A Baker Used 5 7 10 5 \frac{7}{10} 5 10 7 ​ Bags Of Flour One Week. The Same Baker Used 7 3 10 7 \frac{3}{10} 7 10 3 ​ Bags The Next Week. How Many More Bags Of Flour Did The Baker Use The Second Week Than The First Week?A. 1 4 10 1 \frac{4}{10} 1 10 4 ​ Bags B.

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As a baker, it's essential to keep track of the ingredients used in each batch of goods. In this scenario, we're presented with a problem that requires us to calculate the difference in bags of flour used between two consecutive weeks. The baker used $5 \frac{7}{10}$ bags of flour one week and $7 \frac{3}{10}$ bags the next week. Our goal is to determine how many more bags of flour were used in the second week compared to the first week.

Understanding the Problem

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To solve this problem, we need to first understand the concept of mixed numbers and how to perform arithmetic operations with them. A mixed number is a combination of a whole number and a fraction. In this case, we have two mixed numbers: $5 \frac{7}{10}$ and $7 \frac{3}{10}$. We'll need to convert these mixed numbers to improper fractions to facilitate the calculation.

Converting Mixed Numbers to Improper Fractions

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To convert a mixed number to an improper fraction, we multiply the whole number by the denominator and then add the numerator. The result is then written as the new numerator over the denominator.

Converting $5 \frac{7}{10}$ to an Improper Fraction

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To convert $5 \frac{7}{10}$ to an improper fraction, we multiply the whole number (5) by the denominator (10) and add the numerator (7).

$$5 \times 10 + 7 = 50 + 7 = 57$$

So, the improper fraction equivalent of $5 \frac{7}{10}$ is $\frac{57}{10}$.

Converting $7 \frac{3}{10}$ to an Improper Fraction

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Similarly, to convert $7 \frac{3}{10}$ to an improper fraction, we multiply the whole number (7) by the denominator (10) and add the numerator (3).

$$7 \times 10 + 3 = 70 + 3 = 73$$

So, the improper fraction equivalent of $7 \frac{3}{10}$ is $\frac{73}{10}$.

Calculating the Difference

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Now that we have the improper fractions, we can calculate the difference between the two amounts of flour used.

Subtracting $\frac{57}{10}$ from $\frac{73}{10}$

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To subtract $\frac{57}{10}$ from $\frac{73}{10}$, we need to find a common denominator, which in this case is 10. We can then subtract the numerators while keeping the denominator the same.

$$\frac{73}{10} - \frac{57}{10} = \frac{73 - 57}{10} = \frac{16}{10}$$

Simplifying the Result

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The result, $\frac{16}{10}$, can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 2.

$$\frac{16}{10} = \frac{8}{5}$$

Converting the Result to a Mixed Number

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To convert the improper fraction $\frac{8}{5}$ to a mixed number, we divide the numerator (8) by the denominator (5) and write the result as a whole number and a remainder.

$$8 \div 5 = 1 \text{ with a remainder of } 3$$

So, the mixed number equivalent of $\frac{8}{5}$ is $1 \frac{3}{5}$.

Conclusion

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In conclusion, the baker used $1 \frac{3}{5}$ more bags of flour in the second week than in the first week. This calculation demonstrates the importance of understanding mixed numbers and how to perform arithmetic operations with them.

Final Answer

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The final answer is: $\boxed{1 \frac{3}{5}}$

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In our previous article, we explored the problem of calculating the difference in bags of flour used between two consecutive weeks. We converted mixed numbers to improper fractions, performed arithmetic operations, and arrived at the final answer. In this Q&A article, we'll delve deeper into the problem and address some common questions and concerns.

Q: What is the difference between a mixed number and an improper fraction?

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A: A mixed number is a combination of a whole number and a fraction, while an improper fraction is a fraction where the numerator is greater than or equal to the denominator. In the problem, we converted the mixed numbers $5 \frac{7}{10}$ and $7 \frac{3}{10}$ to improper fractions $\frac{57}{10}$ and $\frac{73}{10}$, respectively.

Q: Why do we need to convert mixed numbers to improper fractions?

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A: Converting mixed numbers to improper fractions allows us to perform arithmetic operations more easily. In this case, we needed to subtract $\frac{57}{10}$ from $\frac{73}{10}$, which would have been more complicated if we had worked with mixed numbers.

Q: How do we subtract fractions with different denominators?

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A: To subtract fractions with different denominators, we need to find a common denominator. In this case, the common denominator was 10. We then subtract the numerators while keeping the denominator the same.

Q: What is the greatest common divisor (GCD) and why is it important?

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A: The GCD is the largest number that divides two or more numbers without leaving a remainder. In this case, the GCD of 16 and 10 is 2. We divided both the numerator and the denominator by their GCD to simplify the result.

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

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A: To convert an improper fraction to a mixed number, we divide the numerator by the denominator and write the result as a whole number and a remainder. In this case, we divided 8 by 5 and wrote the result as $1 \frac{3}{5}$.

Q: What is the final answer to the problem?

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A: The final answer to the problem is $1 \frac{3}{5}$, which represents the difference in bags of flour used between the two weeks.

Q: Why is this problem important in real-life scenarios?

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A: This problem is important in real-life scenarios because it demonstrates the importance of understanding mixed numbers and how to perform arithmetic operations with them. In baking, for example, it's essential to accurately measure ingredients to ensure the quality of the final product.

Q: Can you provide more examples of mixed numbers and improper fractions?

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A: Of course! Here are a few examples:

• Mixed number: $3 \frac{2}{5}$
• Improper fraction: $\frac{17}{5}$
• Mixed number: $2 \frac{4}{7}$
• Improper fraction: $\frac{18}{7}$

Q: How do you recommend practicing mixed numbers and improper fractions?

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A: I recommend practicing mixed numbers and improper fractions by working through examples and exercises. You can also try converting mixed numbers to improper fractions and vice versa to build your skills and confidence.

Final Answer

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The final answer is: $\boxed{1 \frac{3}{5}}$