How to divide variables - ISEE Middle Level Quantitative Reasoning
Card 0 of 9
What is the value of 
?
What is the value of
(The numerator and the denominator are both multiplied by 10 in order to convert the fraction to whole numbers.)
Therefore, 30 is the correct answer.
(The numerator and the denominator are both multiplied by 10 in order to convert the fraction to whole numbers.)
Therefore, 30 is the correct answer.
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What is the value of 
?
What is the value of
(The numerator and the denominator are both multiplied by 10 in order to convert the fraction to whole numbers.)
Therefore, 90 is the correct answer.
(The numerator and the denominator are both multiplied by 10 in order to convert the fraction to whole numbers.)
Therefore, 90 is the correct answer.
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Simplify:
Simplify:
Since all of the variables are positive powers, this is easy. Start by reducing the numeric coefficient:
Next, cancel out the variables. Subtract the smaller power from the larger one. Remember that if there is no power listed, it is 1:
Since all of the variables are positive powers, this is easy. Start by reducing the numeric coefficient:
Next, cancel out the variables. Subtract the smaller power from the larger one. Remember that if there is no power listed, it is 1:
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Simplify:
Simplify:
Since all of the variables are positive powers, this is easy. Start by reducing the numeric coefficient:
Next, cancel out the variables. Subtract the smaller power from the larger one. Remember that if there is no power listed, it is 1:
Since all of the variables are positive powers, this is easy. Start by reducing the numeric coefficient:
Next, cancel out the variables. Subtract the smaller power from the larger one. Remember that if there is no power listed, it is 1:
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Simplify:
Simplify:
The easiest way to begin with questions like this one is to "flip" the negative exponents to the top or bottom of the fraction. When you do this, you make the exponent's sign positive:
Now, since all of the variables are positive powers, this is easy. Normally, you would begin by reducing the numeric coefficient. This is not necessary since there is only a 5 in the numerator. Therefore, combine the like variables first:
Next, cancel out the variables. Subtract the smaller power from the larger one. Remember that if there is no power listed, it is 1:
The easiest way to begin with questions like this one is to "flip" the negative exponents to the top or bottom of the fraction. When you do this, you make the exponent's sign positive:
Now, since all of the variables are positive powers, this is easy. Normally, you would begin by reducing the numeric coefficient. This is not necessary since there is only a 5 in the numerator. Therefore, combine the like variables first:
Next, cancel out the variables. Subtract the smaller power from the larger one. Remember that if there is no power listed, it is 1:
Compare your answer with the correct one above
Simplify:
Simplify:
The easiest way to begin with questions like this one is to "flip" the negative exponents to the top or bottom of the fraction. When you do this, you make the exponent's sign positive:
Next, go ahead and reduce the numeric coefficient:
Then, combine the like variables first:
Finally, cancel out the variables. Subtract the smaller power from the larger one. Remember that if there is no power listed, it is 1:
The easiest way to begin with questions like this one is to "flip" the negative exponents to the top or bottom of the fraction. When you do this, you make the exponent's sign positive:
Next, go ahead and reduce the numeric coefficient:
Then, combine the like variables first:
Finally, cancel out the variables. Subtract the smaller power from the larger one. Remember that if there is no power listed, it is 1:
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Solve for 
:
Solve for
To start, notice that the left side of the equation has a common factor of 
. You can factor this out:
becomes
Next, you can divide both sides by 
since you know that it does not equal 
:
Simplifying the right side, you get:
Finally, subtract 
from both sides:
To start, notice that the left side of the equation has a common factor of
becomes
Next, you can divide both sides by
Simplifying the right side, you get:
Finally, subtract
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Solve for 
:
Solve for
To start, notice that the left side of the equation has common factors of 
and 
. You can factor these out:
becomes...
Next, you can divide both sides by 
since you know that it does not equal 
:
Simplify the right side by canceling the 
and reducing the 
:
Finally, add 
to both sides:
To start, notice that the left side of the equation has common factors of
becomes...
Next, you can divide both sides by
Simplify the right side by canceling the
Finally, add
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is the multiplicative inverse of 
. Which is the greater quantity?
(a) 
(b) 
(a)
(b)
is the multiplicative inverse of 
, so, by definition, 
. We show that this is insufficient information, however, with two cases.
Case 1: 
Case 2: 
Therefore,it is not clear which, if either, is the greater, 
or 1.
Case 1:
Case 2:
Therefore,it is not clear which, if either, is the greater,
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