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Amira had (7)/(4) of a bag of cat food. The food lasted 7(7)/(2) weeks. How much cat food did Amira's cats eat per week? bags

Amira had 74 \frac{7}{4} of a bag of cat food. The food lasted 772 7 \frac{7}{2} weeks.\newlineHow much cat food did Amira's cats eat per week?\newlinebags

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Q. Amira had 74 \frac{7}{4} of a bag of cat food. The food lasted 772 7 \frac{7}{2} weeks.\newlineHow much cat food did Amira's cats eat per week?\newlinebags
  1. Identify Total Amount: Identify the total amount of cat food Amira had and the duration it lasted.\newlineAmira had (74)(\frac{7}{4}) of a bag of cat food, and it lasted for 7(72)7(\frac{7}{2}) weeks.
  2. Convert to Improper Fraction: Convert the mixed number 7(72)7\left(\frac{7}{2}\right) to an improper fraction to simplify calculations.7(72)=(7×2+7)/2=(14+7)/2=2127\left(\frac{7}{2}\right) = \left(7\times 2 + 7\right)/2 = \left(14 + 7\right)/2 = \frac{21}{2} weeks.
  3. Calculate Amount Consumed: Calculate the amount of cat food consumed per week.\newlineTo find the amount of cat food consumed per week, divide the total amount of cat food by the number of weeks it lasted.\newline(74)(\frac{7}{4}) bags ÷\div (212)(\frac{21}{2}) weeks = (74)×(221)(\frac{7}{4}) \times (\frac{2}{21}) bags per week.
  4. Perform Multiplication: Perform the multiplication to find the amount of cat food consumed per week.\newline(74)×(221)=(7×24×21)=1484(\frac{7}{4}) \times (\frac{2}{21}) = (\frac{7\times2}{4\times21}) = \frac{14}{84} bags per week.
  5. Simplify Fraction: Simplify the fraction to find the simplest form of the amount of cat food consumed per week. \newline1484\frac{14}{84} can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 1414.\newline1484=16\frac{14}{84} = \frac{1}{6} bags per week.

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