To determine the expressions that represent the time Whitney spends listening to her podcast over a five-day period, we need to calculate the total time. Whitney listens for \( \frac{7}{9} \) of an hour each day, and over five days, that time can be expressed in several ways.
Let's break it down:
- Daily Time: \(\frac{7}{9}\) of an hour for one day.
- Five-Day Total: Over five days, this can be represented as: \[ 5 \times \frac{7}{9} \]
Now let's examine the provided responses:
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\(79 + 79 + 79 + 79 + 79\): This expression calculates the total time in hours but uses the incorrect representation since each 79 is meant to be \( \frac{7}{9} \). Hence, this response is incorrect.
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\( \frac{7}{9} + \frac{7}{9} + \frac{7}{9} + \frac{7}{9} + \frac{7}{9} \): Correctly adds \( \frac{7}{9} \) five times, which equals \( 5 \times \frac{7}{9} \). This is correct.
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\(5 + \frac{7}{9}\): This expression adds a full 5 hours to \(\frac{7}{9}\) of an hour, which does not represent the total time correctly. Hence, this response is incorrect.
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\(359\): This is not a valid representation of the time Whitney spends. It's simply a number. This response is incorrect.
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\(\frac{35}{9}\): This expression is \(5 \times \frac{7}{9}\), which correctly represents the total time in hours. This response is correct.
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\(5 \times \frac{7}{9}\): This correctly represents the total time Whitney spends listening to her podcast over five days. This response is correct.
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\(129\): This is also not a valid representation of time spent across the five days. This response is incorrect.
Based on the analysis, the expressions that represent the time Whitney spends listening to the podcast over a five-day period are:
- \( \frac{7}{9} + \frac{7}{9} + \frac{7}{9} + \frac{7}{9} + \frac{7}{9} \)
- \( \frac{35}{9} \)
- \( 5 \times \frac{7}{9} \)
Thus, the three correct expressions are:
- \( \frac{7}{9} + \frac{7}{9} + \frac{7}{9} + \frac{7}{9} + \frac{7}{9} \)
- \( \frac{35}{9} \)
- \( 5 \times \frac{7}{9} \)
1 answer