac{7}{15}

x = \frac{75}{45}

Correct answer:

x = \frac{5}{3}

Explanation:

x=\frac{7}{9}+\frac{3}{5}+\frac{2}{15}+\frac{7}{45}=\frac{35}{45}+\frac{27}{45}+\frac{6}{45}+\frac{7}{45}=\frac{75}{45}=\frac{5}{3}

Example Question #1 : Operations

What is the result of adding  of  to ?

Possible Answers:

Correct answer:

Explanation:

Let us first get our value for the percentage of the first fraction. 20% of 2/7 is found by multiplying 2/7 by 2/10 (or, simplified, 1/5): (2/7) * (1/5) = (2/35)

Our addition is therefore (2/35) + (1/4). There are no common factors, so the least common denominator will be 35 * 4 or 140. Multiply the numerator and denominator of 2/35 by 4/4 and the numerator of 1/4 by 35/35.

This yields:

(8/140) + (35/140)  = 43/140, which cannot be reduced.

Example Question #3 : How To Add Fractions

Add:

Possible Answers:

Correct answer:

Explanation:

Find the least common denominator to solve this problem

Multiply 27 with , and multiply  with 3 to obtain common denominators.

Convert the fractions.

Combine the terms as one fraction.

The answer is:  

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