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

Convert to Improper Fraction: Paolo worked for 2(3)/(4) hours this week, which is 2 + 3/4 hours. Convert mixed number to improper fraction: 2(3)/(4) = (8/4 + 3/4) = 11/4 hours.Convert Shifts to Improper Fraction: He worked 1(5)/(6) shifts, which is 1 + 5/6 shifts. Convert mixed number to improper fraction: 1(5)/(6) = (6/6 + 5/6) = 11/6 shifts.Find Length of One Shift: To find the length of one shift, divide the total hours worked by the number of shifts. So, (11/4) hours ÷ (11/6) shifts = (11/4) * (6/11) shifts.Simplify Expression: Simplify the expression by canceling out the common factor of 11. (11/4) * (6/11) = (1/4) * 6 = 6/4.Simplify to Lowest Terms: Simplify 6/4 to its lowest terms. 6/4 = 3/2 or 1(1)/(2) hours per shift.

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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

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? $\newline$ $\square$ hours

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Algebra 1

Multiplication with rational exponents

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Q. 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

\square

hours

Convert to Improper Fraction: Paolo worked for $2\left(\frac{3}{4}\right)$ hours this week, which is $2 + \frac{3}{4}$ hours. $\newline$ Convert mixed number to improper fraction: $2\left(\frac{3}{4}\right) = \left(\frac{8}{4} + \frac{3}{4}\right) = \frac{11}{4}$ hours.
Convert Shifts to Improper Fraction: He worked $1\frac{5}{6}$ shifts, which is $1 + \frac{5}{6}$ shifts. $\newline$ Convert mixed number to improper fraction: $1\frac{5}{6} = \left(\frac{6}{6} + \frac{5}{6}\right) = \frac{11}{6}$ shifts.
Find Length of One Shift: To find the length of one shift, divide the total hours worked by the number of shifts. $\newline$ So, $(\frac{11}{4})$ hours $\div$ $(\frac{11}{6})$ shifts = $(\frac{11}{4}) \times (\frac{6}{11})$ shifts.
Simplify Expression: Simplify the expression by canceling out the common factor of $11$ . $\frac{11}{4} \times \frac{6}{11} = \frac{1}{4} \times 6 = \frac{6}{4}$ .
Simplify to Lowest Terms: Simplify $\frac{6}{4}$ to its lowest terms. $\newline$ $\frac{6}{4} = \frac{3}{2}$ or $1\frac{1}{2}$ hours per shift.