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PSAT Math : Algebra

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Example Questions

Example Question #7 : Algebraic Fractions

Simplify. $\frac{4x^{4}z^{3}}{2xz^{2}}$

Possible Answers:

$4x^{3}z$

$2x^{4}z^{3}$

$\frac{2x^{4}z^{3}}{xz}$

$2x^{3}z$

Can't be simplified

Correct answer:

$2x^{3}z$

Explanation:

To simplify exponents which are being divided, subtract the exponents on the bottom from exponents on the top. Remember that only exponents with the same bases can be simplified

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Example Question #8 : Algebraic Fractions

Simplify:

$\frac{x^2-y^2}{x+y}$

Possible Answers:

x+y

x-y

$x-y,\ x+y$

2xy

Correct answer:

x-y

Explanation:

x² – y² can be also expressed as (x + y)(x – y).

Therefore, the fraction now can be re-written as (x + y)(x – y)/(x + y).

This simplifies to (x – y).

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Example Question #1 : How To Simplify A Fraction

Simplify:

$\frac{x\sqrt{2}-2\sqrt{2}}{\sqrt{2x}+2}$

Possible Answers:

$x-\sqrt{2}$

$\sqrt{x}+\sqrt{2}$

$x+\sqrt{2}$

$\frac{x+2}{\sqrt{x-2}}$

$\sqrt{x}-\sqrt{2}$

Correct answer:

$\sqrt{x}-\sqrt{2}$

Explanation:

Notice that the $\sqrt{2}$ term appears frequently. Let's try to factor that out:

$\frac{x\sqrt{2}-2\sqrt{2}}{\sqrt{2x}+2} = \frac{\sqrt{2}*(x-2)}{\sqrt{2}*(\sqrt{x} +\sqrt{2})} = \frac{x-2}{\sqrt{x} +\sqrt{2}}$

Now multiply both the numerator and denominator by the conjugate of the denominator:

$\frac{x-2}{\sqrt{x} +\sqrt{2}} * \frac{\sqrt{x} -\sqrt{2}}{\sqrt{x} -\sqrt{2}} =\frac{(x-2)*(\sqrt{x} -\sqrt{2})}{x-2} =\sqrt{x} -\sqrt{2}$

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Example Question #1 : How To Simplify A Fraction

Simplify:

(2x + 4)/(x + 2)

Possible Answers:

x + 4

x + 1

2x + 2

x + 2

Correct answer:

Explanation:

(2x + 4)/(x + 2)

To simplify you must first factor the top polynomial to 2(x + 2). You may then eliminate the identical (x + 2) from the top and bottom leaving 2.

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Example Question #2 : How To Simplify A Fraction

Simplify the following expression:

$\frac{2x^{4}-32}{2x^{2}-8}$

Possible Answers:

$2(x^{2}-4)$

$x^{2}+4$

$x^{2}-4$

$2$

$(x+2)(x-2)$

Correct answer:

$x^{2}+4$

Explanation:

Factor both the numerator and the denominator:

$\frac{2(x^{2}-4)(x^{2}+4)}{2(x^{2}-4)}$

After reducing the fraction, all that remains is:

$(x^{2}+4)$

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Example Question #3 : How To Simplify A Fraction

Simplify:

$\frac{x^{2}y-5x^{2}y^{2}}{x^{2}y}$

Possible Answers:

1-5x

None of the other answers

y-5y

$5+x^{2}y^{2}$

1-5y

Correct answer:

1-5y

Explanation:

With this problem the first thing to do is cancel out variables. The x²can all be divided by each other because they are present in each system. The equation will now look like this:

$\frac{y-5y^{2}}{y}$

Now we can see that the equation can all be divided by y, leaving the answer to be:

1-5y

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Example Question #4 : How To Simplify A Fraction

Simplify the given fraction:

$\frac{120}{6000}$

Possible Answers:

$\frac{1}{5}$

$\frac{1}{50}$

$\frac{2}{25}$

$\frac{1}{100}$

$\frac{1}{20}$

Correct answer:

$\frac{1}{50}$

Explanation:

120 goes into 6000 evenly 50 times, so we get 1/50 as our simplified fraction.

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Example Question #5 : How To Simplify A Fraction

Simplify the given fraction:

$\frac{125}{2000}$

Possible Answers:

$\frac{5}{16}$

$\frac{1}{32}$

$\frac{2}{16}$

$\frac{1}{8}$

$\frac{1}{16}$

Correct answer:

$\frac{1}{16}$

Explanation:

125 goes into 2000 evenly 16 times. 1/16 is the fraction in its simplest form.

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Example Question #271 : Algebra

Simplify the following expression:

$\frac{4x^6}{8x^3}$

Possible Answers:

Correct answer:

Explanation:

Following this equation, you divide 4 by 8 to get 1/2. When a variable is raised to an exponent, and you are dividing, you subtract the exponents, so 6 – 3 = 3.

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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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PSAT Math : Algebra

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #7 : Algebraic Fractions

Example Question #8 : Algebraic Fractions

Example Question #1 : How To Simplify A Fraction

Example Question #1 : How To Simplify A Fraction

Example Question #2 : How To Simplify A Fraction

Example Question #3 : How To Simplify A Fraction

Example Question #4 : How To Simplify A Fraction

Example Question #5 : How To Simplify A Fraction

Example Question #271 : Algebra

Example Question #12 : How To Simplify A Fraction

All PSAT Math Resources

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