Question

Evaluate the expression shown below and write your answer as a fraction or mixed number in simplest form.
start fraction, start fraction, 2, divided by, 9, end fraction, plus, one ninth, divided by, one quarter, end fraction
4
1
​

9
2
​
+
9
1
​

​

Answer 1

To evaluate the expression \( \frac{2}{9} + \frac{1/9}{1/4} \), we'll start by simplifying the second term.

The term \( \frac{1/9}{1/4} \) can be rewritten using the rule for dividing fractions, which states that to divide by a fraction, you multiply by its reciprocal:

\[
\frac{1/9}{1/4} = \frac{1}{9} \times \frac{4}{1} = \frac{4}{9}
\]

Now, we can substitute this back into our original expression:

\[
\frac{2}{9} + \frac{4}{9}
\]

Since both fractions have the same denominator (9), we can simply add the numerators:

\[
\frac{2 + 4}{9} = \frac{6}{9}
\]

Next, we simplify \( \frac{6}{9} \):

\[
\frac{6}{9} = \frac{2}{3}
\]

Thus, the final answer is:

\[
\frac{2}{3}
\]