GRE Math : Algebraic Fractions

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Example Question #13 :Algebraic Fractions

Simplify the following expression:

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

Possible Answers:

Correct answer:

解释:

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 #14 :Algebraic Fractions

Reduce the fraction:

$\frac{12}{96}$

Possible Answers:

$\frac{1}{4}$

$\frac{7}{12}$

$\frac{1}{8}$

$\frac{3}{24}$

$\frac{4}{16}$

Correct answer:

$\frac{1}{8}$

解释:

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

我f 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.

在数学的话我们得到以下:

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

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Example Question #11 :How To Simplify A Fraction

Simplify.

$\frac{(x^3+8x^2-69x-252)}{(x^2+5x-84)}$

Possible Answers:

$\frac{(x+3)}{(x-7)}$

x+12

x-3

$\frac{1}{(x-7)}$

x+3

Correct answer:

x+3

解释:

When we factor the numerator and denominator, we get:

$\frac{(x-7)(x+12)(x+3)}{(x-7)(x+12)}$ .

After cancelling (x-7)(x+12) , we are left with x+3 .

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Example Question #12 :How To Simplify A Fraction

Which of the following fractions is between $\frac{1}{2}$ and $\frac{3}{4}$ ?

Possible Answers:

$\frac{13}{16}$

$\frac{9}{16}$

$\frac{5}{12}$

$\frac{7}{16}$

$\frac{10}{12}$

Correct answer:

$\frac{9}{16}$

解释:

With common denominators, the range is from

$\frac{6}{12} to \frac{9}{12}$

$\frac{8}{16} to \frac{12}{16}$ .

The only fraction that falls in either of these ranges is $\frac{9}{16}$ .

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Example Question #70 :Algebraic Fractions

$\dpi{100} \small \frac{4 }{x} = \frac{2}{25}$

Findx.

Possible Answers:

$\dpi{100} \small \frac{8}{25}$

$\dpi{100} \small 50$

None

$\dpi{100} \small \frac{25}{8}$

$\dpi{100} \small 0.25$

Correct answer:

$\dpi{100} \small 50$

解释:

Cross multiply:

$\dpi{100} \small 4 \times 25 = 2x$

$\dpi{100} \small 100 = 2x$

$\dpi{100} \small x = 50$

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Example Question #3 :How To Solve For A Variable As Part Of A Fraction

The numerator of a fraction is the sum of 4 and 5 times the denominator. If you divide the fraction by 2, the numerator is 3 times the denominator. Find the simplified version of the fraction.

Possible Answers:

$\frac{1}{2}$

$\frac{1}{3}$

Correct answer:

解释:

Let numerator = N and denominator = D.

According to the first statement,

N = (D x 5) + 4.

According to the second statement, N / 2 = 3 * D.

Let's multiply the second equation by –2 and add itthe first equation:

–N = –6D

+[N = (D x 5) + 4]

–6D + (D x 5) + 4 = 0

–1D + 4 = 0

D = 4

Thus, N = 24.

Therefore, N/D = 24/4 = 6.

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Example Question #1 :How To Solve For A Variable As Part Of A Fraction

我f $\frac{(x-7)}{2x} = \frac{5}{9}$ , what is the value of?

Possible Answers:

$\frac{73}{9}$

$-\frac{35}{13}$

Correct answer:

解释:

Start by cross multiplying to get the equation

$5\cdot2x=(x-7)\cdot 9$

10x = 9x-63 .

Then simplify by subtractingfrom each side to get the solution,

x = -63 .

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Example Question #2 :How To Solve For A Variable As Part Of A Fraction

我f $\frac{x}{4} = 15$ , then what is $\frac{3x}{5} - 36$ equal to?

Possible Answers:

Correct answer:

解释:

We start by solving for x in $\frac{x}{4} = 15$ by multiplying 4 and 15, which gives us x=60 .

Then substituting 60 for x in,

$\frac{3x}{5} - 36$ gives us

$\frac{180}{5} - 36=36-36=0$ which equals 0.

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Example Question #3 :How To Solve For A Variable As Part Of A Fraction

我f $\frac{x-p}{r} = \frac{q}{pr}$ , and x, p, q, r > 0 , what is the value of?

Possible Answers:

x=q + r

$x=\frac{q}{p} - q$

$x=\frac{p}{q} + r$

$x=q + \frac{r}{p}$

$x=\frac{q}{p} + p$

Correct answer:

$x=\frac{q}{p} + p$

解释:

Start by cross multiplying which gives us qr = pr(x-p) .

Simplify by dividing both sides bywhich gives us q = p(x-p) .

我solateby dividing both sides byand then addingto both sides, which gives us $x = \frac{q}{p} +p$ .

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Example Question #4 :How To Solve For A Variable As Part Of A Fraction

我f $\frac{2}{3x} = \frac{4x}{5}$ , and x>0 what is the value of?

Possible Answers:

$-\sqrt{\frac{5}{6}}$

$\sqrt{\frac{5}{6}}$

$\frac{8}{15}$

$\frac{15}{8}$

$\sqrt{10}$

Correct answer:

$\sqrt{\frac{5}{6}}$

解释:

Start by cross multiplying which gives us

4x(3x)=2(5)

$12x^{^{2}} = 10$ .

Divide both sides by 12 and simplify which gives us $x^{^{2}} = \frac{5}{6}$ .

Since x>0 , we only take the positive square root as the solution, ${}x = {\sqrt{\frac{5}{6}}}$ .

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GRE Math : Algebraic Fractions

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #13 :Algebraic Fractions

Example Question #14 :Algebraic Fractions

Example Question #11 :How To Simplify A Fraction

Example Question #12 :How To Simplify A Fraction

Example Question #70 :Algebraic Fractions

Example Question #3 :How To Solve For A Variable As Part Of A Fraction

Example Question #1 :How To Solve For A Variable As Part Of A Fraction

Example Question #2 :How To Solve For A Variable As Part Of A Fraction

Example Question #3 :How To Solve For A Variable As Part Of A Fraction

Example Question #4 :How To Solve For A Variable As Part Of A Fraction

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