To find the time Whitney spends listening to her podcast over a five-day period when she listens for \( \frac{7}{9} \) of an hour each day, we can consider the following:
-
Repeated Addition: Since she listens for \( \frac{7}{9} \) of an hour each day for 5 days, we can express this as: \[ \frac{7}{9} + \frac{7}{9} + \frac{7}{9} + \frac{7}{9} + \frac{7}{9} \] This is equivalent to: \[ 5 \times \frac{7}{9} \]
-
Multiplication: The multiplication directly gives us the total time: \[ 5 \times \frac{7}{9} \]
-
Simplifying: The result of the multiplication can also be expressed as: \[ \frac{5 \times 7}{9} = \frac{35}{9} \]
Now, let's check the provided expressions:
- \( 5 + \frac{7}{9} \): This does not represent the total time over five days.
- \( 5 \times \frac{7}{9} \): This is correct, as it represents the total time.
- \( \frac{35}{9} \): This is correct, as it is the simplified form of \( 5 \times \frac{7}{9} \).
- \( \frac{7}{9} + \frac{7}{9} + \frac{7}{9} + \frac{7}{9} + \frac{7}{9} \): This is also correct, as it expresses the same total time through repeated addition.
- \( \frac{12}{9} \): This does not represent the total time over five days.
The three expressions that represent the time Whitney spends listening to the podcast over a five-day period are:
- \( 5 \times \frac{7}{9} \)
- \( \frac{35}{9} \)
- \( \frac{7}{9} + \frac{7}{9} + \frac{7}{9} + \frac{7}{9} + \frac{7}{9} \)
1 answer