Question
is 4/5 + 15 rational or irrational
Answers
GPT-4o mini
To determine whether \( \frac{4}{5} + 15 \) is rational or irrational, we can first convert the whole number \( 15 \) into a fraction.
We can express \( 15 \) as \( \frac{15}{1} \). Now, we can find a common denominator to add the two fractions:
\[
\frac{4}{5} + \frac{15}{1} = \frac{4}{5} + \frac{15 \times 5}{1 \times 5} = \frac{4}{5} + \frac{75}{5}
\]
Now, add the two fractions:
\[
\frac{4 + 75}{5} = \frac{79}{5}
\]
Since \( \frac{79}{5} \) is expressed as a fraction where both the numerator and the denominator are integers (with the denominator not equal to zero), it is a rational number.
So, \( \frac{4}{5} + 15 \) is rational.
We can express \( 15 \) as \( \frac{15}{1} \). Now, we can find a common denominator to add the two fractions:
\[
\frac{4}{5} + \frac{15}{1} = \frac{4}{5} + \frac{15 \times 5}{1 \times 5} = \frac{4}{5} + \frac{75}{5}
\]
Now, add the two fractions:
\[
\frac{4 + 75}{5} = \frac{79}{5}
\]
Since \( \frac{79}{5} \) is expressed as a fraction where both the numerator and the denominator are integers (with the denominator not equal to zero), it is a rational number.
So, \( \frac{4}{5} + 15 \) is rational.