Question
The closure property implies that the product of 4/5 and 15 is what type of number?
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GPT-4o mini
The closure property refers to the idea that when you perform an operation on numbers within a certain set, the result will also be within that set. Let's calculate the product of \( \frac{4}{5} \) and \( 15 \):
\[
\frac{4}{5} \times 15 = \frac{4 \times 15}{5} = \frac{60}{5} = 12
\]
Now, \( 12 \) is a whole number (also known as an integer). Since \( \frac{4}{5} \) is a rational number and \( 15 \) is also an integer (which can be expressed as a rational number \( \frac{15}{1} \)), their product is still a rational number.
To summarize, the product of \( \frac{4}{5} \) and \( 15 \) is \( 12 \), which is an integer, and it also confirms the closure property for rational numbers since the product is still a rational number.
\[
\frac{4}{5} \times 15 = \frac{4 \times 15}{5} = \frac{60}{5} = 12
\]
Now, \( 12 \) is a whole number (also known as an integer). Since \( \frac{4}{5} \) is a rational number and \( 15 \) is also an integer (which can be expressed as a rational number \( \frac{15}{1} \)), their product is still a rational number.
To summarize, the product of \( \frac{4}{5} \) and \( 15 \) is \( 12 \), which is an integer, and it also confirms the closure property for rational numbers since the product is still a rational number.
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