Question

complex fraction word problems

1. if mark uses 3 ¾ tablespoons of coffee to make 10 cups of coffee, how much would he need to make one cup of coffee?
2. the drama club ordered 15 pizzas for the cast party. if the 25 members ate 12 1/2 pizzas out of the 15. how much pizza did each cast member eat?
3. ethan writes 1/6 of a page in 1/12 of a minute. how much time does it take him to write a full page?
4. william fills 1/3 of a water bottle in 1/6 of a minute. how much time will it take him to fill the bottle?
5. michael plays 1/5 of a song in 1/15 of a minute. how much time will it take him to play an entire song?
6. gabriel used 1/3 of a liter of milk to make 1/9 of a jug of tea. how much milk is required to fill the jug?

Explanation:

Problem 1:

Step1: Convert mixed number to improper fraction

\(3\frac{3}{4}=\frac{3\times4 + 3}{4}=\frac{15}{4}\)

Step2: Divide by number of cups

To find per cup, divide total coffee by cups: \(\frac{15}{4}\div10=\frac{15}{4}\times\frac{1}{10}=\frac{3}{8}\)

Step1: Use total pizza eaten divided by members

Total pizza eaten is \(12\frac{1}{2}=\frac{25}{2}\). Divide by 25: \(\frac{25}{2}\div25=\frac{25}{2}\times\frac{1}{25}=\frac{1}{2}\)

Step1: Set up proportion for time per page

If \(\frac{1}{6}\) page takes \(\frac{1}{12}\) minute, for 1 page, time \(t\) is \(\frac{1}{12}\div\frac{1}{6}=\frac{1}{12}\times6=\frac{1}{2}\) minute

Answer:

\(\frac{3}{8}\) tablespoons

Problem 2: