Adeline

Adeline helped her mother make 7/9 liters of lemonade to treat their guests. She poured the lemonade into cups. Each cup had a capacity of 1/6 liters. She filled some cups entirely except for 1 cup. How much was lemonade in the cup that was not filled?

Correct answer:

x =  2/3

Step-by-step explanation:

$$\begin{gathered} V=\frac{7}{9}\doteq 0.7778\text{l} \\ {V}_1=\frac{1}{6}\doteq 0.1667\text{l} \\ n=V/V_1=\frac{7}{9}/\frac{1}{6}=\frac{7}{9}:\frac{1}{6}=\frac{7}{9}\cdot \frac{6}{1}=\frac{7\cdot 6}{9\cdot 1}=\frac{42}{9}=\frac{14}{3}=4\frac{2}{3}\doteq 4.6667 \\ {n}_1=\lfloor n\rfloor =\lfloor 4.6667\rfloor =4 \\ x=n-n_1=\frac{14}{3}-4=\frac{14}{3}-\frac{4\cdot 3}{3}=\frac{14}{3}-\frac{12}{3}=\frac{14-12}{3}=\frac{2}{3}=0.6667 \end{gathered}$$

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