Question

cooper has $10\frac{1}{4}$ bags of shredded cheese. each week, cooper consumes $1\frac{1}{6}$ bags. how many weeks will the shredded cheese last cooper? enter the answer as a mixed number or as a fraction. show your work here

Explanation:

Step1: Convert mixed numbers to improper fractions

First, convert \(10\frac{1}{4}\) to an improper fraction. The formula for converting a mixed number \(a\frac{b}{c}\) to an improper fraction is \(\frac{a\times c + b}{c}\). So for \(10\frac{1}{4}\), we have \(a = 10\), \(b = 1\), \(c = 4\). Then \(\frac{10\times4 + 1}{4}=\frac{40 + 1}{4}=\frac{41}{4}\).

Next, convert \(1\frac{1}{6}\) to an improper fraction. Using the same formula, with \(a = 1\), \(b = 1\), \(c = 6\), we get \(\frac{1\times6+1}{6}=\frac{6 + 1}{6}=\frac{7}{6}\).

Step2: Divide the total amount by the weekly consumption

To find the number of weeks, we divide the total number of bags (\(\frac{41}{4}\)) by the number of bags consumed per week (\(\frac{7}{6}\)). When dividing fractions, we multiply by the reciprocal of the divisor. So \(\frac{41}{4}\div\frac{7}{6}=\frac{41}{4}\times\frac{6}{7}\).

Step3: Multiply the fractions

Multiply the numerators together and the denominators together: \(\frac{41\times6}{4\times7}=\frac{246}{28}\).

Step4: Simplify the fraction

Simplify \(\frac{246}{28}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 2. So \(\frac{246\div2}{28\div2}=\frac{123}{14}\).

Step5: Convert to a mixed number (optional, but since the problem allows mixed number or fraction)

Divide 123 by 14. \(14\times8 = 112\), and \(123-112 = 11\). So \(\frac{123}{14}=8\frac{11}{14}\).

Answer:

\(8\frac{11}{14}\) (or \(\frac{123}{14}\))