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SAT Math : SAT Mathematics

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #12 : How To Simplify A Fraction

Reduce the fraction:

$\frac{12}{96}$

Possible Answers:

$\frac{1}{8}$

$\frac{3}{24}$

$\frac{7}{12}$

$\frac{1}{4}$

$\frac{4}{16}$

Correct answer:

$\frac{1}{8}$

Explanation:

The numerator and denominator are both divisible by 12. Thus, we divide both by 12 to get our final answer.

If we instead divide by another common factor, we may need to complete the process again to make sure that we have completely reduced the fraction.

In mathematical words we get the following:

$\frac{12}{96}=\frac{1 \cdot 12}{8 \cdot 12}=\frac{1}{8}$

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Example Question #16 : Algebraic Fractions

Simplify the fraction: $\frac{18}{96}$

Possible Answers:

$\frac{3}{16}$

$\frac{3}{23}$

$\frac{6}{16}$

$\frac{9}{23}$

$\frac{6}{23}$

Correct answer:

$\frac{3}{16}$

Explanation:

Break up the fraction into common factors.

$18=3\times 6$

$96 = 16\times 6$

Rewrite the fraction.

$\frac{18}{96}=\frac{3\times 6}{16\times 6}$

Cancel the six.

The correct reduced fraction is $\frac{3}{16}$ .

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Example Question #17 : Algebraic Fractions

Simplify the fraction: $\frac{9}{96}$

Possible Answers:

$\frac{6}{19}$

$\frac{6}{23}$

$\frac{3}{32}$

$\frac{3}{23}$

$\frac{1}{16}$

Correct answer:

$\frac{3}{32}$

Explanation:

Break up the fraction into common factors.

$9=3\times 3$

$96 = 16\times 6$

Rewrite the fraction.

$\frac{9}{96}=\frac{3\times 3}{16\times 3 \times 2}$

Cancel the three on the numerator and denominator.

The fraction becomes:

$\frac{3}{16 \times 2}=\frac{3}{32}$

The correct reduced fraction is $\frac{3}{32}$ .

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Example Question #18 : Algebraic Fractions

Simplify the following fraction.

27a^5b^2c^8 / 3a^2b^4c^5

Possible Answers:

9abc

9a^3c^3 / b^2

9a^2c^2 / b^3

a^2b^5

3a^3c^3 / b^2

Correct answer:

9a^3c^3 / b^2

Explanation:

In order to simplify the fraction, you need to cancel out everything that the numerator and denominator share. Let's separate it into four sections: the numbers, the variable a, the variable b, and the variable c.

27 / 3 = 9

With the variable a, you have

a^5 / a^2

which simplifies to

a^3 in the numerator.

With the variable b, you have

b^2 / b^4

which simplifies to

b^2 in the denominator.

With the variable c, you have

c^8 / c^5

which simplifies to

c^3 in the numerator.

Once you combine everything, you get

9a^3c^3 / b^2

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Example Question #1 : How To Evaluate A Fraction

Evaluate the following equation when x=5 and round your answer to the nearest hundredth.

$\frac{x^{3}-2x^{2}-3x+5}{5x+3}$

Possible Answers:

2.32

4.33

5.00

-1.94

5.28

Correct answer:

2.32

Explanation:

$\frac{x^{3}-2x^{2}-3x+5}{5x+3}$

1. Plug in wherever there is an in the above equation.

$\frac{5^{3}-(2)(5^{2})-(3)(5)+5}{(5)(5)+3}$

2. Perform the above operations.

$\frac{5^{3}-(2)(25)-(3)(5)+5}{(5)(5)+3}$

$\frac{125-50-15+5}{25+3}$

$\frac{65}{28}=2.32$

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Example Question #2 : How To Evaluate A Fraction

If $w=\frac{1}{8}$ then which of the following is equal to $w^\frac{2}{3}$ ?

Possible Answers:

$\frac{1}{2}$

$\frac{1}{64}$

$\frac{1}{4}$

$\frac{1}{16}$

$\frac{1}{32}$

Correct answer:

$\frac{1}{4}$

Explanation:

To raise $\frac{1}{8}$ to the exponent $\frac{2}{3}$ , square $\frac{1}{8}$ and then take the cube root.

$w^\frac{2}{3}=\sqrt[3]{w^2}$

$(\frac{1}{8})^\frac{2}{3}=\sqrt[3]{(\frac{1}{8})^2}=\sqrt[3]{\frac{1}{64}}$

$\sqrt[3]{\frac{1}{64}}=\frac{1}{4}$

$(\frac{1}{8})^{\frac{2}{3}}=\frac{1}{4}$

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Example Question #861 : Algebra

Solve

Possible Answers:

–1

no solution

infinitely many solutions

Correct answer:

infinitely many solutions

Explanation:

The common denominator of the left side is x(x–1). Multiplying the top and bottom of 1/x by (x–1) yields

Since this statement is true, there are infinitely many solutions.

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Example Question #1 : How To Evaluate A Fraction

Evaluate when x=11. Round to the nearest tenth.

Possible Answers:

1.8

1.9

0.2

0.3

Correct answer:

1.8

Explanation:

Wherever there is an x, plug in 11 and perform the given operations. The numerator will be equal to 83 and the denominator will be equal to 46. 83 divided by 46 is equal to 1.804… and since the second decimal place is not greater than or equal to 5, the first decimal place stays the same when rounding so the final answer is 1.8.

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Example Question #863 : Algebra

For this question, the following trigonometric identities apply:

$\csc x=\frac{1}{\sin x}$ ,

$\sec x=\frac{1}{\cos x}$

$\cot x=\frac{1}{\tan x}$

Simplify: $\sin ^{2}x\csc x\cot x$

Possible Answers:

$\tan x$

$\sec x$

$\sin x$

$\cos x$

$\sin x\cos x$

Correct answer:

$\cos x$

Explanation:

To begin a problem like this, you must first convert everything to $\sin x$ and $\cos x$ alone. This way, you can begin to cancel and combine to its most simplified form.

Since $\csc x=\frac{1}{\sin x}$ and $\cot x=\frac{\cos x}{\sin x}$ , we insert those identities into the equation as follows.

$\sin ^{2}x\cdot \frac{1}{\sin x}\cdot \frac{\cos x}{\sin x}$

From here we combine the numerator and denominators of each fraction together to easily see what we can combine and cancel.

$\frac{\sin^{2}x\cdot \cos x}{\sin x\cdot \sin x}$

Since there is a $\sin ^{2}x$ in the numerator and the denominator, we can cancel them as they divide to equal 1. All we have left is $\cos x$ , the answer.

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Example Question #3 : How To Evaluate A Fraction

If 3x = 12, y/4 = 10, and 4z = 9, what is the value of (10xyz)/xy?

Possible Answers:

4 ¹/₂

22 ¹/2

160

360

Correct answer:

22 ¹/2

Explanation:

Solve for the variables, the plug into formula.

x = 12/3 = 4

y = 10 * 4 = 40

z= 9/4 = 2 ¹/₄

10xyz = 3600

Xy = 160

3600/160 = 22 ¹/2

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SAT Math : SAT Mathematics

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #12 : How To Simplify A Fraction

Example Question #16 : Algebraic Fractions

Example Question #17 : Algebraic Fractions

Example Question #18 : Algebraic Fractions

Example Question #1 : How To Evaluate A Fraction

Example Question #2 : How To Evaluate A Fraction

Example Question #861 : Algebra

Example Question #1 : How To Evaluate A Fraction

Example Question #863 : Algebra

Example Question #3 : How To Evaluate A Fraction

All SAT Math Resources

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