Question

Closure property implies that the product of 4/5 and 15 is rational irrational an integer or zero

Answer 1

To determine the type of the product of \( \frac{4}{5} \) and \( 15 \), we can multiply the two numbers:

\[
\frac{4}{5} \times 15 = \frac{4 \times 15}{5} = \frac{60}{5} = 12
\]

Now let's classify the result:

- **Rational numbers** are numbers that can be expressed as a fraction \( \frac{a}{b} \) where \( a \) and \( b \) are integers and \( b \neq 0 \).
- **Irrational numbers** cannot be expressed as such a fraction.
- **Integers** are whole numbers (positive, negative, or zero).
- **Zero** is also considered either an integer or a rational number since it can be expressed as \( \frac{0}{1} \).

Since \( 12 \) is a whole number, it is classified as an integer. Additionally, because it can be expressed as \( \frac{12}{1} \), it is also a rational number.

Thus, the product of \( \frac{4}{5} \) and \( 15 \) is:

- An **integer** (specifically \( 12 \)).
- A **rational number** (since all integers are also rational).

In conclusion, the product \( \frac{4}{5} \times 15 = 12 \) is an **integer** and also a **rational number**. It is not an irrational number or zero.