Math Snap

STEP 1

Assumptions1. We have two fractions, $\frac{}{9}$ and $\frac{9}{11}$.
. We are asked to determine if the sum of these two fractions is a rational or an irrational number.

STEP 2

First, let's add the two fractions. To add fractions, we need to find a common denominator. The common denominator of9 and11 is their product, which is99.
$$\frac{2}{9}+\frac{9}{11} = \frac{2 \times11}{9 \times11} + \frac{9 \times9}{11 \times9}
$$

STEP 3

Now, calculate the numerator and denominator for each fraction.
$$\frac{2 \times11}{9 \times11} + \frac{9 \times9}{11 \times9} = \frac{22}{99} + \frac{81}{99}
$$

STEP 4

Since the denominators are the same, we can add the numerators directly.
$$\frac{22}{99} + \frac{81}{99} = \frac{22 +81}{99}
$$

STEP 5

Calculate the sum in the numerator.
$$\frac{22 +81}{99} = \frac{103}{99}
$$

The sum of the two fractions is $\frac{103}{99}$, which is a fraction. A fraction is a type of rational number, as it can be expressed as the quotient of two integers. Therefore, the sum of the two fractions is a rational number.