Card 0 of 1968
Simplify:
(2_x_ + 4)/(x + 2)
(2_x_ + 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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Simplify:
With this problem the first thing to do is cancel out variables. The x2 can all be divided by each other because they are present in each system. The equation will now look like this:
Now we can see that the equation can all be divided by y, leaving the answer to be:
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Simplify:
_x_2 – _y_2 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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Simplify the following expression:
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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Simplify the given fraction:
125 goes into 2000 evenly 16 times. 1/16 is the fraction in its simplest form.
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Simplify the given fraction:
120 goes into 6000 evenly 50 times, so we get 1/50 as our simplified fraction.
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A train travels at a constant rate of meters per second. How many kilometers does it travel in
minutes?
Set up the conversions as fractions and solve:
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Simplify.
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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Simplify the following expression:
Factor both the numerator and the denominator:
After reducing the fraction, all that remains is:
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Simplify:
Notice that the term appears frequently. Let's try to factor that out:
Now multiply both the numerator and denominator by the conjugate of the denominator:
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Reduce the fraction:
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:
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Which quantity is greater?
Quantity A
Quantity B
This can be solved using 2 methods.
The most time-efficient solution would recognize that is the largest value and nearly equals the sum the other fraction by itself.
The more time consuming method would be to convert each fraction to decimal form and calculate the sum of each quantity.
Quantity A:
Quantity B:
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Simplify.
When we factor the numerator and denominator, we get:
.
After cancelling , we are left with
.
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Which of the following fractions is between and
?
With common denominators, the range is from
or
.
The only fraction that falls in either of these ranges is .
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Column A:
Column B:
2/5% = 0.40% = 0.004. Therefore, Column B is greater.
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For every 1000 cookies baked, 34 are oatmeal raisin.
Quantity A: Percent of cookies baked that are oatmeal raisin
Quantity B: 3.4%
Simplify Quantity A by dividing the number of oatmeal raisin cookies by the total number of cookies to find the percentage of oatmeal raisin cookies. Since a percentage is defined as being out of 100, either multiply the resulting decimal by 100 or reduce the fraction until the denominator is 100. You will find that the two quantities are equal.
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is
percent of
is
percent of
Quantity A:
Quantity B:
To do this problem, translate each expression into mathematical terms:
is
percent of
:
is
percent of
:
Quantity B is greater.
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Quantity A: 20% of
Quantity B: 30% of
To solve this problem, consider writing the quantities in terms of only fractions:
Quantity A: 20% of
Quantity B: 30% of
Quantity B has the smaller denominator for an equal numerator. There is no need for calculation beyond this, and time on the GRE would be best spent elsewhere.
Quantity B is greater.
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What percentage of a solution is blood if it contains ml blood and
ml water? Round to the nearest thousandth?
First, you must find the total amount of solution. This is , or
.
Now, the percentage of the solution that is blood can be represented:
, or
This is the same as % Rounded, it is
%
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What is the percentage increase of an account that began with a balance of and increased to
?
Recall that the formula for percentage increase is:
, where
is your ending value and
is your starting value.
For our numbers, this would be:
Recall that to find a percentage from a decimal, you multiply by :
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