Jerry is a judge. He hears 5 cases every 2(3)/(8) hours. Jerry hears cases at a constant rate. How many cases does he hear per hour? ◻ cases per hour

Convert to Improper Fraction: Convert the mixed number 2(3)/(8) hours to an improper fraction to make calculations easier. 2(3)/(8) hours = (2 * 8 + 3)/8 = (16 + 3)/8 = 19/8 hours.Calculate Rate per Hour: Calculate the rate at which Jerry hears cases per hour by dividing the total number of cases by the total hours. Jerry hears 5 cases every 19/8 hours, so the rate is 5 cases per 19/8 hours. To find cases per hour, divide 5 by 19/8. Rate = 5 / (19/8) = 5 * (8/19) = 40/19 cases per hour.Simplify Fraction: Simplify the fraction to find the exact number of cases Jerry hears per hour. 40/19 cannot be simplified further, so Jerry hears 40/19 cases per hour.

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Jerry is a judge. He hears 5 cases every
2(3)/(8) hours. Jerry hears cases at a constant rate.
How many cases does he hear per hour?

◻ cases per hour

Jerry is a judge. He hears $5$ cases every $\frac{2(3)}{8}$ hours. Jerry hears cases at a constant rate. $\newline$ How many cases does he hear per hour? $\newline$ $\square$ cases per hour

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Grade 6

Ratios and rates: word problems

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Q. Jerry is a judge. He hears

5

cases every

\frac{2(3)}{8}

hours. Jerry hears cases at a constant rate.

\newline

How many cases does he hear per hour?

\newline

\square

cases per hour

Convert to Improper Fraction: Convert the mixed number $2\frac{3}{8}$ hours to an improper fraction to make calculations easier. $\newline$ $2\frac{3}{8}$ hours = $\left(2 \times 8 + 3\right)/8 = \left(16 + 3\right)/8 = \frac{19}{8}$ hours.
Calculate Rate per Hour: Calculate the rate at which Jerry hears cases per hour by dividing the total number of cases by the total hours. $\newline$ Jerry hears $5$ cases every $\frac{19}{8}$ hours, so the rate is $5$ cases per $\frac{19}{8}$ hours. $\newline$ To find cases per hour, divide $5$ by $\frac{19}{8}$ . $\newline$ Rate = $\frac{5}{\left(\frac{19}{8}\right)} = 5 \times \left(\frac{8}{19}\right) = \frac{40}{19}$ cases per hour.
Simplify Fraction: Simplify the fraction to find the exact number of cases Jerry hears per hour. $\frac{40}{19}$ cannot be simplified further, so Jerry hears $\frac{40}{19}$ cases per hour.