To subtract the mixed numbers \( 43 \frac{1}{2} \) and \( 15 \frac{4}{7} \), we'll follow these steps:
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Convert the mixed numbers to improper fractions.
- For \( 43 \frac{1}{2} \): \[ 43 \frac{1}{2} = 43 \times 2 + 1 = 86 + 1 = 87 \implies \frac{87}{2} \]
- For \( 15 \frac{4}{7} \): \[ 15 \frac{4}{7} = 15 \times 7 + 4 = 105 + 4 = 109 \implies \frac{109}{7} \]
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Find a common denominator.
The denominators are 2 and 7. The least common multiple (LCM) of 2 and 7 is 14. -
Convert both fractions to have the common denominator of 14.
- Convert \( \frac{87}{2} \): \[ \frac{87}{2} \times \frac{7}{7} = \frac{609}{14} \]
- Convert \( \frac{109}{7} \): \[ \frac{109}{7} \times \frac{2}{2} = \frac{218}{14} \]
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Subtract the two fractions: \[ \frac{609}{14} - \frac{218}{14} = \frac{609 - 218}{14} = \frac{391}{14} \]
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Convert the improper fraction \( \frac{391}{14} \) back to a mixed number.
- Divide 391 by 14: \[ 391 \div 14 = 27 \quad \text{(whole number part)} \]
- Calculate the remainder: \[ 391 - (14 \times 27) = 391 - 378 = 13 \] Therefore, \( \frac{391}{14} = 27 \frac{13}{14} \).
Thus, the final answer is: \[ 27 \frac{13}{14} \]
Mixed Number:
- Whole number: \( 27 \)
- Numerator: \( 13 \)
- Denominator: \( 14 \)