To determine how much time Whitney spends listening to her podcast over a five-day period, we need to calculate the total time using the daily listening time of \( \frac{7}{9} \) hours.
-
Using multiplication: The expression \( 5 \times \frac{7}{9} \) calculates the total time for 5 days and represents it correctly.
-
Using addition: The expression \( \frac{7}{9} + \frac{7}{9} + \frac{7}{9} + \frac{7}{9} + \frac{7}{9} \) adds up the time for each day directly, which also accurately represents the total time.
-
Using a fractional representation: The expression \( \frac{35}{9} \) is obtained by simplifying \( 5 \times \frac{7}{9} \) (since \( 5 \times 7 = 35 \)), and thus it correctly represents the total time as well.
The correct expressions that represent the time Whitney spends listening to the podcast over a five-day period are:
- \( 5 \times \frac{7}{9} \)
- \( \frac{7}{9} + \frac{7}{9} + \frac{7}{9} + \frac{7}{9} + \frac{7}{9} \)
- \( \frac{35}{9} \)
Therefore, the three expressions are:
- \( 5 \times \frac{7}{9} \)
- \( \frac{7}{9} + \frac{7}{9} + \frac{7}{9} + \frac{7}{9} + \frac{7}{9} \)
- \( \frac{35}{9} \)
The other options, \( \frac{12}{9} \) (which does not represent the total time) and \( 5 + \frac{7}{9} \) (which incorrectly adds a whole number and a fraction), do not apply.