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ISEE Middle Level Math : Numbers and Operations

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All ISEE Middle Level Math Resources

6 Diagnostic Tests 303 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Distributive Property

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

Possible Answers:

$(5+8) \times 10$ $\displaystyle (5+8) \times 10$

$10 \times 5 + 8$ $\displaystyle 10 \times 5 + 8$

$10 \times 5+10 \times8$ $\displaystyle 10 \times 5+10 \times8$

$10 \times (8+5)$ $\displaystyle 10 \times (8+5)$

$10 \times 5 \times8$ $\displaystyle 10 \times 5 \times8$

Correct answer:

$10 \times 5+10 \times8$ $\displaystyle 10 \times 5+10 \times8$

Explanation:

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

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

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

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

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

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Example Question #2 : Distributive Property

$\displaystyle 14(11+2)=$

Possible Answers:

154 $\displaystyle 154$

182 $\displaystyle 182$

180 $\displaystyle 180$

126 $\displaystyle 126$

Correct answer:

182 $\displaystyle 182$

Explanation:

$\displaystyle 14(11+2)$

=14(13) $\displaystyle =14(13)$

=182 $\displaystyle =182$

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Example Question #1 : Distributive Property

$\displaystyle 11(7-3)=$

Possible Answers:

110 $\displaystyle 110$

$\displaystyle 33$

$\displaystyle 77$

$\displaystyle 44$

$\displaystyle -44$

Correct answer:

$\displaystyle 44$

Explanation:

$\displaystyle 11(7-3)=11(4)=44$

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Example Question #4 : How To Find The Distributive Property

$\displaystyle 7( 5+8)=$

Possible Answers:

$\displaystyle 81$

$\displaystyle 20$

$\displaystyle 91$

$\displaystyle 90$

280 $\displaystyle 280$

Correct answer:

$\displaystyle 91$

Explanation:

First add the terms inside the parentheses, then multiply:

$\displaystyle 7( 5+8)=7(13)=91$

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Example Question #5 : How To Find The Distributive Property

8(9-1)= $\displaystyle 8(9-1)=$

Possible Answers:

$\displaystyle 16$

$\displaystyle 64$

$\displaystyle 72$

$\displaystyle 80$

$\displaystyle 17$

Correct answer:

$\displaystyle 64$

Explanation:

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

$\displaystyle 8(9-1)=8(8)=64$

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Example Question #571 : Numbers And Operations

$\displaystyle 4(12-4)=$

Possible Answers:

$\displaystyle 32$

$\displaystyle 12$

$\displaystyle 20$

$\displaystyle 64$

Correct answer:

$\displaystyle 32$

Explanation:

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

$\displaystyle 4(12-4)=4(8)=32$

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Example Question #572 : Numbers And Operations

$\displaystyle 6( 6+8)=$

Possible Answers:

$\displaystyle 84$

$\displaystyle 20$

$\displaystyle 48$

$\displaystyle 36$

Correct answer:

$\displaystyle 84$

Explanation:

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

$\displaystyle 6( 6+8)=6(14)=84$

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Example Question #573 : Numbers And Operations

$\displaystyle 14(5+3)=$

Possible Answers:

121 $\displaystyle 121$

112 $\displaystyle 112$

111 $\displaystyle 111$

2940 $\displaystyle 2940$

Correct answer:

112 $\displaystyle 112$

Explanation:

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

$\displaystyle =14(8)=112$

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Example Question #574 : Numbers And Operations

Simplify the expression:

$\displaystyle 6 (x + 7) - 4(x-3)$

Possible Answers:

$\displaystyle 2 x + 30$

$\displaystyle 5 x + 10$

$\displaystyle 2 x + 10$

$\displaystyle 10 x + 54$

$\displaystyle 2 x + 54$

Correct answer:

$\displaystyle 2 x + 54$

Explanation:

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

$\displaystyle 6 (x + 7) - 4(x-3)$

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

$\displaystyle = 6 x + 42 - 4 x+12$

$\displaystyle = 6 x - 4 x + 42 +12$

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

$\displaystyle =2 x + 54$

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Example Question #14 : How To Find The Distributive Property

Simplify:

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

Possible Answers:

$20 x ^{3} -35$ $\displaystyle 20 x ^{3} -35$

$20 x ^{3} -7$ $\displaystyle 20 x ^{3} -7$

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

$-15 x ^{2}$ $\displaystyle -15 x ^{2}$

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

Correct answer:

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

Explanation:

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

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

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

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

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

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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 : Distributive Property

Example Question #2 : Distributive Property

Example Question #1 : Distributive Property

Example Question #4 : How To Find The Distributive Property

Example Question #5 : How To Find The Distributive Property

Example Question #571 : Numbers And Operations

Example Question #572 : Numbers And Operations

Example Question #573 : Numbers And Operations

Example Question #574 : Numbers And Operations

Example Question #14 : How To Find The Distributive Property

All ISEE Middle Level Math Resources

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