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ISEE Middle Level Quantitative : Numbers and 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 #6 : How To Find The Distributive Property

and are positive numbers. Which is the greater quantity?

(a) 3 (t -2u)

(b) 3t- 2u

Possible Answers:

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

(a) and (b) are equal

(b) is the greater quantity

(a) is the greater quantity

Correct answer:

(b) is the greater quantity

Explanation:

$3 (t -2u) = 3 \cdot t - 3 \cdot 2u = 3 t - 6u$

Since is positive, and -6< -2 , then, by the properties of inequality,

-6u< -2 u

-6u+ 3t < -2 u+ 3t

3t-6u < 3t-2 u

and

3t-2 u >3 (t -2u) .

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Example Question #961 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

is the additive inverse of . Which is the greater quantity?

(a) 2a + 2b

(b)

Possible Answers:

(a) and (b) are equal

(b) is the greater quantity

(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:

is the additive inverse of , so, by definition, a+ b = 0 .

$2a + 2b = 2(a+b) = 2 \cdot 0 = 0$

2>0 .

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Example Question #962 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

is the multiplicative inverse of . Which is the greater quantity?

(a) 2ab

(b)

Possible Answers:

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

(a) and (b) are equal

(b) is the greater quantity

(a) is the greater quantity

Correct answer:

(a) and (b) are equal

Explanation:

is the multiplicative inverse of , so, by definition, ab= 1 . Therefore,

$2ab = 2 (ab) = 2 \cdot 1 = 2$ .

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Example Question #1 : Whole Numbers

Solve:

$\frac{\begin{array}[b]{r}10\\ \times\ 2\end{array}}{\space }$

Possible Answers:

Correct answer:

Explanation:

We can make a rectangular array using squares to help us solve this problem. Our multiplication problem is $10\times 2$ ; therefore, the rectangular array should have squares across the top row and squares down the first column. The rectangular array should look like the image below:

Screen shot 2016 05 18 at 10.32.59 am

We can count the squares to find our answer. The correct answer is is

In order to solve this problem using multiplication, we must multiply the multiplier by each digit of the multiplicand to get the answer, which is called the product.

$\frac{\begin{array}[b]{r}\textup{multiplicand}\\ \times\ \ \ \ \textup{multiplier}\end{array}}{\ \ \ \ \textup{product}}$

For this problem, is the multiplier and is the multiplicand.

First, we multiply and

$\frac{\begin{array}[b]{r}1{\color{Red} 0}\\ \times\ {\color{Red} 2}\end{array}}{\ \ \ \ 0}$

Next, we multiply and

$\frac{\begin{array}[b]{r}{\color{Red} 1}0\\ \times\ {\color{Red} 2}\end{array}}{\ \ \ 20}$

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Example Question #2 : Whole Numbers

Solve:

$\frac{\begin{array}[b]{r}10\\ \times\ 3\end{array}}{\space }$

Possible Answers:

Correct answer:

Explanation:

We can make a rectangular array using squares to help us solve this problem. Our multiplication problem is $10\times 3$ ; therefore, the rectangular array should have squares across the top row and squares down the first column. The rectangular array should look like the image below:

Screen shot 2016 05 18 at 11.07.48 am

We can count the squares to find our answer. The correct answer is is

In order to solve this problem using multiplication, we must multiply the multiplier by each digit of the multiplicand to get the answer, which is called the product.

$\frac{\begin{array}[b]{r}\textup{multiplicand}\\ \times\ \ \ \ \textup{multiplier}\end{array}}{\ \ \ \ \textup{product}}$

For this problem, is the multiplier and is the multiplicand.

First, we multiply and

$\frac{\begin{array}[b]{r}1{\color{Red} 0}\\ \times\ {\color{Red} 3}\end{array}}{\ \ \ \ 0}$

Next, we multiply and

$\frac{\begin{array}[b]{r}{\color{Red} 1}0\\ \times\ {\color{Red} 3}\end{array}}{\ \ \ 30}$

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Example Question #3 : Whole Numbers

Solve:

$\frac{\begin{array}[b]{r}10\\ \times\ 4\end{array}}{\space }$

Possible Answers:

Correct answer:

Explanation:

We can make a rectangular array using squares to help us solve this problem. Our multiplication problem is $10\times 4$ ; therefore, the rectangular array should have squares across the top row and squares down the first column. The rectangular array should look like the image below:

Screen shot 2016 05 18 at 12.00.41 pm

We can count the squares to find our answer. The correct answer is is

In order to solve this problem using multiplication, we must multiply the multiplier by each digit of the multiplicand to get the answer, which is called the product.

$\frac{\begin{array}[b]{r}\textup{multiplicand}\\ \times\ \ \ \ \textup{multiplier}\end{array}}{\ \ \ \ \textup{product}}$

For this problem, is the multiplier and is the multiplicand.

First, we multiply and

$\frac{\begin{array}[b]{r}1{\color{Red} 0}\\ \times\ {\color{Red} 4}\end{array}}{\ \ \ \ 0}$

Next, we multiply and

$\frac{\begin{array}[b]{r}{\color{Red} 1}0\\ \times\ {\color{Red} 4}\end{array}}{\ \ \ 40}$

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Example Question #4 : Whole Numbers

Solve:

$\frac{\begin{array}[b]{r}11\\ \times\ 5\end{array}}{\space }$

Possible Answers:

Correct answer:

Explanation:

We can make a rectangular array using squares to help us solve this problem. Our multiplication problem is $11\times 5$ ; therefore, the rectangular array should have squares across the top row and squares down the first column. The rectangular array should look like the image below:

Screen shot 2016 05 18 at 12.14.20 pm

We can count the squares to find our answer. The correct answer is is

In order to solve this problem using multiplication, we must multiply the multiplier by each digit of the multiplicand to get the answer, which is called the product.

$\frac{\begin{array}[b]{r}\textup{multiplicand}\\ \times\ \ \ \ \textup{multiplier}\end{array}}{\ \ \ \ \textup{product}}$

For this problem, is the multiplier and is the multiplicand.

First, we multiply and

$\frac{\begin{array}[b]{r}1{\color{Red} 1}\\ \times\ {\color{Red} 5}\end{array}}{\ \ \ \ 5}$

Next, we multiply and

$\frac{\begin{array}[b]{r}{\color{Red} 1}1\\ \times\ {\color{Red} 5}\end{array}}{\ \ \ 55}$

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Example Question #5 : Whole Numbers

Solve the following:

$\frac{\begin{array}[b]{r}11\\ \times\ 6\end{array}}{\space }$

Possible Answers:

Correct answer:

Explanation:

We can make a rectangular array using squares to help us solve this problem. Our multiplication problem is $11\times 6$ ; therefore, the rectangular array should have squares across the top row and squares down the first column. The rectangular array should look like the image below:

Screen shot 2016 05 18 at 12.20.54 pm

We can count the squares to find our answer. The correct answer is is

In order to solve this problem using multiplication, we must multiply the multiplier by each digit of the multiplicand to get the answer, which is called the product.

$\frac{\begin{array}[b]{r}\textup{multiplicand}\\ \times\ \ \ \ \textup{multiplier}\end{array}}{\ \ \ \ \textup{product}}$

For this problem, is the multiplier and is the multiplicand.

First, we multiply and

$\frac{\begin{array}[b]{r}1{\color{Red} 1}\\ \times\ {\color{Red} 6}\end{array}}{\ \ \ \ 6}$

Next, we multiply and

$\frac{\begin{array}[b]{r}{\color{Red} 1}1\\ \times\ {\color{Red} 6}\end{array}}{\ \ \ 66}$

Report an Error

Example Question #6 : Whole Numbers

Solve:

$\frac{\begin{array}[b]{r}11\\ \times\ 4\end{array}}{\space }$

Possible Answers:

Correct answer:

Explanation:

We can make a rectangular array using squares to help us solve this problem. Our multiplication problem is $11\times 4$ ; therefore, the rectangular array should have squares across the top row and squares down the first column. The rectangular array should look like the image below:

Screen shot 2016 05 18 at 12.31.20 pm

We can count the squares to find our answer. The correct answer is is

In order to solve this problem using multiplication, we must multiply the multiplier by each digit of the multiplicand to get the answer, which is called the product.

$\frac{\begin{array}[b]{r}\textup{multiplicand}\\ \times\ \ \ \ \textup{multiplier}\end{array}}{\ \ \ \ \textup{product}}$

For this problem, is the multiplier and is the multiplicand.

First, we multiply and

$\frac{\begin{array}[b]{r}1{\color{Red} 1}\\ \times\ {\color{Red} 4}\end{array}}{\ \ \ \ 4}$

Next, we multiply and

$\frac{\begin{array}[b]{r}{\color{Red} 1}1\\ \times\ {\color{Red} 4}\end{array}}{\ \ \ 44}$

Report an Error

Example Question #971 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Solve:

$\frac{\begin{array}[b]{r}12\\ \times\ 4\end{array}}{\space }$

Possible Answers:

Correct answer:

Explanation:

We can make a rectangular array using squares to help us solve this problem. Our multiplication problem is $12\times 4$ ; therefore, the rectangular array should have squares across the top row and squares down the first column. The rectangular array should look like the image below:

Screen shot 2016 05 18 at 12.36.48 pm

We can count the squares to find our answer. The correct answer is is

In order to solve this problem using multiplication, we must multiply the multiplier by each digit of the multiplicand to get the answer, which is called the product.

$\frac{\begin{array}[b]{r}\textup{multiplicand}\\ \times\ \ \ \ \textup{multiplier}\end{array}}{\ \ \ \ \textup{product}}$

For this problem, is the multiplier and is the multiplicand.

First, we multiply and

$\frac{\begin{array}[b]{r}1{\color{Red} 2}\\ \times\ {\color{Red} 4}\end{array}}{\ \ \ \ 8}$

Next, we multiply and

$\frac{\begin{array}[b]{r}{\color{Red} 1}2\\ \times\ {\color{Red} 4}\end{array}}{\ \ \ 48}$

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All ISEE Middle Level Quantitative Resources

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ISEE Middle Level Quantitative : Numbers and Operations

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

All ISEE Middle Level Quantitative Resources

Example Questions

Example Question #6 : How To Find The Distributive Property

Example Question #961 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Example Question #962 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Example Question #1 : Whole Numbers

Example Question #2 : Whole Numbers

Example Question #3 : Whole Numbers

Example Question #4 : Whole Numbers

Example Question #5 : Whole Numbers

Example Question #6 : Whole Numbers

Example Question #971 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

All ISEE Middle Level Quantitative Resources

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