Dianna Made Several Loaves Of Bread Yesterday. Each Loaf Required $2 \frac{2}{3}$ Cups Of Flour. Altogether, She Used $13 \frac{1}{3}$ Cups Of Flour. How Many Loaves Did Dianna Make?A. 3 Loaves B. 4 Loaves C. 5 Loaves D. 7 Loaves

Introduction

In this article, we will delve into the world of mathematics and solve a problem that involves fractions and division. Dianna, a skilled baker, made several loaves of bread yesterday, and we need to determine how many loaves she made. To do this, we will use the information provided about the amount of flour used for each loaf and the total amount of flour used.

The Problem

Dianna made several loaves of bread yesterday. Each loaf required $2 \frac{2}{3}$ cups of flour. Altogether, she used $13 \frac{1}{3}$ cups of flour. We need to find out how many loaves Dianna made.

Step 1: Convert Mixed Numbers to Improper Fractions

To solve this problem, we need to convert the mixed numbers to improper fractions. An improper fraction is a fraction where the numerator is greater than the denominator.

• $2 \frac{2}{3}$ can be converted to an improper fraction as follows:
  • Multiply the whole number part (2) by the denominator (3): 2 × 3 = 6
  • Add the numerator (2) to the result: 6 + 2 = 8
  • Write the result as an improper fraction: $\frac{8}{3}$
• $13 \frac{1}{3}$ can be converted to an improper fraction as follows:
  • Multiply the whole number part (13) by the denominator (3): 13 × 3 = 39
  • Add the numerator (1) to the result: 39 + 1 = 40
  • Write the result as an improper fraction: $\frac{40}{3}$

Step 2: Divide the Total Amount of Flour by the Amount of Flour per Loaf

Now that we have the total amount of flour used and the amount of flour per loaf, we can divide the total amount of flour by the amount of flour per loaf to find the number of loaves.

• Divide the total amount of flour ($\frac{40}{3}$ cups) by the amount of flour per loaf ($\frac{8}{3}$ cups):
  • $\frac{40}{3}$ ÷ $\frac{8}{3}$ = $\frac{40}{3}$ × $\frac{3}{8}$
  • Multiply the numerators: 40 × 3 = 120
  • Multiply the denominators: 3 × 8 = 24
  • Write the result as a fraction: $\frac{120}{24}$
  • Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 24:
    • $\frac{120}{24}$ ÷ 24 = $\frac{5}{1}$

Conclusion

Dianna made 5 loaves of bread yesterday.

Answer

The correct answer is C. 5 loaves.

Discussion

This problem involves fractions and division, which are essential concepts in mathematics. By converting mixed numbers to improper fractions and dividing the total amount of flour by the amount of flour per loaf, we were able to find the number of loaves Dianna made.

Real-World Applications

This problem has real-world applications in baking and cooking. When making bread, it's essential to know the exact amount of ingredients required for each loaf. This problem demonstrates how to use fractions and division to solve real-world problems.

Tips and Variations

• To make this problem more challenging, you can add more variables, such as different types of flour or ingredients.
• To make this problem easier, you can use simpler fractions or whole numbers.
• You can also use this problem as a starting point to explore other mathematical concepts, such as equivalent ratios or proportions.
  Dianna's Loaves of Bread: A Mathematical Mystery =====================================================

Q&A: Solving the Mystery of Dianna's Loaves of Bread

Q: What is the problem about?

A: The problem is about Dianna, a skilled baker, who made several loaves of bread yesterday. Each loaf required $2 \frac{2}{3}$ cups of flour, and altogether, she used $13 \frac{1}{3}$ cups of flour. We need to find out how many loaves Dianna made.

Q: How do we convert mixed numbers to improper fractions?

A: To convert a mixed number to an improper fraction, we multiply the whole number part by the denominator and add the numerator. For example, $2 \frac{2}{3}$ can be converted to an improper fraction as follows:

• Multiply the whole number part (2) by the denominator (3): 2 × 3 = 6
• Add the numerator (2) to the result: 6 + 2 = 8
• Write the result as an improper fraction: $\frac{8}{3}$

Q: How do we divide the total amount of flour by the amount of flour per loaf?

A: To divide the total amount of flour by the amount of flour per loaf, we can use the following steps:

• Divide the total amount of flour ($\frac{40}{3}$ cups) by the amount of flour per loaf ($\frac{8}{3}$ cups):
  • $\frac{40}{3}$ ÷ $\frac{8}{3}$ = $\frac{40}{3}$ × $\frac{3}{8}$
  • Multiply the numerators: 40 × 3 = 120
  • Multiply the denominators: 3 × 8 = 24
  • Write the result as a fraction: $\frac{120}{24}$
  • Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 24:
    • $\frac{120}{24}$ ÷ 24 = $\frac{5}{1}$

Q: What is the answer to the problem?

A: Dianna made 5 loaves of bread yesterday.

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

A: This problem has real-world applications in baking and cooking. When making bread, it's essential to know the exact amount of ingredients required for each loaf. This problem demonstrates how to use fractions and division to solve real-world problems.

Q: Can you make this problem more challenging?

A: Yes, you can make this problem more challenging by adding more variables, such as different types of flour or ingredients.

Q: Can you make this problem easier?

A: Yes, you can make this problem easier by using simpler fractions or whole numbers.

Q: What other mathematical concepts can we explore using this problem?

A: You can use this problem as a starting point to explore other mathematical concepts, such as equivalent ratios or proportions.

Conclusion

The problem of Dianna's loaves of bread is a mathematical mystery that requires the use of fractions and division. By converting mixed numbers to improper fractions and dividing the total amount of flour by the amount of flour per loaf, we were able to find the number of loaves Dianna made. This problem has real-world applications in baking and cooking and can be made more challenging or easier by adding or removing variables.