Real numbers

Integers, whole numbers

Quiz Type

Practice

Subject

Mathematics

Level

Level 100

Questions

10 questions

Created By

Kobby Smith

Quick Rules

Time limit: 50 minutes
Multiple attempts are not allowed
All questions must be answered to submit

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Question 1 of 10

Question 1

Basic multiple choice Remembering

What is an integer?

A whole number that can be positive, negative, or zero

Correct

A natural number that is greater than zero

A fraction that consists of a numerator and denominator

A decimal number that is less than one

Explanation

An integer is defined as a whole number that can be positive, negative, or zero. This includes numbers like -3, 0, and 5.

Question 2

Basic multiple choice Remembering

Which of the following is NOT an integer?

-2

3.5

Correct

Explanation

3.5 is not an integer because integers cannot have fractional or decimal components; they must be whole numbers.

Question 3

Basic multiple choice Remembering

Which of the following groups includes only whole numbers?

0, 1, 2, 3

Correct

-1, 0, 1

-2, -1, 0

1.5, 2, 3

Explanation

Whole numbers are defined as all non-negative integers, starting from 0. Therefore, 0, 1, 2, 3 includes only whole numbers.

Question 4

Basic multiple choice Understanding

What is the sum of -1 and 1?

Correct

-1

Explanation

The sum of -1 and 1 equals 0 because adding a number and its negative yields zero.

Question 5

Basic multiple choice Understanding

Which statement about integers is true?

Integers can be both positive and negative

Correct

Integers only include positive whole numbers

Integers are always less than zero

Integers cannot include zero

Explanation

The definition of integers encompasses both positive and negative whole numbers, including zero.

Question 6

Complex multiple choice Understanding

A teacher presents the concept of integers and whole numbers to her students. She asks them to identify which of the following sets of numbers consists solely of integers. Which option correctly identifies a set that includes integers and excludes any non-integer values?

{-3, 0, 5}

Correct

{1.5, 2, 3}

{4, 4.0, 5}

{-2, 0.1, 1}

Explanation

The correct answer is {-3, 0, 5} because it contains only integers, which are whole numbers, both negative and positive, as well as zero. The other options include non-integer values (1.5, 4.0, 0.1), which disqualify them as sets of integers.

Question 7

Complex multiple choice Analyzing

During a class discussion, a student claims that any whole number is also an integer but not all integers are whole numbers. What would be the most accurate analysis of this assertion regarding the relationship between whole numbers and integers?

The student is correct; whole numbers start from 0 and positive integers are included, while negative integers are not whole numbers.

Correct

The assertion is incorrect because both whole numbers and integers start from 1.

The student is wrong; whole numbers are a subset of integers including only the positive ones.

All integers include fractions, which makes the student’s statement false.

Explanation

The correct answer is that the student is correct; whole numbers include 0 and all positive integers, while integers include both negative and positive whole numbers. Therefore, the assertion directly explains the relationship accurately. Other answers misinterpret the definitions of whole numbers and integers.

Question 8

Case based multiple choice Understanding

[Case Scenario] A teacher is planning a lesson on integers and whole numbers. She asks her students to list five examples of integers and five examples of whole numbers. During the discussion, one student confidently states that numbers like -1, 0, 1, 2, and 3 are all whole numbers while another student claims that -2, -1, 0, 1, and 2 are all integers. The teacher pauses to reflect on the definitions of integers and whole numbers. Based on this discussion, which of the following conclusions can the teacher draw about the students' understanding of these concepts? Question: What is the correct alignment of the students’ definitions of integers and whole numbers?

Both students correctly identified their sets of numbers.

The first student correctly identified whole numbers, while the second identified integers correctly.

Correct

Both students incorrectly defined their respective sets.

The second student incorrectly listed integers while the first was correct in naming whole numbers.

Explanation

In the context of the definitions, whole numbers are defined as non-negative integers (0 and positive numbers), whereas integers are defined as all positive and negative whole numbers, including zero. This reveals a misunderstanding by the first student.

Question 9

Case based multiple choice Understanding

[Case Scenario] A parent is teaching their child a game involving integers and whole numbers. They write down a list of numbers: -3, -1, 0, 4, 7, and ask their child to categorize them into integers and whole numbers. The child correctly identifies that -3, -1, and 4 are integers, and claims that 0, 4, and 7 are whole numbers. The parent is impressed but raises a question on the child’s understanding about negative numbers. Question: Which of the child’s categorizations need correction?

The child correctly categorized all the numbers.

The child needs to change the categorization of -3 and -1 to whole numbers.

The child should realize that only 0, 4, and 7 are whole numbers while -3 and -1 are integers.

Correct

The child incorrectly labeled all numbers and should categorize -1 and 0 as integers only.

Explanation

Whole numbers are defined as non-negative integers, which means the child must understand that numbers like -3 and -1 cannot be considered whole numbers.

Question 10

Case based multiple choice Understanding

[Case Scenario] During a class activity, students are asked to create a number line that includes integers and whole numbers ranging from -5 to 10. A group of students draws the number line accurately including points for -5, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10. Another group claims a number, say -2, should not be on the list because they think only non-negative numbers belong to whole numbers. Question: How should the teacher address the second group’s misunderstanding regarding the inclusion of numbers in the number line?

Explain that only integers are allowed in the number line.

Clarify that whole numbers include only positive integers and zero.

Correct

Address that -2 is an integer and should be included as it represents a valid part of the number line.

Inform them that all numbers are just integers and no other classification is necessary.

Explanation

The second group has mistakenly limited their understanding of whole numbers to only non-negative values. It is essential to clarify the differences between integers and whole numbers in this instance.