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Rewrite (1//6" book ")/(2//3" hour ") as a unit rate.

Rewrite 1/6 book 2/3 hour  \frac{1 / 6 \text { book }}{2 / 3 \text { hour }} as a unit rate.

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Full solution

Q. Rewrite 1/6 book 2/3 hour  \frac{1 / 6 \text { book }}{2 / 3 \text { hour }} as a unit rate.
  1. Divide Books by Hours: To find the unit rate of books per hour, we need to divide the number of books by the number of hours.\newlineCalculation: (16 book)/(23 hour)(\frac{1}{6} \text{ book}) / (\frac{2}{3} \text{ hour})
  2. Invert and Multiply: First, we need to invert the divisor 23\frac{2}{3} hour and multiply it by the dividend 16\frac{1}{6} book.\newlineCalculation: 16\frac{1}{6} book ∗* 32\frac{3}{2} hour−1^{-1}
  3. Multiply Numerators and Denominators: Now, we multiply the numerators and the denominators separately.\newlineCalculation: (1×3)/(6×2)=3/12(1 \times 3) / (6 \times 2) = 3 / 12
  4. Simplify Fraction: Simplify the fraction 312\frac{3}{12} to its lowest terms.\newlineCalculation: 312=14\frac{3}{12} = \frac{1}{4}
  5. Calculate Unit Rate: The unit rate is 14\frac{1}{4} book per hour.

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