Mathematical Operations and Foundational Constraints

Negative Numbers and Division by Zero

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QUESTION OF

Views #: 9

Questions #: 20

Time: 20 minutes

Pass Score: 80.0%

Style

Step

List

Mode

Exam

Practice

Adding Negative Numbers

1 pts

volume_mute

Evaluate: -5 + 2

-7

-3

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Correct Answer

Explanation

Subtracting Integers

1 pts

volume_mute

Evaluate: 6 - 9

-3

-15

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Correct Answer

Explanation

Multiplying Signs

1 pts

volume_mute

Select all products that are positive.

(-2)(-3)

(-4)(2)

(5)(6)

(-1)(7)

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Correct Answer

Explanation

Division of Negative Numbers

1 pts

volume_mute

Evaluate: -20 ÷ 5

-4

-25

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Correct Answer

Explanation

Zero Product

1 pts

Any number multiplied by 0 equals (1).

Please drag and drop the selected option in the right place or type it instead

undefined

infinity

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Correct Answer

Explanation

Division by Zero

1 pts

volume_mute

Which operation is undefined?

8 ÷ 2

0 ÷ 5

7 ÷ 0

9 ÷ 3

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Correct Answer

Explanation

Integer Operations

1 pts

Please drag and drop the options to sort them

Arrange the results from least to greatest: -2, 5, -7, 0

-2

-7

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Correct Answer

Explanation

Match Integer Rules

1 pts

Match each rule with its result sign.

To complete the line match

Click on an item in the first group
Click on the match in the second group

To delete a match, double click on a line

Rule

Negative × Negative

Positive × Negative

Result sign

Negative

Positive

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Correct Answer

Explanation

Classify Integer Results

2 pts

Classify the following values.

drag and drop the selected option to the right place

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Correct Answer

Explanation

Undefined Operations

1 pts

volume_mute

The expression $\frac{5}{0}$ is:

undefined

negative

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Correct Answer

Explanation

Why Negative Numbers are Necessary

1 pts

volume_mute

Which of the following equations cannot be solved if negative numbers are not accepted?

$2x + 5 = 9$

$2x + 5 = 0$

$x^2 = 4$

$3x = 12$

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Correct Answer

Explanation

Product of Two Negative Numbers

1 pts

volume_mute

Solve the equation $7x - 5 = 10x - 11$ by transposing unknowns to the right side. The resulting step requires $-3x = -6$, which gives $x = \frac{-6}{-3}$.

What must $(-1) \times (-1)$ equal for the solution to be consistent?

-1

Cannot be determined

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Explanation

Division by Zero — Case 1

1 pts

volume_mute

Consider the expression $\frac{a}{0}$ where $a \neq 0$. Division is defined as finding $x$ such that $0 \cdot x = a$. What is the result?

The result is 0

The result is $\infty$

There is no such number $x$ — the expression is meaningless

The result is $a$

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Explanation

Division by Zero — Case 2: 0/0

1 pts

volume_mute

If division by zero were permitted, what would $\frac{0}{0}$ represent?

The number 1

The number 0

Any number whatsoever — it is indeterminate

Positive infinity

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Explanation

Why Division by Zero is Undefined

2 pts

Please drag and drop the options to sort them

Sort the following logical steps in the correct order to show why division by zero leads to a contradiction.

Conclude all different numbers are equal — an absurd result

Assume division by zero is permitted

Observe that $0 \cdot x = 0$ is satisfied by every number $x$

Division must yield a unique result, but $0/0$ does not

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Explanation

Operations with Negative Numbers

2 pts

Classify each of the following expressions as Positive, Negative, or Zero.

drag and drop the selected option to the right place

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Explanation

Division by Zero — True or False

1 pts

volume_mute

True or False: The expression $\frac{5}{0}$ is equal to infinity ($\infty$) in standard mathematics.

True

False

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Explanation

Identifying Undefined Expressions

2 pts

volume_mute

Which of the following expressions are undefined in standard mathematics? (Select all that apply.)

$\frac{7}{0}$

$\frac{0}{7}$

$\frac{0}{0}$

$0^0$

$(-3)^2$

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Correct Answer

Explanation

Sign Rules: Match Operation to Result

2 pts

Match each operation involving signed numbers to the correct sign of its result.

To complete the line match

Click on an item in the first group
Click on the match in the second group

To delete a match, double click on a line

Operation

Negative ÷ Negative

Positive × Negative

Negative × Negative

Positive × Positive

Sign of Result

Always Positive

Always Negative

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Correct Answer

Explanation

Division Defined Through Multiplication

1 pts

According to the formal definition in algebra, dividing a number $a$ by a number $b$ (where $b \neq 0$) means finding a number $x$ such that: 1($)

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Explanation

Year 7 Year 8

Adding Negative Numbers

Correct Answer

Explanation

Subtracting Integers

Correct Answer

Explanation

Multiplying Signs

Correct Answer

Explanation

Division of Negative Numbers

Correct Answer

Explanation

Zero Product

Correct Answer

Explanation

Division by Zero

Correct Answer

Explanation

Integer Operations

Correct Answer

Explanation

Match Integer Rules

Rule

Result sign

Correct Answer

Explanation

Classify Integer Results

drag and drop the selected option to the right place

Correct Answer

Explanation

Undefined Operations

Correct Answer

Explanation

Why Negative Numbers are Necessary

Correct Answer

Explanation

Product of Two Negative Numbers

Correct Answer

Explanation

Division by Zero — Case 1

Correct Answer

Explanation

Division by Zero — Case 2: 0/0

Correct Answer

Explanation

Why Division by Zero is Undefined

Correct Answer

Explanation

Operations with Negative Numbers

drag and drop the selected option to the right place

Correct Answer

Explanation

Division by Zero — True or False

Correct Answer

Explanation

Identifying Undefined Expressions

Correct Answer

Explanation

Sign Rules: Match Operation to Result

Operation

Sign of Result

Correct Answer

Explanation

Division Defined Through Multiplication

Correct Answer

Explanation

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