Question

build a venn diagram.

• use the names of the sets to label the regions.
• place the numbers in the correct regions.

names of the sets
whole numbers
rational numbers
integers
numbers
7.23 -22
0 -44
-5/3

Explanation:

Step1: Recall number - set definitions

Whole numbers are non - negative integers: 0, 1, 2, 3, ... Integers are whole numbers and their negatives: ..., - 2, - 1, 0, 1, 2, ... Rational numbers are numbers that can be written as a fraction $\frac{a}{b}$ where $a,b\in\mathbb{Z}$ and $b
eq0$.

Step2: Analyze each number

• $7.23=\frac{723}{100}$, so it is a rational number but not an integer or a whole number. It goes in the part of the rational - numbers circle that is not in the integers circle.
• $-22$ is an integer. Since whole numbers are non - negative, $-22$ is not a whole number. It goes in the part of the integers circle that is not in the whole - numbers circle.
• $0$ is both a whole number and an integer. It goes in the intersection of the whole - numbers and integers circles.
• $-44$ is an integer but not a whole number. It goes in the part of the integers circle that is not in the whole - numbers circle.
• $-\frac{5}{3}$ is a rational number but not an integer or a whole number. It goes in the part of the rational - numbers circle that is not in the integers circle.

We would have a large circle labeled "Rational numbers". Inside it, a smaller circle labeled "Integers". And inside the "Integers" circle, a smaller circle labeled "Whole numbers".

• Place $7.23$ and $-\frac{5}{3}$ in the region of the "Rational numbers" circle that is outside the "Integers" circle.
• Place $-22$ and $-44$ in the region of the "Integers" circle that is outside the "Whole numbers" circle.
• Place $0$ in the intersection of the "Whole numbers" and "Integers" circles.

Answer:

The Venn - diagram should have a large circle labeled "Rational numbers" with a smaller circle labeled "Integers" inside it and an even smaller circle labeled "Whole numbers" inside the "Integers" circle. Place $7.23$ and $-\frac{5}{3}$ in the part of the "Rational numbers" circle that is outside the "Integers" circle. Place $-22$ and $-44$ in the part of the "Integers" circle that is outside the "Whole numbers" circle. Place $0$ in the intersection of the "Whole numbers" and "Integers" circles.