Question
is -7 8/37 rational or irrational
Answers
GPT-4o mini
The number \(-7 \frac{8}{37}\) can be expressed as a mix of an integer and a fraction. To determine if it's rational or irrational, we can convert it into an improper fraction.
First, convert \(-7\) into a fraction:
\[
-7 = \frac{-259}{37}
\]
because \(-7 \times 37 = -259\).
Now, we can add \(-\frac{259}{37}\) and \(\frac{8}{37}\):
\[
-\frac{259}{37} + \frac{8}{37} = \frac{-259 + 8}{37} = \frac{-251}{37}
\]
Since \(-251\) and \(37\) are both integers and \(37 \neq 0\), the resulting fraction \(-\frac{251}{37}\) is a rational number.
Thus, \(-7 \frac{8}{37}\) is a rational number.
First, convert \(-7\) into a fraction:
\[
-7 = \frac{-259}{37}
\]
because \(-7 \times 37 = -259\).
Now, we can add \(-\frac{259}{37}\) and \(\frac{8}{37}\):
\[
-\frac{259}{37} + \frac{8}{37} = \frac{-259 + 8}{37} = \frac{-251}{37}
\]
Since \(-251\) and \(37\) are both integers and \(37 \neq 0\), the resulting fraction \(-\frac{251}{37}\) is a rational number.
Thus, \(-7 \frac{8}{37}\) is a rational number.