Question
is 0.5 + 3/4 a rational or irrational
Answers
GPT-4o mini
To determine whether \(0.5 + \frac{3}{4}\) is rational or irrational, we can first convert \(0.5\) to a fraction.
The decimal \(0.5\) can be expressed as \(\frac{1}{2}\).
Now, let's add \(\frac{1}{2}\) and \(\frac{3}{4}\):
\[
\frac{1}{2} + \frac{3}{4}
\]
To add these fractions, we need a common denominator. The least common denominator (LCD) for \(2\) and \(4\) is \(4\). We can convert \(\frac{1}{2}\) to a fraction with a denominator of \(4\):
\[
\frac{1}{2} = \frac{2}{4}
\]
Now we can add:
\[
\frac{2}{4} + \frac{3}{4} = \frac{2 + 3}{4} = \frac{5}{4}
\]
Since \(\frac{5}{4}\) is a fraction where both the numerator and denominator are integers (and the denominator is not zero), it is considered a rational number.
Therefore, \(0.5 + \frac{3}{4}\) is a **rational** number.
The decimal \(0.5\) can be expressed as \(\frac{1}{2}\).
Now, let's add \(\frac{1}{2}\) and \(\frac{3}{4}\):
\[
\frac{1}{2} + \frac{3}{4}
\]
To add these fractions, we need a common denominator. The least common denominator (LCD) for \(2\) and \(4\) is \(4\). We can convert \(\frac{1}{2}\) to a fraction with a denominator of \(4\):
\[
\frac{1}{2} = \frac{2}{4}
\]
Now we can add:
\[
\frac{2}{4} + \frac{3}{4} = \frac{2 + 3}{4} = \frac{5}{4}
\]
Since \(\frac{5}{4}\) is a fraction where both the numerator and denominator are integers (and the denominator is not zero), it is considered a rational number.
Therefore, \(0.5 + \frac{3}{4}\) is a **rational** number.