Question

1. a list of numbers is shown below. \\(-8.5, 2, \frac{2}{3}, 0, 6, \frac{9}{4}, -246\\) which venn diagram correctly classifies the list of numbers? three venn diagrams labeled a, b, c are shown, each classifying numbers into natural (counting) numbers, whole numbers, integers, and rational numbers with different placements of the given numbers

Explanation:

Step1: Recall Number Sets

Natural (Counting) Numbers: \(1, 2, 3, \dots\) (so \(2, 6\) here). Whole Numbers: Natural + \(0\) (so \(0, 2, 6\)). Integers: Whole + negatives (so \(-246, 0, 2, 6\)). Rational Numbers: All fractions/decimals that terminate/repeat (\(-8.5, \frac{2}{3}, \frac{9}{4}, -246, 0, 2, 6\)).

Step2: Analyze Venn Diagrams

• Option A: Whole Numbers include \(0, 2, 6\); Integers include Whole + \(-246\); Rational include Integers + \(-8.5, \frac{2}{3}, \frac{9}{4}\). Matches number classifications.
• Option B: Misplaces \(-8.5, \frac{2}{3}, \frac{9}{4}\) (not in Integers).
• Option C: Misplaces \(0\) (Whole, not just with Integers outside Natural).

Answer:

A