How to find the distributive property - ISEE Middle Level Quantitative Reasoning
Card 0 of 590
Which is the greater quantity?
(a) 
(b) 
Which is the greater quantity?
(a)
(b)
Apply the distributive property to the expression in (a):
, so 
regardless of 
.
Therefore, 
Apply the distributive property to the expression in (a):
Therefore,
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Which is the greater quantity?
(a) 
(b) 
Which is the greater quantity?
(a)
(b)
Apply the distributive and commutative properties to the expression in (a):
The two expressions are equivalent.
Apply the distributive and commutative properties to the expression in (a):
The two expressions are equivalent.
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Which is the greater quantity?
(a) 
(b) 
Which is the greater quantity?
(a)
(b)
We show that there is at least one value of 
that makes the (a) greater and at least one that makes (b) greater:
Case 1: 
(a) 
(b) 
(b) is greater here
Case 2: 
(a) 
(b) 
(a) is greater here
We show that there is at least one value of
Case 1:
(a)
(b)
(b) is greater here
Case 2:
(a)
(b)
(a) is greater here
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Which is the greater quantity?
(a) 
(b) 
Which is the greater quantity?
(a)
(b)
Apply the distributive property to the expression in (a):
Since 
, 
, and therefore, regardless of 
,
Apply the distributive property to the expression in (a):
Since
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and 
are positive integers.
Which of the following is greater?
(A) 
(b) 
Which of the following is greater?
(A)
(b)
(A) and (B) are equivalent variable expressions and are therefore equal regardless of the values of 
and 
.
(A) and (B) are equivalent variable expressions and are therefore equal regardless of the values of
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Which of the following is equivalent to 
?
Which of the following is equivalent to
We can best solve this by factoring 4 from both terms, and distributing it out:
We can best solve this by factoring 4 from both terms, and distributing it out:
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Simplify the below:
Simplify the below:
In order to simiplify we must first distribute the -2 only to what is inside the ( ):
Now, we must combine like terms:
This gives us the final answer:
In order to simiplify we must first distribute the -2 only to what is inside the ( ):
Now, we must combine like terms:
This gives us the final answer:
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Simplify the below:
Simplify the below:
We must use the distributive property in this case to multiply the 4 by both the 3x and 5.
We must use the distributive property in this case to multiply the 4 by both the 3x and 5.
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and 
are positive numbers. Which is the greater quantity?
(a) 
(b) 
(a)
(b)
Since 
is positive, and 
, then, by the properties of inequality,
and
.
Since
and
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is the additive inverse of 
. Which is the greater quantity?
(a) 
(b) 
(a)
(b)
is the additive inverse of 
, so, by definition, 
.
.
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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, 
. Therefore,
.
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Which is the greater quantity?
(a)
(b)
Which is the greater quantity?
(a)
(b)
Apply the distributive property to the expression in (a):
, so regardless of .
Therefore,
Apply the distributive property to the expression in (a):
Therefore,
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Which is the greater quantity?
(a)
(b)
Which is the greater quantity?
(a)
(b)
Apply the distributive and commutative properties to the expression in (a):
The two expressions are equivalent.
Apply the distributive and commutative properties to the expression in (a):
The two expressions are equivalent.
Compare your answer with the correct one above
Which is the greater quantity?
(a)
(b)
Which is the greater quantity?
(a)
(b)
We show that there is at least one value of that makes the (a) greater and at least one that makes (b) greater:
Case 1:
(a)
(b)
(b) is greater here
Case 2:
(a)
(b)
(a) is greater here
We show that there is at least one value of
Case 1:
(a)
(b)
(b) is greater here
Case 2:
(a)
(b)
(a) is greater here
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Which is the greater quantity?
(a)
(b)
Which is the greater quantity?
(a)
(b)
Apply the distributive property to the expression in (a):
Since , , and therefore, regardless of ,
Apply the distributive property to the expression in (a):
Since
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and are positive integers.
Which of the following is greater?
(A)
(b)
Which of the following is greater?
(A)
(b)
(A) and (B) are equivalent variable expressions and are therefore equal regardless of the values of and .
(A) and (B) are equivalent variable expressions and are therefore equal regardless of the values of
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Which of the following is equivalent to ?
Which of the following is equivalent to
We can best solve this by factoring 4 from both terms, and distributing it out:
We can best solve this by factoring 4 from both terms, and distributing it out:
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Simplify the below:
Simplify the below:
In order to simiplify we must first distribute the -2 only to what is inside the ( ):
Now, we must combine like terms:
This gives us the final answer:
In order to simiplify we must first distribute the -2 only to what is inside the ( ):
Now, we must combine like terms:
This gives us the final answer:
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Simplify the below:
Simplify the below:
We must use the distributive property in this case to multiply the 4 by both the 3x and 5.
We must use the distributive property in this case to multiply the 4 by both the 3x and 5.
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and are positive numbers. Which is the greater quantity?
(a)
(b)
(a)
(b)
Since is positive, and , then, by the properties of inequality,
and
.
Since
and
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