Monica has \( 9 \frac{1}{10} \) liters of lemonade in a container. Megan added \( 14 \frac{2}{5} \) liters of juice to the same container. If the container has a capacity of \( 26 \frac{3}{8} \) liters, how many more liters are needed to fill it? F \( 2 \frac{7}{8} \) liters G \( 3 \frac{1}{8} \) liters H \( 2 \frac{1}{2} \) liters J \( 2 \frac{2}{5} \) liters

To determine how many more liters are needed to fill the container, we first need to calculate the total amount of liquid Monica and Megan have combined. Monica has \( 9 \frac{1}{10} \) liters of lemonade. We can convert this to an improper fraction: \[ 9 \frac{1}{10} = \frac{91}{10} \text{ liters} \] Megan added \( 14 \frac{2}{5} \) liters of juice, which can also be converted: \[ 14 \frac{2}{5} = \frac{72}{5} \text{ liters} \] To add these two amounts together, we need a common denominator. The least common multiple of \( 10 \) and \( 5 \) is \( 10 \). Now, we convert \( \frac{72}{5} \) to have a denominator of \( 10 \): \[ \frac{72}{5} = \frac{72 \times 2}{5 \times 2} = \frac{144}{10} \] Now, we can add the amounts together: \[ \frac{91}{10} + \frac{144}{10} = \frac{235}{10} = 23.5 \text{ liters} \] Next, we check the capacity of the container, which is \( 26 \frac{3}{8} \): \[ 26 \frac{3}{8} = \frac{211}{8} \text{ liters} \] We convert \( 23.5 \) liters to a fraction to make further calculations easier: \[ 23.5 = 23 \frac{1}{2} = 23 \frac{4}{8} = \frac{188}{8} \] To find out how many more liters are needed to fill the container, we now subtract the current amount from the total capacity: \[ \frac{211}{8} - \frac{188}{8} = \frac{23}{8} \text{ liters} \] To convert this back to a mixed number, we have: \[ \frac{23}{8} = 2 \frac{7}{8} \] So the answer is \( F: 2 \frac{7}{8} \) liters. --- Did you know that fractions can trace their roots back to ancient civilizations? The Egyptians used fractions over 4,000 years ago, having a unique system utilizing unit fractions, which have a numerator of 1! Imagine reading hieroglyphics with fractions embedded within—now that’s some serious math history! If you're looking to sharpen your skills with fractions, there are countless online resources and games. One popular option is to use flashcards for practicing simplification, addition, and conversion between mixed numbers and improper fractions. Making it into a friendly competition with friends or family can add some fun to the learning process!