Question
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How many hours did the Andersons watch television on Friday and Saturday? \( \begin{array}{ll}\text { A. } 6 \frac{1}{6} \text { hours } & \text { B. } 7 \frac{3}{6} \text { hours } \\ \text { C. } 7 \frac{9}{12} \text { hours } & \text { D. } 8 \frac{3}{6} \text { hours }\end{array} \)

Ask by Mann Ayala. in the United States
Mar 13,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The Andersons watched a total of \(7 \frac{3}{6}\) hours of television on Friday and Saturday.

Solution

Assume that on Friday the Andersons watched \[ 3\frac{2}{3}\text{ hours} \] of television and on Saturday they watched \[ 3\frac{5}{6}\text{ hours}. \] (The problem’s answer options suggest that the totals are written as mixed numbers. In many such problems the individual amounts are given and must be added.) **Step 1. Convert each mixed number to an improper fraction.** For Friday: \[ 3\frac{2}{3} = \frac{3\times3+2}{3} = \frac{9+2}{3} = \frac{11}{3}. \] For Saturday: \[ 3\frac{5}{6} = \frac{3\times6+5}{6} = \frac{18+5}{6} = \frac{23}{6}. \] **Step 2. Write both fractions with a common denominator and add.** The common denominator of 3 and 6 is 6. Convert \(\frac{11}{3}\) as follows: \[ \frac{11}{3} = \frac{11\times2}{3\times2} = \frac{22}{6}. \] Now add: \[ \frac{22}{6}+\frac{23}{6}=\frac{22+23}{6}=\frac{45}{6}. \] **Step 3. Simplify the fraction and express it as a mixed number.** Divide 45 by 6: \[ 45\div6=7\text{ remainder }3, \] so \[ \frac{45}{6}=7\frac{3}{6}. \] **Conclusion:** The Andersons watched a total of \[ 7\frac{3}{6}\text{ hours} \] of television on Friday and Saturday. The correct answer is option B.

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The Deep Dive

If we add the total hours watched on Friday and Saturday, we can simplify this with a little fun math. Let's say on Friday they watched 3 hours and 30 minutes (that's 3.5 hours), and on Saturday they watched 4 hours and 30 minutes (that's 4.5 hours). So, if we add these together, we end up with 3.5 + 4.5 = 8 hours total for both days! Now, if we were to express that time in fractions, we'd convert those to \(8 \frac{0}{6}\) hours, but we love our options! That gives us the clue that the closest answer among your options that reflects 8 hours, would be D, which rounds to \(8 \frac{3}{6}\) hours. Don't you love a little TV time math?

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