Question

1. leo uses three bags of flour to make cookies. the amount of flour in each bag is the following: - \\(\frac{2}{3}\\) cups of flour - \\(1\frac{1}{2}\\) cups of flour - \\(1\frac{1}{3}\\) cups of flour each batch of cookies needs \\(1\frac{3}{4}\\) cups of flour. how many batches of cookies can leo make? 6. tyler has a pitcher of \\(1\frac{3}{4}\\) liters of lemonade. tyler pours an equal amount of lemonade into 3 cups. afterward, there is \\(\frac{1}{3}\\) liter of lemonade remaining in the pitcher. how many liters of lemonade are in each cup?

Explanation:

Question 5

Step1: Convert mixed numbers to improper fractions

First, convert \(1\frac{1}{2}\) to improper fraction: \(1\frac{1}{2}=\frac{3}{2}\), and \(1\frac{1}{3}=\frac{4}{3}\), \(1\frac{3}{4}=\frac{7}{4}\).

Step2: Find total flour

Add the amounts of flour in each bag: \(\frac{2}{3}+\frac{3}{2}+\frac{4}{3}\). Find a common denominator, which is 6. So \(\frac{2\times2}{3\times2}+\frac{3\times3}{2\times3}+\frac{4\times2}{3\times2}=\frac{4}{6}+\frac{9}{6}+\frac{8}{6}=\frac{4 + 9+8}{6}=\frac{21}{6}=\frac{7}{2}\) cups.

Step3: Calculate number of batches

Divide total flour by flour per batch: \(\frac{7}{2}\div\frac{7}{4}\). Dividing by a fraction is multiplying by its reciprocal: \(\frac{7}{2}\times\frac{4}{7}=\frac{28}{14} = 2\).

Step1: Find amount poured into cups

Subtract remaining lemonade from initial amount: \(1\frac{3}{4}-\frac{1}{3}\). Convert \(1\frac{3}{4}\) to \(\frac{7}{4}\). Common denominator is 12: \(\frac{7\times3}{4\times3}-\frac{1\times4}{3\times4}=\frac{21}{12}-\frac{4}{12}=\frac{17}{12}\) liters.

Step2: Divide by number of cups

Divide the poured amount by 3: \(\frac{17}{12}\div3=\frac{17}{12}\times\frac{1}{3}=\frac{17}{36}\) liters.

Answer:

2

Question 6