Last Winter, Armand Had { \frac{5}{6}$}$ Of A Row Of Stacked Logs. At The End Of The Winter, He Had { \frac{8}{15}$}$ Of The Same Row Left. How Much Wood Did He Burn Over The Winter?A. ${ 1 \frac{9}{16}\$} Rows B. [$1
Introduction
In this article, we will explore a mathematical problem involving the amount of wood burned over winter. We will use fractions to represent the initial and final amounts of wood and calculate the difference to determine the amount of wood burned.
Understanding the Problem
Armand had {\frac{5}{6}$}$ of a row of stacked logs at the beginning of winter. At the end of the winter, he had {\frac{8}{15}$}$ of the same row left. We need to find out how much wood he burned over the winter.
Calculating the Amount of Wood Burned
To calculate the amount of wood burned, we need to find the difference between the initial and final amounts of wood. We can do this by subtracting the final amount from the initial amount.
Let's start by finding a common denominator for the fractions {\frac{5}{6}$}$ and {\frac{8}{15}$}$. The least common multiple (LCM) of 6 and 15 is 30.
We can rewrite the fractions with a common denominator:
{\frac{5}{6} = \frac{5 \times 5}{6 \times 5} = \frac{25}{30}$]
[$\frac{8}{15} = \frac{8 \times 2}{15 \times 2} = \frac{16}{30}$]
Now that we have a common denominator, we can subtract the final amount from the initial amount:
[$\frac{25}{30} - \frac{16}{30} = \frac{25 - 16}{30} = \frac{9}{30}$]
Simplifying the Fraction
We can simplify the fraction [$\frac{9}{30}$] by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 3.
[$\frac{9}{30} = \frac{9 \div 3}{30 \div 3} = \frac{3}{10}$]
Converting the Fraction to a Mixed Number
We can convert the fraction [$\frac{3}{10}$] to a mixed number by dividing the numerator by the denominator and finding the remainder.
[\frac{3}{10} = 0 \text{ R } 3}
So, the mixed number is ${$0 \frac{3}{10}$].
Converting the Fraction to a Decimal
We can convert the fraction [$\frac{3}{10}$] to a decimal by dividing the numerator by the denominator.
[\frac{3}{10} = 0.3}
Calculating the Amount of Wood Burned in Rows
Since Armand had {\frac{5}{6}$}$ of a row of stacked logs at the beginning of winter, we can multiply the amount of wood burned by the initial amount to find the amount of wood burned in rows.
{\frac{9}{30} \times \frac{5}{6} = \frac{9 \times 5}{30 \times 6} = \frac{45}{180}$]
We can simplify the fraction [$\frac{45}{180}$] by dividing both the numerator and the denominator by their GCD, which is 45.
[$\frac{45}{180} = \frac{45 \div 45}{180 \div 45} = \frac{1}{4}$]
So, Armand burned [$\frac{1}{4}$] of a row of stacked logs over the winter.
Converting the Fraction to a Mixed Number
We can convert the fraction [$\frac{1}{4}$] to a mixed number by dividing the numerator by the denominator and finding the remainder.
[\frac{1}{4} = 0 \text{ R } 1}
So, the mixed number is [$0 \frac{1}{4}$].
Conclusion
In this article, we calculated the amount of wood burned over winter by subtracting the final amount from the initial amount. We found that Armand burned [$\frac{1}{4}$] of a row of stacked logs over the winter. We can convert this fraction to a mixed number or a decimal to make it easier to understand.
Final Answer
Introduction
In our previous article, we calculated the amount of wood burned over winter by subtracting the final amount from the initial amount. We found that Armand burned [$\frac{1}{4}$] of a row of stacked logs over the winter. In this article, we will answer some frequently asked questions about the problem.
Q: What is the initial amount of wood?
A: The initial amount of wood is [$\frac{5}{6}$] of a row of stacked logs.
Q: What is the final amount of wood?
A: The final amount of wood is [$\frac{8}{15}$] of a row of stacked logs.
Q: How do I calculate the amount of wood burned?
A: To calculate the amount of wood burned, you need to subtract the final amount from the initial amount. You can do this by finding a common denominator for the fractions and then subtracting the final amount from the initial amount.
Q: What is the amount of wood burned in rows?
A: The amount of wood burned in rows is [$\frac{1}{4}$] of a row of stacked logs.
Q: Can I convert the fraction to a mixed number or a decimal?
A: Yes, you can convert the fraction to a mixed number or a decimal to make it easier to understand. To convert the fraction to a mixed number, you need to divide the numerator by the denominator and find the remainder. To convert the fraction to a decimal, you need to divide the numerator by the denominator.
Q: What is the mixed number for the amount of wood burned?
A: The mixed number for the amount of wood burned is [$0 \frac{1}{4}$].
Q: What is the decimal equivalent of the amount of wood burned?
A: The decimal equivalent of the amount of wood burned is 0.25.
Q: Can I use a calculator to calculate the amount of wood burned?
A: Yes, you can use a calculator to calculate the amount of wood burned. However, it's always a good idea to understand the math behind the calculation.
Q: What is the final answer?
A: The final answer is [$0 \frac{1}{4}$] rows.
Conclusion
In this article, we answered some frequently asked questions about the problem of calculating the amount of wood burned over winter. We hope this article has been helpful in understanding the math behind the calculation.
Final Answer
The final answer is [$0 \frac{1}{4}$] rows.
Additional Resources
If you want to learn more about fractions and decimals, you can check out the following resources:
- Khan Academy: Fractions and Decimals
- Mathway: Fractions and Decimals
- Wolfram Alpha: Fractions and Decimals
We hope this article has been helpful in understanding the math behind the calculation. If you have any further questions, please don't hesitate to ask.