Calculating the Amount of Lemonade per Friend

Oct 13, 2025 by miodeya.com 124 views

Introduction

In this article, we will delve into a mathematical problem presented by Zane, who has mixed two containers of lemonade. The first container holds $5 \frac{1}{4}$ liters of lemonade, while the second container holds $7 \frac{7}{8}$ liters of lemonade. Zane wishes to divide the lemonade evenly among 5 friends. Our goal is to determine how many liters of lemonade each friend will receive.

Understanding the Problem

To begin, let's analyze the given information. We have two containers of lemonade, each with a different volume. The first container holds $5 \frac{1}{4}$ liters, which can be expressed as a mixed number. To simplify this, we can convert the mixed number to an improper fraction. The improper fraction equivalent of $5 \frac{1}{4}$ is $\frac{21}{4}$ .

Similarly, the second container holds $7 \frac{7}{8}$ liters, which can also be expressed as a mixed number. To simplify this, we can convert the mixed number to an improper fraction. The improper fraction equivalent of $7 \frac{7}{8}$ is $\frac{63}{8}$ .

Adding the Volumes

Now that we have expressed both volumes as improper fractions, we can add them together to find the total volume of lemonade. To add these fractions, we need to find a common denominator. The least common multiple (LCM) of 4 and 8 is 8. Therefore, we can rewrite $\frac{21}{4}$ as $\frac{21 \times 2}{4 \times 2} = \frac{42}{8}$ .

Now that both fractions have the same denominator, we can add them together: $\frac{42}{8} + \frac{63}{8} = \frac{105}{8}$ .

Simplifying the Result

The result of adding the two volumes is $\frac{105}{8}$ . However, this is not in the simplest form. To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 105 and 8 is 1, so the fraction $\frac{105}{8}$ is already in its simplest form.

Dividing the Lemonade

Now that we have found the total volume of lemonade, we can divide it evenly among 5 friends. To do this, we can divide the total volume by 5: $\frac{105}{8} \div 5 = \frac{105}{8} \times \frac{1}{5} = \frac{105}{40}$ .

Simplifying the Result

The result of dividing the total volume by 5 is $\frac{105}{40}$ . However, this is not in the simplest form. To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 105 and 40 is 5, so we can divide both the numerator and the denominator by 5: $\frac{105 \div 5}{40 \div 5} = \frac{21}{8}$ .

Conclusion

In conclusion, Zane has mixed two containers of lemonade, one holding $5 \frac{1}{4}$ liters and the other holding $7 \frac{7}{8}$ liters. To divide the lemonade evenly among 5 friends, we first added the volumes of the two containers to find the total volume. We then simplified the result and divided it by 5 to find the amount of lemonade each friend will receive. The final answer is $\frac{21}{8}$ liters per friend.

Calculating the Amount of Lemonade per Friend

To calculate the amount of lemonade per friend, we can multiply the fraction $\frac{21}{8}$ by 1 (since we want to find the amount of lemonade per friend): $\frac{21}{8} \times 1 = \frac{21}{8}$ .

Converting the Fraction to a Decimal

To make the calculation easier, we can convert the fraction $\frac{21}{8}$ to a decimal. To do this, we can divide the numerator by the denominator: $\frac{21}{8} = 2.625$ .

Conclusion

In conclusion, Zane's lemonade conundrum has been solved. Each friend will receive 2.625 liters of lemonade.

Real-World Applications

This problem has real-world applications in various fields, such as:

Beverage Industry: This problem can be applied to the beverage industry, where companies need to calculate the amount of liquid in a container to ensure that it is evenly distributed among customers.
Cooking: This problem can be applied to cooking, where chefs need to calculate the amount of ingredients to use in a recipe to ensure that it is evenly distributed among diners.
Science: This problem can be applied to science, where scientists need to calculate the amount of a substance to use in an experiment to ensure that it is evenly distributed among test subjects.

Conclusion

Q: What is the total volume of lemonade in the two containers?

A: The total volume of lemonade in the two containers is $\frac{105}{8}$ liters.

Q: How did you calculate the total volume of lemonade?

A: To calculate the total volume of lemonade, we added the volumes of the two containers. The first container holds $5 \frac{1}{4}$ liters, which can be expressed as a mixed number. To simplify this, we can convert the mixed number to an improper fraction. The improper fraction equivalent of $5 \frac{1}{4}$ is $\frac{21}{4}$ . The second container holds $7 \frac{7}{8}$ liters, which can also be expressed as a mixed number. To simplify this, we can convert the mixed number to an improper fraction. The improper fraction equivalent of $7 \frac{7}{8}$ is $\frac{63}{8}$ . We then added these two fractions together to find the total volume of lemonade.

Q: How do you add fractions with different denominators?

A: To add fractions with different denominators, we need to find a common denominator. The least common multiple (LCM) of the two denominators is the common denominator. We can then rewrite each fraction with the common denominator and add them together.

Q: How do you simplify a fraction?

A: To simplify a fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD). If the GCD is 1, then the fraction is already in its simplest form.

Q: How do you divide a fraction by a whole number?

A: To divide a fraction by a whole number, we can multiply the fraction by the reciprocal of the whole number. For example, to divide $\frac{21}{8}$ by 5, we can multiply it by $\frac{1}{5}$ .

Q: What is the amount of lemonade each friend will receive?

A: The amount of lemonade each friend will receive is $\frac{21}{8}$ liters.

Q: How do you convert a fraction to a decimal?

A: To convert a fraction to a decimal, we can divide the numerator by the denominator. For example, to convert $\frac{21}{8}$ to a decimal, we can divide 21 by 8.

Q: What are some real-world applications of this problem?

A: This problem has real-world applications in various fields, such as the beverage industry, cooking, and science. In the beverage industry, companies need to calculate the amount of liquid in a container to ensure that it is evenly distributed among customers. In cooking, chefs need to calculate the amount of ingredients to use in a recipe to ensure that it is evenly distributed among diners. In science, scientists need to calculate the amount of a substance to use in an experiment to ensure that it is evenly distributed among test subjects.

Q: What is the final answer to Zane's lemonade conundrum?

A: The final answer to Zane's lemonade conundrum is $\frac{21}{8}$ liters per friend.