Question

jamal purchased $16\frac{1}{4}$ pints of ice cream for a party. if each guest will be served exactly $\frac{13}{16}$ pint of ice cream, how many guests can jamal serve?

Explanation:

Step1: Convert mixed number to improper fraction

The total ice cream is \(16\frac{1}{4}\) pints. To convert the mixed number to an improper fraction, we use the formula \(a\frac{b}{c}=\frac{a\times c + b}{c}\). So, \(16\frac{1}{4}=\frac{16\times4 + 1}{4}=\frac{64 + 1}{4}=\frac{65}{4}\) pints.

Step2: Divide total ice cream by per - guest serving

To find the number of guests, we divide the total amount of ice cream by the amount served per guest. That is, we calculate \(\frac{65}{4}\div\frac{13}{16}\). When dividing fractions, we multiply by the reciprocal of the divisor, so \(\frac{65}{4}\times\frac{16}{13}\).
We can simplify before multiplying. 65 and 13 have a common factor of 13 (\(65\div13 = 5\), \(13\div13 = 1\)), and 16 and 4 have a common factor of 4 (\(16\div4 = 4\), \(4\div4 = 1\)). So the expression becomes \(\frac{5}{1}\times\frac{4}{1}=20\).

Answer:

Jamal can serve 20 guests.