Let's analyze the problem using the
Venn diagram provided and the definitions of number sets:
Number Set Definitions:
-
Whole numbers: Non-negative integers (0, 1, 2, 3, ...).
So: $ \{0, 1, 2, 3, ...\} $
-
Integers: Whole numbers and their negatives (..., -3, -2, -1, 0, 1, 2, 3, ...)
So: $ \{...,-3,-2,-1,0,1,2,3,...\} $
-
Rational numbers: Numbers that can be written as a fraction $ \frac{p}{q} $ where $ p $ and $ q $ are integers and $ q \neq 0 $. This includes all integers, fractions, and terminating or repeating decimals.
---
The Diagram Shows:
-
Whole numbers are inside
Integers, which are inside
Rational numbers.
- Examples:
- $-21$ is in
Integers but not in
Whole numbers → it’s negative.
- $115$ is in
Whole numbers → so also an integer.
- $-\frac{1}{3}$ is in
Rational numbers but
not in Integers (it's a fraction).
- $-23\frac{5}{9}$ is a mixed number (equal to $-\frac{212}{9}$) → not an integer.
---
Now evaluate each option:
1.
$-23\frac{5}{9}$
This is a mixed number = $-\frac{212}{9}$ → not a whole number, not an integer.
✘ Not an integer
2.
$-21$
Negative whole number → is an integer (but not a whole number).
✔ Is an integer
3.
$-\frac{1}{3}$
Fraction, not a whole number, not an integer.
✘ Not an integer
4.
$115$
Positive whole number → is an integer.
✔ Is an integer
---
✔ Correct Answers:
- $-21$
- $115$
---
Final Answer:
✔ -21
✔ 115
These are the
integers from the list.
>
Note: The checkboxes in your image show all four selected, but based on correct math, only
-21 and
115 are integers. So you should
uncheck $-23\frac{5}{9}$ and $-\frac{1}{3}$.
Parent Tip: Review the logic above to help your child master the concept of classify rational numbers worksheet.
