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ISEE Middle Level Math : Numbers and Operations

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Example Questions

Example Question #1 : How To Find The Distributive Property

Which of the following expressions is equal to $10 \times (5+8)$ according to the distributive property of multiplication over addition?

Possible Answers:

$10 \times (8+5)$

$10 \times 5 + 8$

$10 \times 5 \times8$

$(5+8) \times 10$

$10 \times 5+10 \times8$

Correct answer:

$10 \times 5+10 \times8$

Explanation:

According to the distributive property, for any values of a,b,c ,

$a (b + c) = a \cdot b + a \cdot c$

If we set a=10,b=5,c=8 , this becomes the statement

$10 \times (5+8) = 10 \times 5+10 \times8$ .

Note that two of the other choices are equal to $10 \times (5+8)$ , but for different reasons; $10 \times (8+5)$ is equivalent because of the commutative property of addition, and $(5+8) \times 10$ is equivalent because of the commutative property of multiplication. The other two choices are not equal to $10 \times (5+8)$ at all.

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Example Question #3 : How To Find The Distributive Property

14(11+2)=

Possible Answers:

126

182

180

154

Correct answer:

182

Explanation:

14(11+2)

=14(13)

=182

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Example Question #4 : How To Find The Distributive Property

11(7-3)=

Possible Answers:

110

Correct answer:

Explanation:

11(7-3)=11(4)=44

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Example Question #5 : How To Find The Distributive Property

7( 5+8)=

Possible Answers:

280

Correct answer:

Explanation:

First add the terms inside the parentheses, then multiply:

7( 5+8)=7(13)=91

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Example Question #6 : How To Find The Distributive Property

8(9-1)=

Possible Answers:

Correct answer:

Explanation:

Subtract the terms inside the parentheses, and then multiply by the term outside of the parentheses:

8(9-1)=8(8)=64

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Example Question #11 : How To Find The Distributive Property

4(12-4)=

Possible Answers:

Correct answer:

Explanation:

First complete the subtraction inside the parentheses, and then multiply:

4(12-4)=4(8)=32

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Example Question #12 : How To Find The Distributive Property

6( 6+8)=

Possible Answers:

Correct answer:

Explanation:

First complete the addition inside the parentheses, and then multiply the result by the constant outside of the parentheses:

6( 6+8)=6(14)=84

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Example Question #571 : Numbers And Operations

14(5+3)=

Possible Answers:

111

121

2940

112

Correct answer:

112

Explanation:

First complete the addition inside of the parentheses, then multiply by the constant outside of the parentheses:

=14(8)=112

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Example Question #578 : Numbers And Operations

Simplify the expression:

6 (x + 7) - 4(x-3)

Possible Answers:

5 x + 10

2 x + 10

2 x + 30

10 x + 54

2 x + 54

Correct answer:

2 x + 54

Explanation:

Distribute, then collect like terms, making sure you switch the symbols in the second disribution due to the minus:

6 (x + 7) - 4(x-3)

$= 6 \cdot x + 6 \cdot 7 - 4 \cdot x+4 \cdot 3$

= 6 x + 42 - 4 x+12

= 6 x - 4 x + 42 +12

$=\left ( 6 - 4 \right ) x + 42 +12$

=2 x + 54

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Example Question #14 : How To Find The Distributive Property

Simplify:

$5x ^{2} (4x - 7)$

Possible Answers:

$-15 x ^{2}$

$20 x ^{3} -35$

$20 x ^{3} -7 x ^{2}$

$20 x ^{3} -35 x ^{2}$

$20 x ^{3} -7$

Correct answer:

$20 x ^{3} -35 x ^{2}$

Explanation:

$5x ^{2} (4x - 7)$

$= 5x ^{2} \cdot 4x - 5x ^{2} \cdot7$

$=\left ( 5\cdot 4 \right ) \left ( x ^{2} \cdot x \right )-\left ( 5 \cdot 7 \right )\cdot x ^{2}$

$=20 x ^{2+1} -35 x ^{2}$

$=20 x ^{3} -35 x ^{2}$

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All ISEE Middle Level Math Resources

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ISEE Middle Level Math : Numbers and Operations

Study concepts, example questions & explanations for ISEE Middle Level Math

All ISEE Middle Level Math Resources

Example Questions

Example Question #1 : How To Find The Distributive Property

Example Question #3 : How To Find The Distributive Property

Example Question #4 : How To Find The Distributive Property

Example Question #5 : How To Find The Distributive Property

Example Question #6 : How To Find The Distributive Property

Example Question #11 : How To Find The Distributive Property

Example Question #12 : How To Find The Distributive Property

Example Question #571 : Numbers And Operations

Example Question #578 : Numbers And Operations

Example Question #14 : How To Find The Distributive Property

All ISEE Middle Level Math Resources

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