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 of the following expressions is equivalent to the expression below?
Which of the following expressions is equivalent to the expression below?
First, we can distribute the 
into the parentheses.
Now we can simplify the terms.
Subtracting a negative is the same as adding a positive.
First, we can distribute the
Now we can simplify the terms.
Subtracting a negative is the same as adding a positive.
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Using the distributive property, multiply 3 times each of the numbers in parentheses, then add both products:
The answer is 27.
Alternatively, add the two terms inside the parentheses and then multiply the sum by 3:
Using the distributive property, multiply 3 times each of the numbers in parentheses, then add both products:
The answer is 27.
Alternatively, add the two terms inside the parentheses and then multiply the sum by 3:
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Using the distributive property, multiply 
times each of the numbers in parenthesis then add.
The answer is 
Alternatively, add the two terms inside the parentheses and then multiply the sum by 
:
Using the distributive property, multiply
The answer is
Alternatively, add the two terms inside the parentheses and then multiply the sum by
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First, using the distributive property, multiply 5 times each number in parenthesis, then add the products.
Finally, divide the numerator by the denominator.
The answer is 7.
Alternatively, first cancel the 5s and then add the terms in the parentheses:
First, using the distributive property, multiply 5 times each number in parenthesis, then add the products.
Finally, divide the numerator by the denominator.
The answer is 7.
Alternatively, first cancel the 5s and then add the terms in the parentheses:
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Using the distributive property, multiply 12 by each of the numbers is parentheses:
Add the products to find the answer:
The answer is 
Using the distributive property, multiply 12 by each of the numbers is parentheses:
Add the products to find the answer:
The answer is
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First complete the addition in the parentheses, then multiply the two values:
11 (8 + 3)
= 11 (11)
= 121
First complete the addition in the parentheses, then multiply the two values:
11 (8 + 3)
= 11 (11)
= 121
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Simplify the expression: 
Simplify the expression:
Apply the distributive property:
Apply the distributive property:
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Simplify the expression: 
Simplify the expression:
Apply the distributive property:
Apply the distributive property:
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Which of the following expressions is equal to 
according to the distributive property of multiplication over addition?
Which of the following expressions is equal to
According to the distributive property, for any values of 
,
If we set 
, this becomes the statement
.
Note that two of the other choices are equal to 
, but for different reasons; 
is equivalent because of the commutative property of addition, and 
is equivalent because of the commutative property of multiplication. The other two choices are not equal to 
at all.
According to the distributive property, for any values of
If we set
Note that two of the other choices are equal to
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