Let's analyze the diagram and the question step by step.
Diagram Explanation:
The diagram shows
nested sets of numbers:
- The
largest circle is
Rational Numbers.
- Inside it is the set of
Integers.
- Inside the Integers is the set of
Whole Numbers.
This means:
- All
integers are rational numbers.
- All
whole numbers are integers (and therefore rational).
- But
not all rational numbers are integers — some rational numbers are fractions or decimals that are not whole numbers.
Examples in the diagram:
- $ \frac{3}{10} $: This is a rational number, but
not an integer.
- $ -25 $: This is an integer (and rational).
- $ 74 $: This is a whole number (so also an integer and rational).
- $ 170 $: Also a whole number → integer → rational.
---
Question:
> Which of the following is a
rational number but not an integer?
Options:
- 170
- 74
- $ \frac{3}{10} $
- -25
Let’s evaluate each:
1.
170: Whole number → integer → rational
✔
But it
is an integer →
✘ not the answer.
2.
74: Whole number → integer → rational
✔
But it
is an integer →
✘ not the answer.
3.
$ \frac{3}{10} $: This is a fraction. It can be written as a ratio of two integers (3 and 10), so it is
rational.
But it is
not a whole number, nor an integer (since it's not a whole number without a fractional part).
So:
rational but not an integer →
✔ Correct!
4.
-25: Integer (negative whole number) → rational
✔
But it
is an integer →
✘ not the answer.
---
✔ Final Answer:
$$
\boxed{\frac{3}{10}}
$$
This is a
rational number but not an integer.
Parent Tip: Review the logic above to help your child master the concept of whole numbers integers and rational numbers worksheet.
