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SAT Math : SAT Mathematics

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #1 : Operations

What is the result of adding $20\%$ of $\frac{2}{7}$ to $\frac{1}{4}$ ?

Possible Answers:

$\frac{23}{11}$

$\frac{3}{28}$

$\frac{47}{140}$

$\frac{3}{39}$

$\frac{43}{140}$

Correct answer:

$\frac{43}{140}$

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.

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Example Question #211 : New Sat

Add:

$\frac{2}{9x}+\frac{4}{27}$

Possible Answers:

$\frac{6}{27x}$

$\frac{2x+6}{27x}$

$\frac{4x+6}{27}$

$\frac{10}{27x}$

$\frac{4x+6}{27x}$

Correct answer:

$\frac{4x+6}{27x}$

Explanation:

Find the least common denominator to solve this problem

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

Convert the fractions.

$\frac{2}{9x}+\frac{4}{27}=\frac{6}{27x}+\frac{4x}{27x}$

Combine the terms as one fraction.

The answer is: $\frac{4x+6}{27x}$

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Example Question #132 : Arithmetic

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

Possible Answers:

$\frac{7}{8}$

$\frac{5}{7}$

$\frac{31}{56}$

$\frac{33}{56}$

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 $\frac{31}{56}$ .

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Example Question #1 : How To Find The Reciprocal Of A Fraction

What is the reciprocal of the following fraction: 18/27

Possible Answers:

27/18

9/27

-18/27

Correct answer:

27/18

Explanation:

A fraction multiplied by its reciprocal will equal 1. To find the reciprocal of a fraction, switch the denominator and numerator. The reciprocal of 18/27 is 27/18.

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Example Question #1 : How To Find The Reciprocal Of A Fraction

What is the reciprocal of the fraction below?

$\frac{2}{9}$

Possible Answers:

$\frac{9}{11}$

$\frac{9}{2}$

$\frac{9}{18}$

$\frac{2}{11}$

Correct answer:

$\frac{9}{2}$

Explanation:

The reciprocal of a fraction can be obtained by switching the numerator and denominator.

The numerator in this case is so that will become the denominator.

The denominator in this case is so that will become the numerator.

Threfore the reciprocal of $\frac{2}{9}$ is $\frac{9}{2}$ .

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Example Question #1 : How To Find The Reciprocal Of A Fraction

What is the reciprocal of $\frac{2}{11}$ ?

Possible Answers:

$\frac{11}{2}$

$-\frac{11}{2}$

$-\frac{2}{11}$

Correct answer:

$\frac{11}{2}$

Explanation:

The reciprocal can be determined by taking one dividing the entire quantity.

$\frac{1}{\frac{2}{11}}=\frac{11}{2}$

This is just flipping the numerator and the denominator.

The answer is $\frac{11}{2}$ .

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Example Question #2 : How To Find The Reciprocal Of A Fraction

What is the reciprocal of $-\frac{13}{2}$ ?

Possible Answers:

$\frac{2}{13}$

$-\frac{2}{13}$

$\frac{13}{2}$

Correct answer:

$-\frac{2}{13}$

Explanation:

To find the reciprocal, take 1 and divide by the entire quantity of the fraction. The reciprocal is simply swapping the placement of the numerator and the denominator.

$-\frac{1}{\frac{13}{2}}=-\frac{2}{13}$

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Example Question #623 : Arithmetic

What is the negative reciprocal of $-\frac{1}{9}$ ?

Possible Answers:

$-\frac{1}{9}$

$\frac{1}{9}$

Correct answer:

Explanation:

The negative reciprocal of a number is to take negative one, and divide by the value. Simply swap the numerator and denominator and add a negative sign.

Recall that dividing by a fraction is the same as multiplying by the reciprocal.

$-\frac{1}{-\frac{1}{9}}=-1\cdot -\frac{9}{1}=9$

The correct answer is:

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Example Question #1 : How To Find The Reciprocal Of A Fraction

Find the reciprocal of the fraction: $\frac{8}{9}$

Possible Answers:

$-\frac{9}{8}$

$\frac{9}{8}$

$-\frac{8}{9}$

Correct answer:

$\frac{9}{8}$

Explanation:

The reciprocal of a fraction is one over the quantity of the fraction.

$\frac{1}{\frac{8}{9}}$

Simply switch the terms of the numerator and denominator.

The answer is $\frac{9}{8}$ .

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Example Question #1 : Reciprocals

The reciprocal of is equal to $3 \frac{1}{2}$ .

What is the reciprocal of y + 3 ?

Possible Answers:

$\frac{7} {23}$

$-\frac{7} {19}$

$\frac{2}{13}$

$3 \frac{2}{7}$

Correct answer:

$\frac{7} {23}$

Explanation:

The reciprocal of is equal to $3 \frac{1}{2}$ , so - which is the reciprocal of the reciprocal of - is the reciprocal of $3 \frac{1}{2}$ . $3 \frac{1}{2} = \frac{7}{2}$ , so is the reciprocal of this, or $\frac{2}{7}$ .

Since $y = \frac{2}{7}$ ,

$y + 3 = \frac{2}{7} + 3 = \frac{2}{7} + \frac{21}{7} = \frac{23}{7}$

The reciprocal of y + 3 is $\frac{7} {23}$ .

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SAT Math : SAT Mathematics

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #1 : Operations

Example Question #211 : New Sat

Example Question #132 : Arithmetic

Example Question #1 : How To Find The Reciprocal Of A Fraction

Example Question #1 : How To Find The Reciprocal Of A Fraction

Example Question #1 : How To Find The Reciprocal Of A Fraction

Example Question #2 : How To Find The Reciprocal Of A Fraction

Example Question #623 : Arithmetic

Example Question #1 : How To Find The Reciprocal Of A Fraction

Example Question #1 : Reciprocals

All SAT Math Resources

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