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Math  /  Numbers & Operations

Question1. Adding and Subtracting Rational Numbers A. Sketch a Venn diagrant to show all of the sets and subsets of numbers that you know. Use your Venn diagram to decide whether each statement is true or false. Explain your reasoning,
1. All integers are included in the set of natural numbers. False. 0 is an inierger but is not inciuded in the ser of naturaul numbers
2. All whole numbers are included in the set of integers. True. whole number s include 0
3. All rational numbers are included in the
4. 29\frac{2}{9} is included in the set of integers. set of whole numbers.
5. -3 is included in the set of
6. 35\frac{3}{5} is included in the set of rational numbers. rational numbers. True. 3 is a number form being eaval to "o" which is the clefenition of rationall F

Studdy Solution

STEP 1

1. We are dealing with different sets of numbers: natural numbers, whole numbers, integers, and rational numbers.
2. We need to determine the truth value of each statement based on these sets.

STEP 2

1. Define the sets of numbers.
2. Evaluate each statement using the definitions of these sets.

STEP 3

Define the sets of numbers: - **Natural Numbers**: Typically the set {1,2,3,…}\{1, 2, 3, \ldots\}. Some definitions include 00. - **Whole Numbers**: The set {0,1,2,3,…}\{0, 1, 2, 3, \ldots\}. - **Integers**: The set {…,−3,−2,−1,0,1,2,3,…}\{\ldots, -3, -2, -1, 0, 1, 2, 3, \ldots\}. - **Rational Numbers**: Numbers that can be expressed as a fraction ab\frac{a}{b} where aa and bb are integers and b≠0b \neq 0.

STEP 4

Evaluate each statement:
Statement 1: All integers are included in the set of natural numbers. - **False**: Integers include negative numbers and zero, which are not part of the natural numbers.
Statement 2: All whole numbers are included in the set of integers. - **True**: Whole numbers are non-negative integers, which are a subset of integers.
Statement 3: All rational numbers are included in the set of whole numbers. - **False**: Rational numbers include fractions and decimals, which are not whole numbers.
Statement 4: 29\frac{2}{9} is included in the set of integers. - **False**: 29\frac{2}{9} is a fraction and not a whole number.
Statement 5: -3 is included in the set of rational numbers. - **True**: -3 can be expressed as −31\frac{-3}{1}, which is a rational number.
Statement 6: 35\frac{3}{5} is included in the set of rational numbers. - **True**: 35\frac{3}{5} is a fraction, which fits the definition of a rational number.

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