SAT Math : Arithmetic

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #611 : Arithmetic

Evaluate the following:

Possible Answers:

\frac{400}{507}

\frac{4}{5}

\frac{507}{400}

None of the available answers

\frac{25}{507}

Correct answer:

\frac{400}{507}

Explanation:

First we will evaluate the terms in the parentheses:

Next, we will square the first fraction:

\frac{100}{169}\div \frac{3}{4}

We can evaluate the division as such:

\frac{100}{169}\times\frac{4}{3}=\frac{400}{507}

Example Question #5 : How To Divide Fractions

Evaluate the expression:

Possible Answers:

Correct answer:

Explanation:

When dividing fractions, you invert the second term and multiply the numbers. 

 

You can reduce the numbers that are diagonal from each other to make the numbers smaller and easier to multiply. 

Example Question #1 : How To Divide Fractions

Simplify

Possible Answers:

Fractions with variables cannot be divided

Correct answer:

Explanation:

When you dividing fractions, multiply by the reciprocal of the denominator.

Example Question #152 : Fractions

Which fraction has a value greater than that of X?

Possible Answers:

Correct answer:

Explanation:

First, start by putting changing the fractions in the equation so that they have the same denominator.

Then, you can easily subtract the numerators. The denominator stays the same at this point:

At this point, you can reduce the fraction by dividing the numerator and the denominator by :

Then, to easily compare the fraction to the answer choices, you can change the fraction to a decimal:

By changing the answer choices to decimals as well, you can easily figure out which value is greater than :

, so  is the correct answer.

Example Question #612 : Arithmetic

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:

(11/15)*X

(7/12)*X

(2/5)*X

(3/9)*X

(4/15)*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 #12 : Operations With Fractions

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

Possible Answers:

5/6

2

6/5

13/6

1

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 #131 : Arithmetic

Alternating1

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

Alternating2

Alternating3

Example Question #613 : Arithmetic

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{75}{45}

x = \frac{5}{3}

x = \frac{115}{45}

x = \frac{7}{15}

x =2

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 : How To Add Fractions

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 #614 : Arithmetic

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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