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? hours

Question

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? hours

Bytelearn · Accepted Answer

Convert to Improper Fractions: Convert the mixed numbers to improper fractions to make the calculations easier. 2(3/4) hours can be converted to an improper fraction by multiplying the whole number by the denominator of the fraction, adding the numerator, and 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 in the same way. 1(5/6) = (1 * 6 + 5)/6 = (6 + 5)/6 = 11/6 shifts.Calculate Total Time Worked: To find the length of a single shift, divide the total hours worked by the number of shifts. We have 11/4 hours for the total time worked and 11/6 shifts. (11/4) ÷ (11/6) = (11/4) * (6/11) = (11 * 6) / (4 * 11).Simplify Expression: Simplify the expression by canceling out the common factors. The number 11 in the numerator and denominator cancels out, as does one factor of 2 in the 6 and 4. This leaves us with 6/4 after canceling out 11, and then we simplify 6/4 by dividing both the numerator and the denominator by 2. 6/4 = (6/2) / (4/2) = 3/2.Convert Back to Mixed Number: Convert the improper fraction back to a mixed number if necessary. 3/2 hours is the same as 1 1/2 hours or 1.5 hours. So, a single shift is 1 1/2 hours long.

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. $\newline$ How long is a single shift? $\newline$ hours

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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. $\newline$ How long is a single shift? $\newline$ hours