Emmy's Cafe uses $2\frac{1}{2}$ bags of coffee every day. How many days will $7\frac{1}{2}$ bags of coffee last? $\newline$ Write your answer as a fraction or as a whole or mixed number. $\newline$ $\_\_\_$ days

Full solution

Q. Emmy's Cafe uses

2\frac{1}{2}

bags of coffee every day. How many days will

7\frac{1}{2}

bags of coffee last?

\newline

Write your answer as a fraction or as a whole or mixed number.

\newline

\_\_\_

days

Identify Total Amount: Identify the total amount of coffee available and the daily usage. $\newline$ Total bags of coffee: $7 \frac{1}{2}$ bags $\newline$ Daily usage: $2 \frac{1}{2}$ bags $\newline$ We need to divide the total bags by the daily usage to find out how many days the coffee will last. $\newline$ Calculation: $7 \frac{1}{2} \div 2 \frac{1}{2}$
Convert to Improper Fractions: Convert mixed numbers to improper fractions for easier division. $\newline$ $7 \frac{1}{2} = (7\times2 + 1)/2 = \frac{15}{2}$ $\newline$ $2 \frac{1}{2} = (2\times2 + 1)/2 = \frac{5}{2}$ $\newline$ Now, divide the fractions. $\newline$ Calculation: $\frac{15}{2} \div \frac{5}{2}$
Perform Division of Fractions: Perform the division of fractions by multiplying by the reciprocal. $\newline$ $(\frac{15}{2}) \div (\frac{5}{2}) = (\frac{15}{2}) \times (\frac{2}{5}) = \frac{30}{10} = 3$