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):
, so
regardless of
.
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 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
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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 ,
, and therefore, regardless of
,
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and
are positive integers.
Which of the following is greater?
(A) 
(b) 
and
are positive integers.
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 and
.
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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:
Compare your answer with the correct one above
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.
Compare your answer with the correct one above
and
are positive numbers. Which is the greater quantity?
(a) 
(b) 
and
are positive numbers. Which is the greater quantity?
(a)
(b)

Since
is positive, and
, then, by the properties of inequality,



and
.
Since is positive, and
, then, by the properties of inequality,
and
.
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is the additive inverse of
. Which is the greater quantity?
(a) 
(b) 
is the additive inverse of
. Which is the greater quantity?
(a)
(b)
is the additive inverse of
, so, by definition,
.

.
is the additive inverse of
, so, by definition,
.
.
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is the multiplicative inverse of
. Which is the greater quantity?
(a) 
(b) 
is the multiplicative inverse of
. Which is the greater quantity?
(a)
(b)
is the multiplicative inverse of
, so, by definition,
. Therefore,
.
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):
, so
regardless of
.
Therefore,
Compare your answer with the correct one above
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 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
Compare your answer with the correct one above
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 ,
, and therefore, regardless of
,
Compare your answer with the correct one above
and
are positive integers.
Which of the following is greater?
(A) 
(b) 
and
are positive integers.
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 and
.
Compare your answer with the correct one above
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:
Compare your answer with the correct one above
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:
Compare your answer with the correct one above
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.
Compare your answer with the correct one above
and
are positive numbers. Which is the greater quantity?
(a) 
(b) 
and
are positive numbers. Which is the greater quantity?
(a)
(b)

Since
is positive, and
, then, by the properties of inequality,



and
.
Since is positive, and
, then, by the properties of inequality,
and
.
Compare your answer with the correct one above