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ISEE Middle Level Quantitative : Algebraic Concepts

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

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All ISEE Middle Level Quantitative Resources

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Example Questions

Example Question #41 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

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

Possible Answers:

$t ^{42}$ $\displaystyle t ^{42}$

42t $\displaystyle 42t$

$42t^{2}$ $\displaystyle 42t^{2}$

$13t^{2}$ $\displaystyle 13t^{2}$

13t $\displaystyle 13t$

Correct answer:

$42t^{2}$ $\displaystyle 42t^{2}$

Explanation:

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

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

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Example Question #41 : Variables

Define an operation on the real numbers as follows:

For all real values of $\displaystyle a$ and $\displaystyle b$ ,

$a \bigstar b = ab-a$ $\displaystyle a \bigstar b = ab-a$

$\displaystyle N$ is a positive number. Which is the greater quantity?

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

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

Possible Answers:

(b) is the greater quantity

(a) and (b) are equal

(a) is the greater quantity

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

Correct answer:

(b) is the greater quantity

Explanation:

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

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

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

Since $\displaystyle N$ is positive,

N > -N $\displaystyle N > -N$ ,

and by the addition property of inequality,

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

and

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

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Example Question #12 : How To Multiply Variables

Which of the following is equivalent to 20y? $\displaystyle 20y?$

Possible Answers:

$\displaystyle 4 (3y + 2y)$

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

5 (4y) $\displaystyle 5 (4y)$

$\displaystyle 5(3y + y)$

4 (5y) $\displaystyle 4 (5y)$

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 $\displaystyle 20y$ .

By the associative property of multiplication,

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

and

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

By combining like terms, and applying the distribution property:

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

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

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

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

Possible Answers:

$\displaystyle 20$

$\displaystyle 10$

$\displaystyle 1$

$\displaystyle 11$

$\displaystyle 30$

Correct answer:

$\displaystyle 10$

Explanation:

To solve this problem, we multiply $\displaystyle 1$ by the ones position and the tens position.

$1\times0=0$ $\displaystyle 1\times0=0$

$1\times1=1$ $\displaystyle 1\times1=1$

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

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Example Question #2 : Multiply One Digit Numbers By Multiples Of 10: Ccss.Math.Content.3.Nbt.A.3

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

Possible Answers:

$\displaystyle 40$

$\displaystyle 50$

$\displaystyle 20$

$\displaystyle 22$

$\displaystyle 42$

Correct answer:

$\displaystyle 40$

Explanation:

To solve this problem, we multiply $\displaystyle 2$ by the ones position and the tens position.

$2\times0=0$ $\displaystyle 2\times0=0$

$2\times2=4$ $\displaystyle 2\times2=4$

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

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

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

Possible Answers:

120 $\displaystyle 120$

160 $\displaystyle 160$

180 $\displaystyle 180$

$\displaystyle 60$

$\displaystyle 80$

Correct answer:

160 $\displaystyle 160$

Explanation:

To solve this problem, we multiply $\displaystyle 4$ by the ones position and the tens position.

$4\times0=0$ $\displaystyle 4\times0=0$

$4\times4=16$ $\displaystyle 4\times4=16$

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

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

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

Possible Answers:

110 $\displaystyle 110$

$\displaystyle 10$

250 $\displaystyle 250$

$\displaystyle 25$

$\displaystyle 45$

Correct answer:

250 $\displaystyle 250$

Explanation:

To solve this problem, we multiply $\displaystyle 5$ by the ones position and the tens position.

$5\times0=0$ $\displaystyle 5\times0=0$

$5\times5=25$ $\displaystyle 5\times5=25$

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

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Example Question #4 : Multiply One Digit Numbers By Multiples Of 10: Ccss.Math.Content.3.Nbt.A.3

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

Possible Answers:

240 $\displaystyle 240$

180 $\displaystyle 180$

120 $\displaystyle 120$

360 $\displaystyle 360$

540 $\displaystyle 540$

Correct answer:

360 $\displaystyle 360$

Explanation:

To solve this problem, we multiply $\displaystyle 6$ by the ones position and the tens position.

$6\times0=0$ $\displaystyle 6\times0=0$

$6\times6=36$ $\displaystyle 6\times6=36$

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

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Example Question #3261 : Ssat Elementary Level Quantitative (Math)

Solve the following:

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

Possible Answers:

500 $\displaystyle 500$

520 $\displaystyle 520$

140 $\displaystyle 140$

420 $\displaystyle 420$

490 $\displaystyle 490$

Correct answer:

490 $\displaystyle 490$

Explanation:

To solve this problem, we multiply $\displaystyle 7$ by the ones position and the tens position.

$7\times0=0$ $\displaystyle 7\times0=0$

$7\times7=49$ $\displaystyle 7\times7=49$

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

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Example Question #3084 : Ssat Elementary Level Quantitative (Math)

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

Possible Answers:

480 $\displaystyle 480$

440 $\displaystyle 440$

680 $\displaystyle 680$

160 $\displaystyle 160$

640 $\displaystyle 640$

Correct answer:

640 $\displaystyle 640$

Explanation:

To solve this problem, we multiply $\displaystyle 8$ by the ones position and the tens position.

$8\times0=0$ $\displaystyle 8\times0=0$

$8\times8=64$ $\displaystyle 8\times8=64$

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

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All ISEE Middle Level Quantitative Resources

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ISEE Middle Level Quantitative : Algebraic Concepts

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

All ISEE Middle Level Quantitative Resources

Example Questions

Example Question #41 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Example Question #41 : Variables

Example Question #12 : How To Multiply Variables

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

Example Question #2 : Multiply One Digit Numbers By Multiples Of 10: Ccss.Math.Content.3.Nbt.A.3

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

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

Example Question #4 : Multiply One Digit Numbers By Multiples Of 10: Ccss.Math.Content.3.Nbt.A.3

Example Question #3261 : Ssat Elementary Level Quantitative (Math)

Example Question #3084 : Ssat Elementary Level Quantitative (Math)

All ISEE Middle Level Quantitative Resources

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