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ISEE Middle Level Quantitative : Operations

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

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All ISEE Middle Level Quantitative Resources

6 Diagnostic Tests 110 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #41 : Algebraic Concepts

Which of the following is equivalent to $6t \cdot 7t$ ?

Possible Answers:

13t

$13t^{2}$

$42t^{2}$

$t ^{42}$

42t

Correct answer:

$42t^{2}$

Explanation:

Use the commutative and associative properties to reorder the expression and group like-terms together.

$6t \cdot 7t = 6\cdot 7\cdot t \cdot t = 42 \cdot t^{2}=42t^2$

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Example Question #12 : How To Multiply Variables

Define an operation on the real numbers as follows:

For all real values of and ,

$a \bigstar b = ab-a$

is a positive number. Which is the greater quantity?

(a) $N \bigstar (-N)$

(b) $(-N) \bigstar N$

Possible Answers:

(a) is the greater quantity

(a) and (b) are equal

(b) is the greater quantity

It is impossible to determine which is greater from the information given

Correct answer:

(b) is the greater quantity

Explanation:

$a \bigstar b = ab-a$ , so

$N \bigstar (-N) = N (-N ) - N= -N^{2} - N$

$(-N) \bigstar N = (-N )N - (-N)= -N^{2}+N$

Since is positive,

N > -N ,

and by the addition property of inequality,

$-N^{2}+N > -N^{2} - N$

and

$(-N) \bigstar N > N \bigstar (-N)$

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Example Question #41 : Variables

Which of the following is equivalent to 20y?

Possible Answers:

4 (5y)

5 (4y)

4 (3y + 2y)

5(3y + y)

All four of the expressions given in the other responses are correct.

Correct answer:

All four of the expressions given in the other responses are correct.

Explanation:

We demonstrate that all four of the expressions are equivalent to 20y .

By the associative property of multiplication,

$4 (5y) = (4 \cdot 5) \cdot y = 20y$

and

$5 (4y) = (5\cdot 4) \cdot y = 20y$

By combining like terms, and applying the distribution property:

$5(3y + y) = 5(3y + 1 y) = 5[ (3 + 1 ) y] = 5 \left ( 4 y \right )= 20y$

$4 (3y + 2y) = 4\left [ (3 + 2) y \right ] = 4\left ( 5y\right ) = 20y$

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Example Question #41 : Operations

$\frac{\begin{array}[b]{r}10\\ \times\ 1\end{array}}{ \ \ \ \space}$

Possible Answers:

Correct answer:

Explanation:

To solve this problem, we multiply by the ones position and the tens position.

$1\times0=0$

$1\times1=1$

$\frac{\begin{array}[b]{r}10\\ \times\ 1\end{array}}{ \ \ \space10}$

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Example Question #42 : Operations

$\frac{\begin{array}[b]{r}20\\ \times\ 2\end{array}}{ \ \ \ \space}$

Possible Answers:

Correct answer:

Explanation:

To solve this problem, we multiply by the ones position and the tens position.

$2\times0=0$

$2\times2=4$

$\frac{\begin{array}[b]{r}20\\ \times\ 2\end{array}}{ \ \ \space40}$

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Example Question #1 : Multiply One Digit Numbers By Multiples Of 10: Ccss.Math.Content.3.Nbt.A.3

$\frac{\begin{array}[b]{r}40\\ \times\ 4\end{array}}{ \ \ \ \space}$

Possible Answers:

180

160

120

Correct answer:

160

Explanation:

To solve this problem, we multiply by the ones position and the tens position.

$4\times0=0$

$4\times4=16$

$\frac{\begin{array}[b]{r}40\\ \times\ 4\end{array}}{ \ \space160}$

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Example Question #43 : Operations

$\frac{\begin{array}[b]{r}50\\ \times\ 5\end{array}}{ \ \ \ \space}$

Possible Answers:

110

250

Correct answer:

250

Explanation:

To solve this problem, we multiply by the ones position and the tens position.

$5\times0=0$

$5\times5=25$

$\frac{\begin{array}[b]{r}50\\ \times\ 5\end{array}}{ \ \space250}$

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Example Question #44 : Operations

$\frac{\begin{array}[b]{r}60\\ \times\ 6\end{array}}{ \ \ \ \space}$

Possible Answers:

540

360

240

180

120

Correct answer:

360

Explanation:

To solve this problem, we multiply by the ones position and the tens position.

$6\times0=0$

$6\times6=36$

$\frac{\begin{array}[b]{r}60\\ \times\ 6\end{array}}{ \ \space360}$

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Example Question #45 : Operations

Solve the following:

$\frac{\begin{array}[b]{r}70\\ \times\ 7\end{array}}{ \ \ \ \space}$

Possible Answers:

140

500

520

420

490

Correct answer:

490

Explanation:

To solve this problem, we multiply by the ones position and the tens position.

$7\times0=0$

$7\times7=49$

$\frac{\begin{array}[b]{r}70\\ \times\ 7\end{array}}{ \ \space490}$

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Example Question #46 : Operations

$\frac{\begin{array}[b]{r}80\\ \times\ 8\end{array}}{ \ \ \ \space}$

Possible Answers:

160

440

640

480

680

Correct answer:

640

Explanation:

To solve this problem, we multiply by the ones position and the tens position.

$8\times0=0$

$8\times8=64$

$\frac{\begin{array}[b]{r}80\\ \times\ 8\end{array}}{ \ \space640}$

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All ISEE Middle Level Quantitative Resources

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ISEE Middle Level Quantitative : Operations

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

All ISEE Middle Level Quantitative Resources

Example Questions

Example Question #41 : Algebraic Concepts

Example Question #12 : How To Multiply Variables

Example Question #41 : Variables

Example Question #41 : Operations

Example Question #42 : Operations

Example Question #1 : Multiply One Digit Numbers By Multiples Of 10: Ccss.Math.Content.3.Nbt.A.3

Example Question #43 : Operations

Example Question #44 : Operations

Example Question #45 : Operations

Example Question #46 : Operations

All ISEE Middle Level Quantitative Resources

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