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Amira had 34\frac{3}{4} of a bag of cat food. The food lasted 7127\frac{1}{2} weeks. How much cat food did Amira's cats eat per week?

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Multiply and divide rational numbers: word problemsright chevron icon

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Q. Amira had 34\frac{3}{4} of a bag of cat food. The food lasted 7127\frac{1}{2} weeks. How much cat food did Amira's cats eat per week?
  1. Identify Total Amount: Identify the total amount of cat food and the total number of weeks.\newlineAmira had 34\frac{3}{4} of a bag of cat food, and it lasted for 7127 \frac{1}{2} weeks.
  2. Convert to Improper Fraction: Convert the mixed number (712)(7 \frac{1}{2}) to an improper fraction to make the division easier.7127 \frac{1}{2} weeks can be written as (7×2+1)/2=(14+1)/2=152(7 \times 2 + 1)/2 = (14 + 1)/2 = \frac{15}{2} weeks.
  3. Divide for Weekly Consumption: Divide the total amount of cat food by the total number of weeks to find the amount of cat food consumed per week.\newline(34)÷(152)=(34)×(215)=(3×24×15)=660(\frac{3}{4}) \div (\frac{15}{2}) = (\frac{3}{4}) \times (\frac{2}{15}) = (\frac{3 \times 2}{4 \times 15}) = \frac{6}{60}.
  4. Simplify Fraction: Simplify the fraction 660\frac{6}{60} to its lowest terms.\newline660\frac{6}{60} can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 66.\newline660=110\frac{6}{60} = \frac{1}{10}.

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