To determine the correct expressions that represent the time Whitney spends listening to her favorite podcast over a five-day period, we first calculate the time she spends each day and then extend that over five days.
Whitney listens to her podcast for \( \frac{7}{9} \) of an hour each day. Over a five-day period, she would listen to the podcast for: \[ 5 \times \frac{7}{9} \text{ hours} \] This represents the total time spent over five days.
Now, let's analyze the provided expressions:
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\( 5 \times \frac{7}{9} \): This expression correctly represents the total time over five days. (Correct)
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\( \frac{35}{9} \): Calculating \( 5 \times \frac{7}{9} \) gives \( \frac{35}{9} \), which is the same as the previous expression. (Correct)
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\( \frac{7}{9} + \frac{7}{9} + \frac{7}{9} + \frac{7}{9} + \frac{7}{9} \): This expression sums the time for each of the five days (adding \( \frac{7}{9} \) five times), which is equal to \( 5 \times \frac{7}{9} \). (Correct)
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\( 5 + \frac{7}{9} \): This represents an incorrect calculation. The addition here does not accurately reflect the time spent in the podcast. (Incorrect)
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\( 79 + 79 + 79 + 79 + 79 \): This sums the time incorrectly; it adds whole numbers instead of fractions. (Incorrect)
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\( 5 + 79 \): Similar to the previous one, this doesn't accurately represent the total time spent in the podcast over five days. (Incorrect)
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\( 129 \): This is a whole number that does not represent the total time in hours and minutes. It also does not equal any of the expressions we calculated. (Incorrect)
Based on the analysis, the three applicable expressions that represent the time Whitney spends listening to her 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