Thomas Has Some Leftover Paint That He Would Like To Sell. He Mixes $4 \frac{3}{8}$ Gallons Of Blue Paint With $6 \frac{5}{8}$ Gallons Of White Paint. Then, He Pours This Light-blue Mixture Into \$\frac{1}{4}$[/tex\]

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Introduction

Thomas has a surplus of paint that he wants to get rid of, and he's decided to mix some blue paint with white paint to create a light-blue mixture. He has $4 \frac{3}{8}$ gallons of blue paint and $6 \frac{5}{8}$ gallons of white paint. After mixing them together, he pours the resulting mixture into a container that holds $\frac{1}{4}$ gallons. In this article, we'll delve into the world of mathematics to determine how much of the light-blue mixture Thomas will have left over.

Understanding the Problem

To tackle this problem, we need to first understand the concept of mixed numbers and how to add them together. A mixed number is a combination of a whole number and a fraction. In this case, Thomas has $4 \frac{3}{8}$ gallons of blue paint, which can be broken down into 4 whole gallons and $\frac{3}{8}$ gallons. Similarly, he has $6 \frac{5}{8}$ gallons of white paint, which can be broken down into 6 whole gallons and $\frac{5}{8}$ gallons.

Adding Mixed Numbers

When adding mixed numbers, we need to add the whole numbers together and then add the fractions together. To add the fractions, we need to find a common denominator, which is the least common multiple (LCM) of the denominators. In this case, the LCM of 8 and 8 is 8.

# Define the mixed numbers
blue_paint = 4 + 3/8
white_paint = 6 + 5/8

# Add the mixed numbers
total_paint = blue_paint + white_paint

Calculating the Total Paint

Using the code above, we can calculate the total amount of paint Thomas has. We'll first add the whole numbers together:

# Add the whole numbers
whole_numbers = 4 + 6
print(whole_numbers)  # Output: 10

Next, we'll add the fractions together:

# Add the fractions
fractions = 3/8 + 5/8
print(fractions)  # Output: 8/8 = 1

Since the fractions add up to 1, we can simplify the total paint to:

# Simplify the total paint
total_paint = 10 + 1
print(total_paint)  # Output: 11

However, we need to remember that the total paint is a mixed number, so we need to break it down into a whole number and a fraction. In this case, the total paint is 11 gallons and $\frac{0}{8}$ gallons.

Pouring the Mixture into a Container

Thomas pours the light-blue mixture into a container that holds $\frac{1}{4}$ gallons. To determine how much of the mixture he'll have left over, we need to subtract the capacity of the container from the total amount of paint.

# Define the capacity of the container
container_capacity = 1/4

# Subtract the capacity of the container from the total paint
leftover_paint = total_paint - container_capacity

Calculating the Leftover Paint

Using the code above, we can calculate the amount of leftover paint. We'll first subtract the capacity of the container from the total paint:

# Subtract the capacity of the container from the total paint
leftover_paint = 11 - 1/4
print(leftover_paint)  # Output: 10.75

Since the leftover paint is a decimal number, we can convert it to a mixed number:

# Convert the leftover paint to a mixed number
leftover_paint = 10 + 3/4
print(leftover_paint)  # Output: 10 3/4

Therefore, Thomas will have $10 \frac{3}{4}$ gallons of light-blue paint left over after pouring the mixture into the container.

Conclusion

Introduction

In our previous article, we explored the world of mathematics to determine how much of the light-blue mixture Thomas would have left over after pouring it into a container. We added mixed numbers, calculated the total paint, and subtracted the capacity of the container to find the leftover paint. In this article, we'll answer some frequently asked questions (FAQs) related to Thomas's paint sale.

Q: What is the total amount of paint Thomas has?

A: Thomas has a total of 11 gallons of paint, which is equivalent to $11 \frac{0}{8}$ gallons.

Q: How much paint does Thomas have left over after pouring the mixture into the container?

A: Thomas has $10 \frac{3}{4}$ gallons of light-blue paint left over after pouring the mixture into the container.

Q: What is the capacity of the container that Thomas pours the mixture into?

A: The capacity of the container is $\frac{1}{4}$ gallons.

Q: How did you calculate the leftover paint?

A: We calculated the leftover paint by subtracting the capacity of the container from the total amount of paint. The formula is:

Leftover paint = Total paint - Container capacity

Q: Can you explain the concept of mixed numbers?

A: A mixed number is a combination of a whole number and a fraction. For example, $4 \frac{3}{8}$ is a mixed number that represents 4 whole gallons and $\frac{3}{8}$ gallons.

Q: How do you add mixed numbers?

A: To add mixed numbers, we need to add the whole numbers together and then add the fractions together. We need to find a common denominator, which is the least common multiple (LCM) of the denominators.

Q: What is the least common multiple (LCM) of 8 and 8?

A: The LCM of 8 and 8 is 8.

Q: Can you provide an example of how to add mixed numbers?

A: Let's say we have two mixed numbers: $4 \frac{3}{8}$ and $6 \frac{5}{8}$. To add them together, we need to add the whole numbers together and then add the fractions together.

# Define the mixed numbers
mixed_number1 = 4 + 3/8
mixed_number2 = 6 + 5/8

# Add the mixed numbers
total_mixed_number = mixed_number1 + mixed_number2

Q: How do you simplify a mixed number?

A: To simplify a mixed number, we need to convert the fraction to a decimal number and then add it to the whole number.

Q: Can you provide an example of how to simplify a mixed number?

A: Let's say we have a mixed number: $10 \frac{3}{4}$. To simplify it, we need to convert the fraction to a decimal number and then add it to the whole number.

# Define the mixed number
mixed_number = 10 + 3/4

# Simplify the mixed number
simplified_mixed_number = 10 + 0.75
print(simplified_mixed_number)  # Output: 10.75

Conclusion

In this article, we've answered some frequently asked questions related to Thomas's paint sale. We've explained the concept of mixed numbers, added mixed numbers, and simplified mixed numbers. We've also provided examples of how to add and simplify mixed numbers.