Annette Ordered Coffee Beans To Give As Christmas Gifts To Her Teachers. She Orders $\frac{4}{5}$ Pounds And Needs To Share It Equally Between Three Teachers. How Many Pounds Of Coffee Beans Will Each Teacher Receive?

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Introduction

As the holiday season approaches, people often look for ways to show appreciation for their teachers. Annette, a thoughtful student, decided to order coffee beans as a gift for her teachers. She ordered 45\frac{4}{5} pounds of coffee beans and wanted to share it equally among three teachers. In this article, we will explore how to divide fractions and find out how many pounds of coffee beans each teacher will receive.

Understanding Fractions

Before we dive into dividing fractions, let's quickly review what fractions are. A fraction is a way to represent a part of a whole. It consists of two parts: a numerator (the top number) and a denominator (the bottom number). The numerator tells us how many equal parts we have, while the denominator tells us how many parts the whole is divided into.

For example, the fraction 45\frac{4}{5} represents 4 equal parts out of a total of 5 parts. To divide a fraction, we need to follow a specific set of rules.

Dividing Fractions

When dividing fractions, we need to invert the second fraction (i.e., flip the numerator and denominator) and then multiply the two fractions together. This may seem a bit confusing at first, but it's actually quite simple.

Let's go back to Annette's problem. She ordered 45\frac{4}{5} pounds of coffee beans and wants to share it equally among three teachers. To find out how many pounds each teacher will receive, we need to divide the total amount of coffee beans by 3.

To do this, we will invert the second fraction (3) and multiply it by the first fraction (45\frac{4}{5}). This gives us:

45รท3=45ร—13\frac{4}{5} \div 3 = \frac{4}{5} \times \frac{1}{3}

Now, let's multiply the two fractions together:

45ร—13=4ร—15ร—3=415\frac{4}{5} \times \frac{1}{3} = \frac{4 \times 1}{5 \times 3} = \frac{4}{15}

So, each teacher will receive 415\frac{4}{15} pounds of coffee beans.

Real-World Applications

Dividing fractions is an essential skill in many real-world applications, including cooking, science, and finance. For example, if you're making a recipe that calls for 34\frac{3}{4} cup of flour and you want to make half the recipe, you'll need to divide the fraction by 2.

Similarly, if you're investing in the stock market and you want to divide a portfolio of stocks equally among three investment accounts, you'll need to divide the fraction representing the total value of the portfolio by 3.

Conclusion

Dividing fractions may seem like a complex topic, but it's actually quite straightforward once you understand the rules. By following the steps outlined in this article, you'll be able to divide fractions with ease and apply this skill to real-world problems.

In the case of Annette's Christmas gift, each teacher will receive 415\frac{4}{15} pounds of coffee beans. Whether you're a student, a cook, or a scientist, dividing fractions is an essential skill that will serve you well in your daily life.

Practice Problems

Here are a few practice problems to help you reinforce your understanding of dividing fractions:

  1. Divide 23\frac{2}{3} by 4.
  2. Divide 56\frac{5}{6} by 2.
  3. Divide 34\frac{3}{4} by 3.

Answer Key

  1. 23รท4=23ร—14=212=16\frac{2}{3} \div 4 = \frac{2}{3} \times \frac{1}{4} = \frac{2}{12} = \frac{1}{6}
  2. 56รท2=56ร—12=512\frac{5}{6} \div 2 = \frac{5}{6} \times \frac{1}{2} = \frac{5}{12}
  3. 34รท3=34ร—13=312=14\frac{3}{4} \div 3 = \frac{3}{4} \times \frac{1}{3} = \frac{3}{12} = \frac{1}{4}
    Dividing Fractions: A Q&A Guide =====================================

Introduction

In our previous article, we explored the concept of dividing fractions and how to apply it to real-world problems. However, we know that practice makes perfect, and the best way to learn is by asking questions and getting answers. In this article, we'll address some common questions and concerns about dividing fractions.

Q: What is the rule for dividing fractions?

A: The rule for dividing fractions is to invert the second fraction (i.e., flip the numerator and denominator) and then multiply the two fractions together.

Q: Why do we need to invert the second fraction?

A: Inverting the second fraction is necessary because division is the same as multiplying by the reciprocal of the divisor. By inverting the second fraction, we're essentially multiplying by its reciprocal.

Q: Can I divide a fraction by a whole number?

A: Yes, you can divide a fraction by a whole number. To do this, simply invert the whole number (i.e., write it as a fraction with a denominator of 1) and then multiply the two fractions together.

Q: How do I divide a fraction by a fraction?

A: To divide a fraction by a fraction, simply invert the second fraction and then multiply the two fractions together.

Q: What if the denominators are different?

A: If the denominators are different, you'll need to find the least common multiple (LCM) of the two denominators and then multiply both fractions by the LCM.

Q: Can I divide a mixed number by a fraction?

A: Yes, you can divide a mixed number by a fraction. To do this, convert the mixed number to an improper fraction and then follow the usual rules for dividing fractions.

Q: How do I divide a fraction by a decimal?

A: To divide a fraction by a decimal, convert the decimal to a fraction and then follow the usual rules for dividing fractions.

Q: What if I get a negative result?

A: If you get a negative result, it means that the fraction is negative. To simplify the result, you can multiply both the numerator and denominator by -1.

Q: Can I use a calculator to divide fractions?

A: Yes, you can use a calculator to divide fractions. However, make sure to enter the fractions correctly and follow the order of operations.

Q: How do I check my answer?

A: To check your answer, multiply the result by the divisor (i.e., the fraction you divided by) and make sure it equals the original dividend (i.e., the fraction you started with).

Conclusion

Dividing fractions may seem like a complex topic, but with practice and patience, you'll become a pro in no time. Remember to follow the rules, invert the second fraction, and multiply the two fractions together. If you have any more questions or concerns, feel free to ask.

Practice Problems

Here are a few practice problems to help you reinforce your understanding of dividing fractions:

  1. Divide 34\frac{3}{4} by 2.
  2. Divide 56\frac{5}{6} by 34\frac{3}{4}.
  3. Divide 23\frac{2}{3} by 4.

Answer Key

  1. 34รท2=34ร—12=38\frac{3}{4} \div 2 = \frac{3}{4} \times \frac{1}{2} = \frac{3}{8}
  2. 56รท34=56ร—43=2018=109\frac{5}{6} \div \frac{3}{4} = \frac{5}{6} \times \frac{4}{3} = \frac{20}{18} = \frac{10}{9}
  3. 23รท4=23ร—14=212=16\frac{2}{3} \div 4 = \frac{2}{3} \times \frac{1}{4} = \frac{2}{12} = \frac{1}{6}