To find out how many more bags of flour the baker used in the second week compared to the first week, we need to subtract the amount used the first week from the amount used the second week.
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Convert the mixed number to an improper fraction:
First week: \( 5 \frac{7}{10} \)
To convert to an improper fraction: \[ 5 \frac{7}{10} = \frac{5 \times 10 + 7}{10} = \frac{50 + 7}{10} = \frac{57}{10} \]
Second week: \( \frac{7}{310} \) (already a proper fraction)
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Find a common denominator:
The denominators are \( 10 \) and \( 310 \). The least common multiple is \( 310 \).Convert \( \frac{57}{10} \) to have a denominator of \( 310 \): \[ \frac{57}{10} = \frac{57 \times 31}{10 \times 31} = \frac{1767}{310} \]
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Now, subtract the second week's usage from the first week's usage: \[ \frac{1767}{310} - \frac{7}{310} = \frac{1767 - 7}{310} = \frac{1760}{310} \]
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Simplify the fraction:
Divide both the numerator and the denominator by their greatest common divisor, which is \( 10 \): \[ \frac{1760 \div 10}{310 \div 10} = \frac{176}{31} \] -
Convert back to a mixed number: Divide to find how many whole times 31 goes into 176: \[ 31 \times 5 = 155 \quad \text{(which is } 5\text{ whole)}\ 176 - 155 = 21 \] So, we have: \[ \frac{176}{31} = 5 \frac{21}{31} \]
Now, we need to find the fractional values in the list of responses given.
- Compare \( 1 4/10 \), \( 1 6/10 \), \( 2 4/10 \), and \( 2 6/10 \) with \( 5 \frac{21}{31} \) - to convert into decimal or further evaluate we may break down:
First let’s evaluate all the values:
\[ 2 \frac{6}{10} = 2.6 \ 2 \frac{4}{10} = 2.4 \ 1 \frac{6}{10} = 1.6 \ 1 \frac{4}{10} = 1.4 \]
Now looking at the numbers we've calculated earlier, \( \frac{176}{31} \approx 5.677 \), therefore the best fit of the bag usage based on other values isn’t directly in the options.
The reason lies in the values computed and how specific values relate to reduction hence based on classic methods the numeric comparison leads to the simpler output.
The answer is:
- The differences thus could approximate to \( 1.77 \), thus fitting none.
Please let me know if you want a different approach or additional clarity on these steps.
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