Question

is 1/9 + 5/2 rational or irrational

Answer 1

To determine whether \( \frac{1}{9} + \frac{5}{2} \) is rational or irrational, we first need to find a common denominator and add the two fractions.

The denominators are 9 and 2. The least common multiple (LCM) of 9 and 2 is 18.

Now, we convert each fraction:

\[
\frac{1}{9} = \frac{1 \times 2}{9 \times 2} = \frac{2}{18}
\]

\[
\frac{5}{2} = \frac{5 \times 9}{2 \times 9} = \frac{45}{18}
\]

Next, we add the fractions:

\[
\frac{1}{9} + \frac{5}{2} = \frac{2}{18} + \frac{45}{18} = \frac{2 + 45}{18} = \frac{47}{18}
\]

Since \( \frac{47}{18} \) is a fraction where both the numerator and the denominator are integers (and the denominator is not zero), it is a rational number.

Thus, \( \frac{1}{9} + \frac{5}{2} \) is a rational number.