To find out how much longer Kiki runs during the second week of track practice than the first week, we need to subtract the distance she ran in the first week from the distance she ran in the second week.
First, let's convert the mixed numbers into improper fractions.
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For the first week, Kiki runs \( 4 \frac{3}{7} \): \[ 4 \frac{3}{7} = \frac{4 \times 7 + 3}{7} = \frac{28 + 3}{7} = \frac{31}{7} \]
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For the second week, Kiki runs \( 6 \frac{2}{3} \): \[ 6 \frac{2}{3} = \frac{6 \times 3 + 2}{3} = \frac{18 + 2}{3} = \frac{20}{3} \]
Next, we need to find a common denominator to subtract these two fractions. The least common multiple of 7 and 3 is 21.
Now, convert both fractions to have a denominator of 21: \[ \frac{31}{7} = \frac{31 \times 3}{7 \times 3} = \frac{93}{21} \] \[ \frac{20}{3} = \frac{20 \times 7}{3 \times 7} = \frac{140}{21} \]
Now, we subtract the two fractions: \[ \frac{140}{21} - \frac{93}{21} = \frac{140 - 93}{21} = \frac{47}{21} \]
Next, we can convert \(\frac{47}{21}\) back into a mixed number: \[ 47 \div 21 = 2 \quad \text{remainder } 5 \] So, \(\frac{47}{21} = 2 \frac{5}{21}\).
Kiki runs \( 2 \frac{5}{21} \) miles longer during the second week of track practice than the first week.
The correct option from the responses is: 2 5/21 mi (2 and 5 over 21 mi).
1 answer