How to divide variables - ISEE Upper Level (grades 9-12) Quantitative Reasoning
Card 0 of 8
The ratio of 10 to 14 is closest to what value?
The ratio of 10 to 14 is closest to what value?
Another way to express ratios is through division. 10 divided by 14 is approximate 0.71.
Another way to express ratios is through division. 10 divided by 14 is approximate 0.71.
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If 
is the quotient of 
and 
, which statement could be true?
If
A quotient is the result of division. If 
is the quotient of 
and 
, that means that 
could be true.
A quotient is the result of division. If
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is a negative integer. Which is the greater quantity?
(A) 
(B) 
(A)
(B)
Since the quotient of negative numbers is positive, both results will be positive.
We can rewrite both of these as quotients of positive numbers, as follows:
Since the expressions have the same dividend and the second has the greater divisor, the first has the greater quotient.
Therefore, (A) is greater.
Since the quotient of negative numbers is positive, both results will be positive.
We can rewrite both of these as quotients of positive numbers, as follows:
Since the expressions have the same dividend and the second has the greater divisor, the first has the greater quotient.
Therefore, (A) is greater.
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Let 
be negative. Which of the following is the greater quantity?
(A) 
(B) 
Let
(A)
(B)
The quotient of two negative numbers is positive. The expressions can be rewritten as follows:
Both expressions have the same dividend; the second has the lesser divisor so it has the greater quotient. This makes (B) greater.
The quotient of two negative numbers is positive. The expressions can be rewritten as follows:
Both expressions have the same dividend; the second has the lesser divisor so it has the greater quotient. This makes (B) greater.
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is a negative integer. Which is the greater quantity?
(A) 
(B) 
(A)
(B)
Since the quotient of negative numbers is positive, both results will be positive.
We can rewrite both of these as products of positive numbers, as follows:
, so
, and
making (B) greater.
Since the quotient of negative numbers is positive, both results will be positive.
We can rewrite both of these as products of positive numbers, as follows:
making (B) greater.
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When evaluating the expression
,
assuming you know the values of all five variables, what is the second operation that must be performed?
When evaluating the expression
assuming you know the values of all five variables, what is the second operation that must be performed?
In the order of operations, any expression within parentheses must be performed first. Between the parentheses, there are two operations, an exponentiation (squaring), and a subtraction. By the order of operations, the exponentiation is performed first; the subtraction is performed second, making this the correct response.
In the order of operations, any expression within parentheses must be performed first. Between the parentheses, there are two operations, an exponentiation (squaring), and a subtraction. By the order of operations, the exponentiation is performed first; the subtraction is performed second, making this the correct response.
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; 
.
Which is the greater quantity?
(a) The reciprocal of 
(b) The reciprocal of 
Which is the greater quantity?
(a) The reciprocal of
(b) The reciprocal of
We show that the given information is insufficient by examining two cases.
Case 1:
The reciprocal of 
is 
, or 
.
Also, 
, the reciprocal of which is 
.
, so (b) is the greater quantity.
Case 2: 
.
The reciprocal of 
is 
, or 2.
Also, 
, the reciprocal of which is 
.
, so (a) is the greater quantity.
in both cases, but in one case, (a) is greater and in the other, (b) is greater.
We show that the given information is insufficient by examining two cases.
Case 1:
The reciprocal of
Also,
Case 2:
The reciprocal of
Also,
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is a negative number.
Which is the greater quantity?
(a) The reciprocal of 
(b) The reciprocal of 
Which is the greater quantity?
(a) The reciprocal of
(b) The reciprocal of
Since 
is negative, its reciprocal 
is also negative. Since
,
by the Multiplication Property of Inequality,
That is, the reciprocal of 
is greater than that of 
.
Since
by the Multiplication Property of Inequality,
That is, the reciprocal of
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