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This week Michael practiced the piano for [tex]4 \frac{7}{12}[/tex] hours, and last week he practiced for [tex]5 \frac{3}{4}[/tex] hours. How many hours did he practice during these 2 weeks?

Answer :

Final answer:

Michael practiced the piano for a total of 10 1/3 hours over the past two weeks by summing the hours for each week after converting them to improper fractions and finding a common denominator.

Explanation:

The student is asking about the total number of hours Michael practiced the piano over two weeks. First, we need to convert his practice times into improper fractions for easier calculation. For the 4 7/12 hours practiced this week, we convert it into an improper fraction by multiplying the whole number by the denominator, adding the numerator, and then writing the result over the original denominator, giving us (4 × 12) + 7 = 55/12.

For the 5 3/4 hours practiced last week, we do a similar process to get (5 × 4) + 3 = 23/4. To find the total hours practiced over two weeks, we add the two fractions: 55/12 + 23/4. To add fractions, they must have a common denominator, which is in this case 12, so we convert 23/4 to 23 × 3 = 69/12. Adding these gives us a total of 55/12 + 69/12 = 124/12 hours. Converting this back into a mixed number, we divide 124 by 12, which equals 10 with a remainder of 4, so the final answer is 10 4/12 hours. Simplifying the fraction gives us 10 1/3 hours. Hence, Michael practiced a total of 10 1/3 hours over the two weeks.

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