Question

10. Ariana's iPod battery lasts 6 hours. She listens to her iPod for 2/3 of an hour in theafternoon and another 2 5/6 hours in the evening.a) How much listening time is left on Ariana's iPod?b) What fraction of the battery's power is left? Justify your answer with adiagram.

Answer 1

We have the following:

The first thing is to transform the mixed numbers to decimal numbers, in the following way:

$\begin{gathered} \frac{2}{3}=0.67 \\ 2\frac{5}{6}=2.83 \end{gathered}$

a.

to calculate the remaining time we must subtract the times where music is heard from 6 hours

$6-0.67-2.83=2.5$

Therefore, the answer is 2.5 hours or 5/2 hours battery remaining

b.

To calculate the fraction we must calculate that it represents 2.5 or 5/2 hours in the total, that is, 6 hours

$\frac{\frac{5}{2}}{6}=\frac{\frac{5}{2}}{\frac{6}{1}}=\frac{5\cdot1}{6\cdot2}=\frac{5}{12}$

The diagram is: