Question

1. emilio has a bag of dog food. the bag contains $24\frac{3}{4}$ cups of dog food. emilio feeds his dog $2\frac{3}{4}$ cups of dog food each day. what is the total number of days emilio can feed his dog from this bag of dog food?

Explanation:

Step1: Convert mixed numbers to improper fractions

First, convert \(24\frac{3}{4}\) to an improper fraction. We use the formula \(a\frac{b}{c}=\frac{a\times c + b}{c}\). So, \(24\frac{3}{4}=\frac{24\times4 + 3}{4}=\frac{96+3}{4}=\frac{99}{4}\).
Next, convert \(2\frac{3}{4}\) to an improper fraction. Using the same formula, \(2\frac{3}{4}=\frac{2\times4 + 3}{4}=\frac{8 + 3}{4}=\frac{11}{4}\).

Step2: Divide the total amount by the daily amount

To find the number of days, we divide the total cups of dog food by the cups fed per day. So we calculate \(\frac{99}{4}\div\frac{11}{4}\). When dividing fractions, we multiply by the reciprocal, so \(\frac{99}{4}\times\frac{4}{11}\). The 4s cancel out, and we have \(\frac{99}{11}=9\).

Answer:

9