Ms. B Bought Food For Her Ferrets. She Bought The Following Items:$\[ \begin{tabular}{|l|l|} \hline Veggie & Amount \\ \hline Carrots & \(\frac{31}{3}\) Pounds \\ \hline Potatoes & \(2 \frac{1}{4}\) Pounds \\ \hline Celery & \(\frac{15}{6}\) Pounds

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Ms. B's Ferret Food Shopping: A Math Problem

Ms. B, a loving ferret owner, recently went shopping for her furry friends. She bought a variety of vegetables, including carrots, potatoes, and celery. As a math enthusiast, we can use this scenario to practice our math skills, particularly when it comes to working with fractions and mixed numbers. In this article, we will explore the quantities of each vegetable Ms. B purchased and calculate the total amount of each item.

The Items on the Shopping List

Ms. B bought the following items for her ferrets:

  • Carrots: 313\frac{31}{3} pounds
  • Potatoes: 2142 \frac{1}{4} pounds
  • Celery: 156\frac{15}{6} pounds

Converting Mixed Numbers to Improper Fractions

Before we can add or compare these quantities, we need to convert the mixed numbers to improper fractions. An improper fraction is a fraction where the numerator is greater than or equal to the denominator.

  • Potatoes: 2142 \frac{1}{4} pounds can be converted to an improper fraction by multiplying the whole number part (2) by the denominator (4) and then adding the numerator (1). This gives us 2×4+1=92 \times 4 + 1 = 9. So, the improper fraction for potatoes is 94\frac{9}{4} pounds.
  • Celery: 156\frac{15}{6} pounds can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 3. This gives us 52\frac{5}{2} pounds.

Adding Fractions with Different Denominators

Now that we have converted the mixed numbers to improper fractions, we can add the quantities of each vegetable. However, we need to find a common denominator for the fractions. The least common multiple (LCM) of 3 and 4 is 12. We can convert each fraction to have a denominator of 12.

  • Carrots: 313\frac{31}{3} pounds can be converted to have a denominator of 12 by multiplying the numerator and the denominator by 4. This gives us 31×43×4=12412\frac{31 \times 4}{3 \times 4} = \frac{124}{12} pounds.
  • Potatoes: 94\frac{9}{4} pounds can be converted to have a denominator of 12 by multiplying the numerator and the denominator by 3. This gives us 9×34×3=2712\frac{9 \times 3}{4 \times 3} = \frac{27}{12} pounds.
  • Celery: 52\frac{5}{2} pounds can be converted to have a denominator of 12 by multiplying the numerator and the denominator by 6. This gives us 5×62×6=3012\frac{5 \times 6}{2 \times 6} = \frac{30}{12} pounds.

Adding the Quantities

Now that we have converted each fraction to have a common denominator, we can add the quantities of each vegetable.

12412+2712+3012=18112\frac{124}{12} + \frac{27}{12} + \frac{30}{12} = \frac{181}{12} pounds

Simplifying the Result

The result of the addition is an improper fraction. We can simplify it by dividing the numerator by the denominator.

18112=15.0833...\frac{181}{12} = 15.0833... pounds

In this article, we used Ms. B's ferret food shopping list to practice our math skills, particularly when it comes to working with fractions and mixed numbers. We converted mixed numbers to improper fractions, added fractions with different denominators, and simplified the result. This problem demonstrates the importance of having a solid understanding of fractions and mixed numbers in mathematics.

Key Takeaways

  • Converting mixed numbers to improper fractions is an essential skill in mathematics.
  • Adding fractions with different denominators requires finding a common denominator.
  • Simplifying the result of an addition can be done by dividing the numerator by the denominator.

Real-World Applications

Understanding fractions and mixed numbers has many real-world applications, such as:

  • Cooking and baking: Recipes often require precise measurements, which can be expressed as fractions or mixed numbers.
  • Science and engineering: Scientists and engineers often work with fractions and mixed numbers when measuring quantities or calculating proportions.
  • Finance: Financial calculations, such as interest rates and investment returns, often involve fractions and mixed numbers.

By mastering fractions and mixed numbers, we can better understand and apply mathematical concepts in various aspects of life.
Ms. B's Ferret Food Shopping: A Math Problem - Q&A

In our previous article, we explored the quantities of vegetables Ms. B purchased for her ferrets and calculated the total amount of each item. We also discussed the importance of understanding fractions and mixed numbers in mathematics. In this article, we will answer some frequently asked questions related to the problem and provide additional insights.

Q: What is the total amount of carrots Ms. B bought?

A: To find the total amount of carrots, we need to convert the mixed number to an improper fraction and then add it to the other quantities. However, since we are only asked about carrots, we can simply convert the mixed number to an improper fraction: 313\frac{31}{3} pounds.

Q: How do I convert a mixed number to an improper fraction?

A: To convert a mixed number to an improper fraction, you need to multiply the whole number part by the denominator and then add the numerator. For example, 2142 \frac{1}{4} can be converted to an improper fraction by multiplying 2 by 4 and adding 1: 2×4+1=92 \times 4 + 1 = 9. So, the improper fraction for potatoes is 94\frac{9}{4} pounds.

Q: What is the least common multiple (LCM) of 3 and 4?

A: The LCM of 3 and 4 is 12. This is the smallest number that both 3 and 4 can divide into evenly.

Q: How do I add fractions with different denominators?

A: To add fractions with different denominators, you need to find a common denominator. The common denominator is the least common multiple (LCM) of the two denominators. Once you have the common denominator, you can convert each fraction to have that denominator and then add them.

Q: What is the total amount of all the vegetables Ms. B bought?

A: To find the total amount of all the vegetables, we need to add the quantities of each vegetable. We already calculated the total amount of each vegetable: carrots = 12412\frac{124}{12} pounds, potatoes = 2712\frac{27}{12} pounds, and celery = 3012\frac{30}{12} pounds. We can add these fractions by finding a common denominator, which is 12. So, the total amount of all the vegetables is 12412+2712+3012=18112\frac{124}{12} + \frac{27}{12} + \frac{30}{12} = \frac{181}{12} pounds.

Q: Can I simplify the result of the addition?

A: Yes, you can simplify the result of the addition by dividing the numerator by the denominator. In this case, 18112=15.0833...\frac{181}{12} = 15.0833... pounds.

Q: What are some real-world applications of fractions and mixed numbers?

A: Fractions and mixed numbers have many real-world applications, such as:

  • Cooking and baking: Recipes often require precise measurements, which can be expressed as fractions or mixed numbers.
  • Science and engineering: Scientists and engineers often work with fractions and mixed numbers when measuring quantities or calculating proportions.
  • Finance: Financial calculations, such as interest rates and investment returns, often involve fractions and mixed numbers.

In this article, we answered some frequently asked questions related to the problem and provided additional insights. We hope this Q&A article has helped you better understand the concepts of fractions and mixed numbers and how they are used in real-world applications.

Key Takeaways

  • Converting mixed numbers to improper fractions is an essential skill in mathematics.
  • Adding fractions with different denominators requires finding a common denominator.
  • Simplifying the result of an addition can be done by dividing the numerator by the denominator.
  • Fractions and mixed numbers have many real-world applications, such as cooking, science, engineering, and finance.