Question

extended response

1. place the following numbers in the venn diagram.

integers
rational numbers
-0.462 -56 735 0.326 12

Explanation:

Step1: Recall definitions

Integers are whole - numbers and their negatives. Rational numbers are numbers that can be written as a fraction $\frac{a}{b}$ where $a,b$ are integers and $b
eq0$. All integers are rational numbers.

Step2: Categorize numbers

• $-56$ is an integer and a rational number.
• $735$ is an integer and a rational number.
• $12$ is an integer and a rational number.
• $- 0.462=\frac{-462}{1000}$ is a rational number but not an integer.
• $0.326=\frac{326}{1000}$ is a rational number but not an integer.

We place $-56$, $735$, $12$ in the intersection of the Integers and Rational Numbers circles. We place $-0.462$ and $0.326$ in the Rational Numbers circle but outside the Integers circle.

Answer:

In the intersection of Integers and Rational Numbers: $-56$, $735$, $12$. In the Rational Numbers circle (but not in the Integers circle): $-0.462$, $0.326$.