Integers And Set Of Real Numbers Quiz

1. Identify the set(s) to which the number 1/2 belongs.

Natural numbers

Whole numbers

Integers

Rational numbers

The number 1/2 belongs to the set of rational numbers because it can be expressed as a fraction, where the numerator is 1 and the denominator is 2. Rational numbers are numbers that can be expressed as a fraction of two integers, where the denominator is not zero.

Explanation

The number 1/2 belongs to the set of rational numbers because it can be expressed as a fraction, where the numerator is 1 and the denominator is 2. Rational numbers are numbers that can be expressed as a fraction of two integers, where the denominator is not zero.

2. _________ is the set of numbers that includes positive and negative numbers.

Whole numbers

Rational numbers

Natural numbers

Integers

Integers is the correct answer because it is the set of numbers that includes both positive and negative numbers, as well as zero. Whole numbers only include positive numbers and zero, while rational numbers include fractions and decimals. Natural numbers only include positive numbers, excluding zero and negative numbers. Therefore, integers is the most inclusive set that includes both positive and negative numbers.

Explanation

Integers is the correct answer because it is the set of numbers that includes both positive and negative numbers, as well as zero. Whole numbers only include positive numbers and zero, while rational numbers include fractions and decimals. Natural numbers only include positive numbers, excluding zero and negative numbers. Therefore, integers is the most inclusive set that includes both positive and negative numbers.

3. The number that can be written as a fraction is what?

Natural number

Rational number

Whole number

All of the above

A rational number is a number that can be expressed as a fraction, where the numerator and denominator are both integers. This includes all natural numbers, whole numbers, and integers, as they can be written as fractions with a denominator of 1. Therefore, the correct answer is "Rational number".

Explanation

A rational number is a number that can be expressed as a fraction, where the numerator and denominator are both integers. This includes all natural numbers, whole numbers, and integers, as they can be written as fractions with a denominator of 1. Therefore, the correct answer is "Rational number".

4. Identify the set(s) to which the number -1/8 belongs.

Natural numbers

Whole numbers

Integers

Rational numbers

The number -1/8 belongs to the set of rational numbers because it can be expressed as a fraction, where the numerator is an integer (-1) and the denominator is a non-zero integer (8). Rational numbers are numbers that can be expressed as a fraction of two integers.

Explanation

The number -1/8 belongs to the set of rational numbers because it can be expressed as a fraction, where the numerator is an integer (-1) and the denominator is a non-zero integer (8). Rational numbers are numbers that can be expressed as a fraction of two integers.

5. Identify the set(s) to which the number 21 belongs.

Natural numbers

Whole numbers

Integers

Rational numbers

The number 21 belongs to the set of natural numbers because it is a positive whole number. It also belongs to the set of whole numbers because it includes zero as well. Additionally, 21 belongs to the set of integers because it is a whole number that can be positive or negative. Lastly, 21 belongs to the set of rational numbers because it can be expressed as a fraction, 21/1. Therefore, 21 belongs to the sets of natural numbers, whole numbers, integers, and rational numbers.

Explanation

The number 21 belongs to the set of natural numbers because it is a positive whole number. It also belongs to the set of whole numbers because it includes zero as well. Additionally, 21 belongs to the set of integers because it is a whole number that can be positive or negative. Lastly, 21 belongs to the set of rational numbers because it can be expressed as a fraction, 21/1. Therefore, 21 belongs to the sets of natural numbers, whole numbers, integers, and rational numbers.

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6. Identify the set(s) to which the number -15 belongs.

Natural numbers

Whole numbers

Integers

Rational

Natural numbers are positive counting numbers starting from 1 (1, 2, 3, ...). Since -15 is negative, it is not a natural number.

Whole numbers include all natural numbers and 0, but not negative numbers. Therefore, -15 is not a whole number.

Integers include all positive and negative whole numbers, as well as 0. Since -15 is a negative whole number, it belongs to the set of integers.

Rational numbers are numbers that can be expressed as a fraction of two integers (e.g., -15 can be written as -15/1), so -15 is a rational number.

Thus, -15 belongs to the sets of integers and rational numbers.

Explanation

Natural numbers are positive counting numbers starting from 1 (1, 2, 3, ...). Since -15 is negative, it is not a natural number.

Whole numbers include all natural numbers and 0, but not negative numbers. Therefore, -15 is not a whole number.

Integers include all positive and negative whole numbers, as well as 0. Since -15 is a negative whole number, it belongs to the set of integers.

Rational numbers are numbers that can be expressed as a fraction of two integers (e.g., -15 can be written as -15/1), so -15 is a rational number.

Thus, -15 belongs to the sets of integers and rational numbers.

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7. Choose the equation(s) that fit the pattern n/n = 1.

3/3 =1

1.5/1.5 =1

1,435/1,435 =1

0/0 = 1

Dividing by 0 gives an undefined answer, so it cannot = 1

Explanation

Dividing by 0 gives an undefined answer, so it cannot = 1

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8. Which of the following does not apply to 7/8?

Integer

Rational number

Fraction

Whole number

A and D

A and B

A and C

None of the above

7/8 is a rational number because it can be written as a fraction. It is also a fraction by definition. However, it is not an integer or a whole number because integers and whole numbers are whole numbers without any fractional parts. Therefore, "Integer" and "Whole number" do not apply to 7/8.

Explanation

7/8 is a rational number because it can be written as a fraction. It is also a fraction by definition. However, it is not an integer or a whole number because integers and whole numbers are whole numbers without any fractional parts. Therefore, "Integer" and "Whole number" do not apply to 7/8.

9. Identify the set(s) to which the number 0 belongs. (Select all that apply)

Natural numbers

Whole numbers

Integers

Rational numbers

The number 0 belongs to the set of whole numbers because it is a non-negative integer. It also belongs to the set of integers because it can be expressed as a fraction with a denominator of 1. Additionally, 0 is a rational number because it can be expressed as the ratio of two integers.

Explanation

The number 0 belongs to the set of whole numbers because it is a non-negative integer. It also belongs to the set of integers because it can be expressed as a fraction with a denominator of 1. Additionally, 0 is a rational number because it can be expressed as the ratio of two integers.

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10. Which of the following is NOT an integer?

-5

0

3/4

100

Integers are whole numbers (no fractions or decimals) that can be positive, negative, or zero. The number 3/4 is a fraction, representing three-quarters of a whole, and therefore does not fit the definition of an integer. The other options, -5, 0, and 100, are all whole numbers and thus integers.

Explanation

Integers are whole numbers (no fractions or decimals) that can be positive, negative, or zero. The number 3/4 is a fraction, representing three-quarters of a whole, and therefore does not fit the definition of an integer. The other options, -5, 0, and 100, are all whole numbers and thus integers.