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Naysha listens to the radio for 56

of an hour each day. Which expressions represent the time Naysha spends listening to the radio in a 7-day period? Check the THREE that apply.



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(3 points)
Responses

126
12 sixths

7×56
7 times 5 sixths

7+56
7 plus 5 sixths

356
35 sixths

56+56+56+56+56+56+56

1 answer

To find the total time Naysha spends listening to the radio over a 7-day period, we can calculate it as follows:

Naysha listens to the radio for \( \frac{5}{6} \) of an hour each day for 7 days.

  1. Total Time Calculation:
    • Total time = \( 7 \times \frac{5}{6} \)

Now, let's evaluate the expressions given in the options to see which ones represent the same total time:

  1. 126: This does not represent the total time correctly.

  2. 12 sixths: This can be reduced to 2, which is not correct.

  3. 7 × 56: This is incorrect because it does not take into account that the listening time per day is \( \frac{5}{6} \) hours, not 56 hours.

  4. 7 times 5 sixths: This is equal to \( 7 \times \frac{5}{6} \). This is correct.

  5. 7 + 56: This does not represent the total time correctly.

  6. 35 sixths: This equals \( \frac{35}{6} \), which is the same as \( 7 \times \frac{5}{6} \) when simplified. This is also correct.

  7. 56 + 56 + 56 + 56 + 56 + 56 + 56: This equals \( 7 \times 56 \), which is \( 392 \), and it does not represent the correct amount of time spent listening to the radio.

The correct responses are:

  • 7 times 5 sixths
  • 35 sixths
  • 56 + 56 + 56 + 56 + 56 + 56 + 56 (this adds up to the number of hours listed rather than the total listening time, so it is not valid).

Thus, the actual correct representations of the time Naysha spends listening to the radio in a 7-day period are:

  • 7 times 5 sixths
  • 35 sixths
  • 5/6 listened per day for 7 days (not listed directly in options)

Only the 1st and 4th choices are strictly correct as written based on Naysha's listening time.