The uploaded image shows a question about classifying numbers into various sets (Rational, Irrational, Whole, Integers, and Natural). Let's break it down step by step:

Numbers and their classifications:

1. −π

   • Rational? No (π is irrational, and multiplying by −1 doesn’t change that).
   • Irrational? Yes (π is irrational, so −π is too).
   • Whole? No (Whole numbers are non-negative integers, and −π is neither).
   • Integers? No (It’s not a whole number or integer since π isn’t an integer).
   • Natural? No (It’s not positive or whole).

2. 1.4

   • Rational? Yes (1.4 can be expressed as $\frac{14}{10}$ or $\frac{7}{5}$).
   • Irrational? No (It’s a finite decimal, so it’s rational).
   • Whole? No (It’s not a whole number since it’s a decimal).
   • Integers? No (It’s not a whole number or integer due to the decimal part).
   • Natural? No (Natural numbers are positive whole numbers).

3. $\frac{3}{2}$

   • Rational? Yes (It’s a ratio of two integers, hence rational).
   • Irrational? No (Irrational numbers cannot be expressed as a fraction).
   • Whole? No (Not a whole number due to the fractional part).
   • Integers? No (It’s not a whole number or integer).
   • Natural? No (It’s not positive or whole).

4. −3

   • Rational? Yes (Any integer is also rational).
   • Irrational? No (It can be expressed as $\frac{-3}{1}$, so it’s rational).
   • Whole? No (Whole numbers are non-negative).
   • Integers? Yes (−3 is an integer).
   • Natural? No (It’s negative, so it’s not natural).

Matched Results:

• −π: Irrational
• 1.4: Rational
• $\frac{3}{2}$: Rational
• −3: Rational, Integers

Let me know if you have questions or want further explanations!

Related Questions:

1. Can you define rational and irrational numbers in simpler terms?
2. Why isn’t $\frac{3}{2}$ considered an integer even though it’s a fraction?
3. How do natural numbers differ from whole numbers?
4. Could you give examples of numbers that are both integers and whole numbers?
5. How does the classification change if we deal with repeating decimals like 0.333...?

Tip:

When classifying numbers, start with the broadest sets (rational vs. irrational) and narrow down to specifics like integers or naturals.