Paolo helped in the community garden for 2 3/4 hours this week. That was 1 5/6 equal-length shifts, because Paolo stopped early one day when it started to rain. How long is a single shift?

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Convert to Improper Fractions: Convert the mixed numbers to improper fractions. 2 3/4 hours can be converted to an improper fraction by multiplying the whole number by the denominator and adding the numerator, then placing the result over the original denominator. 2 3/4 = (2 * 4 + 3)/4 = (8 + 3)/4 = 11/4 hours. 1 5/6 shifts can be converted similarly. 1 5/6 = (1 * 6 + 5)/6 = (6 + 5)/6 = 11/6 shifts.Find Shift Length: Divide the total hours worked by the number of shifts to find the length of one shift. To find the length of one shift, we divide the total hours worked by the number of shifts. (11/4) hours ÷ (11/6) shifts = (11/4) * (6/11) = (11 * 6) / (4 * 11).Simplify Fraction: Simplify the fraction. (11 * 6) / (4 * 11) simplifies because the 11s in the numerator and denominator cancel each other out. (11 * 6) / (4 * 11) = 6/4.Divide by GCD: Simplify the fraction further by dividing both the numerator and the denominator by their greatest common divisor, which is 2. 6/4 = (6/2) / (4/2) = 3/2.Convert to Mixed Number: Convert the improper fraction back to a mixed number if necessary. 3/2 is an improper fraction and can be written as a mixed number. Since 2 goes into 3 once with a remainder of 1, the mixed number is: 3/2 = 1 1/2.

Paolo helped in the community garden for $2\frac{3}{4}$ hours this week. That was $1\frac{5}{6}$ equal-length shifts, because Paolo stopped early one day when it started to rain. How long is a single shift?

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Paolo helped in the community garden for $2\frac{3}{4}$ hours this week. That was $1\frac{5}{6}$ equal-length shifts, because Paolo stopped early one day when it started to rain. How long is a single shift?