"A Day at the Farm" worksheet: Determine if statements about rational numbers are true or false.

Let's go through each statement one by one and determine whether it is true or false, based on the definition of rational numbers.

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🔹 Definition Reminder:

A rational number is any number that can be expressed as a fraction of two integers, where the denominator is not zero.
In other words, a number is rational if it can be written in the form:
$$
\frac{p}{q}, \quad \text{where } p \text{ and } q \text{ are integers and } q \ne 0.
$$

Rational numbers include:
- Integers (e.g., 5 = 5/1)
- Terminating decimals (e.g., 0.25 = 1/4)
- Repeating decimals (e.g., 0.333... = 1/3)

Irrational numbers cannot be written as such fractions (e.g., π, √2).

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Now let’s evaluate each statement:

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✔ Statement 1:

"Rational numbers are numbers that cannot be expressed as the fraction of two integers."

This is incorrect because rational numbers can be expressed as a fraction of two integers. The statement says they cannot, which is the opposite.

👉 Answer: FALSE

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✔ Statement 2:

"Numbers that have terminating and repeating decimals are considered rational numbers."

Yes! This is correct.
- Terminating decimals like 0.5 = 1/2
- Repeating decimals like 0.666... = 2/3
→ Both are rational.

👉 Answer: TRUE

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✔ Statement 3:

"The number pi is an example of rational number."

No! π (pi) is approximately 3.14159..., but its decimal never ends and never repeats. It cannot be written as a fraction of two integers.

So, π is irrational.

👉 Answer: FALSE

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✔ Statement 4:

"Rational numbers can be expressed in the form of decimals."

Yes! All rational numbers can be written as decimals — either terminating or repeating.

For example:
- 1/2 = 0.5 (terminating)
- 1/3 = 0.333... (repeating)

So this is true.

👉 Answer: TRUE

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✔ Statement 5:

"The number ⅓ is an example of rational number."

Yes! ⅓ is already a fraction of two integers: 1 and 3. So it is rational.

Even though its decimal is repeating (0.333...), it's still rational.

👉 Answer: TRUE

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✔ Final Answers:

| Statement | Answer |
|---------|--------|
| 1 | FALSE |
| 2 | TRUE |
| 3 | FALSE |
| 4 | TRUE |
| 5 | TRUE |

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✔ Summary:
Rational numbers = can be written as fractions → include terminating/repeating decimals → examples: ½, ⅓, 0.75
Irrational numbers = cannot be written as fractions → examples: π, √2

Let me know if you'd like a printable version or explanation for students! 🌾🌼