Pam Baked Some Cupcakes For Her Friends. She Baked 24 Cupcakes, And Each Cupcake Is $\frac{2}{15}$ Pound. If She Packed 6 Cupcakes In Each Box, What Is The Weight Of Each Box?
Introduction
Pam, a skilled baker, has prepared a delightful treat for her friends - a batch of 24 cupcakes. Each cupcake weighs a fraction of a pound, and she plans to pack them in boxes of 6. In this article, we will delve into the world of mathematics to determine the weight of each box.
The Cupcake Conundrum
Pam baked 24 cupcakes, each weighing pound. To find the total weight of all the cupcakes, we need to multiply the number of cupcakes by the weight of each cupcake.
Total\ weight = Number\ of\ cupcakes \times Weight\ of\ each\ cupcake
Total\ weight = 24 \times \frac{2}{15}
To simplify the calculation, we can multiply the numerator (2) by 24 and keep the denominator (15) the same.
Total\ weight = \frac{24 \times 2}{15}
Total\ weight = \frac{48}{15}
Now, we can simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 3.
Total\ weight = \frac{48 \div 3}{15 \div 3}
Total\ weight = \frac{16}{5}
So, the total weight of all the cupcakes is pounds.
Packing the Cupcakes
Pam plans to pack 6 cupcakes in each box. To find the weight of each box, we need to multiply the weight of 6 cupcakes by the weight of each cupcake.
Weight\ of\ each\ box = Weight\ of\ 6\ cupcakes \times Weight\ of\ each\ cupcake
Weight\ of\ each\ box = 6 \times \frac{2}{15}
To simplify the calculation, we can multiply the numerator (2) by 6 and keep the denominator (15) the same.
Weight\ of\ each\ box = \frac{6 \times 2}{15}
Weight\ of\ each\ box = \frac{12}{15}
Now, we can simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 3.
Weight\ of\ each\ box = \frac{12 \div 3}{15 \div 3}
Weight\ of\ each\ box = \frac{4}{5}
So, the weight of each box is pounds.
Conclusion
In this article, we have solved a mathematical problem involving fractions and multiplication. We have determined the total weight of all the cupcakes and the weight of each box. The weight of each box is pounds, which is a delightful treat for Pam's friends.
Real-World Applications
This problem has real-world applications in various fields, such as:
- Cooking: When baking, it's essential to know the weight of ingredients to ensure accurate measurements.
- Packaging: Manufacturers need to calculate the weight of products to determine packaging requirements.
- Science: Scientists use mathematical calculations to determine the weight of objects and substances.
Tips and Tricks
When working with fractions, remember to:
- Simplify fractions: Divide both the numerator and the denominator by their greatest common divisor (GCD) to simplify fractions.
- Multiply fractions: Multiply the numerators and denominators separately to multiply fractions.
- Use real-world examples: Use real-world examples to make mathematical problems more engaging and relevant.
Final Thoughts
Introduction
In our previous article, we solved a mathematical problem involving fractions and multiplication to determine the weight of each box of cupcakes. In this article, we will answer some frequently asked questions (FAQs) related to the problem.
Q&A
Q: What is the total weight of all the cupcakes?
A: The total weight of all the cupcakes is pounds.
Q: How do I simplify a fraction?
A: To simplify a fraction, divide both the numerator and the denominator by their greatest common divisor (GCD).
Q: What is the weight of each cupcake?
A: The weight of each cupcake is pound.
Q: How do I multiply fractions?
A: To multiply fractions, multiply the numerators and denominators separately.
Q: What is the weight of each box?
A: The weight of each box is pounds.
Q: Why is it essential to know the weight of ingredients when baking?
A: It's essential to know the weight of ingredients when baking to ensure accurate measurements.
Q: Can I use this problem in a real-world scenario?
A: Yes, this problem can be used in various real-world scenarios, such as cooking, packaging, and science.
Q: How do I determine the weight of a product to determine packaging requirements?
A: To determine the weight of a product, multiply the number of units by the weight of each unit.
Q: What is the significance of using real-world examples in mathematical problems?
A: Using real-world examples makes mathematical problems more engaging and relevant.
Q: Can I use this problem to teach fractions to students?
A: Yes, this problem can be used to teach fractions to students by simplifying and multiplying fractions.
Q: How do I make mathematical problems more engaging and relevant?
A: Use real-world examples and make the problems more relatable to everyday life.
Conclusion
In this article, we have answered some frequently asked questions (FAQs) related to the problem of determining the weight of each box of cupcakes. We have also highlighted the significance of using real-world examples in mathematical problems and the importance of knowing the weight of ingredients when baking.
Real-World Applications
This problem has real-world applications in various fields, such as:
- Cooking: When baking, it's essential to know the weight of ingredients to ensure accurate measurements.
- Packaging: Manufacturers need to calculate the weight of products to determine packaging requirements.
- Science: Scientists use mathematical calculations to determine the weight of objects and substances.
Tips and Tricks
When working with fractions, remember to:
- Simplify fractions: Divide both the numerator and the denominator by their greatest common divisor (GCD) to simplify fractions.
- Multiply fractions: Multiply the numerators and denominators separately to multiply fractions.
- Use real-world examples: Use real-world examples to make mathematical problems more engaging and relevant.
Final Thoughts
In conclusion, this problem has demonstrated the importance of mathematical calculations in real-world applications. By simplifying fractions and multiplying them, we can determine the weight of each box. This problem has also highlighted the significance of using real-world examples to make mathematical problems more engaging and relevant.