To perform the subtraction \(73 \frac{7}{10} - 25 \frac{5}{8}\), we first convert the mixed numbers into improper fractions.
- Convert \(73 \frac{7}{10}\) to an improper fraction:
\[ 73 \frac{7}{10} = \frac{73 \times 10 + 7}{10} = \frac{730 + 7}{10} = \frac{737}{10} \]
- Convert \(25 \frac{5}{8}\) to an improper fraction:
\[ 25 \frac{5}{8} = \frac{25 \times 8 + 5}{8} = \frac{200 + 5}{8} = \frac{205}{8} \]
- Now we need to perform the subtraction:
\[ \frac{737}{10} - \frac{205}{8} \]
- Find a common denominator. The least common multiple (LCM) of 10 and 8 is 40. Convert both fractions:
\[ \frac{737}{10} = \frac{737 \times 4}{10 \times 4} = \frac{2948}{40} \]
\[ \frac{205}{8} = \frac{205 \times 5}{8 \times 5} = \frac{1025}{40} \]
- Subtract the fractions:
\[ \frac{2948}{40} - \frac{1025}{40} = \frac{2948 - 1025}{40} = \frac{1923}{40} \]
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Simplify \(\frac{1923}{40}\) if possible. Since 1923 and 40 have no common factors other than 1, the improper fraction can't be simplified further.
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Convert back to a mixed number:
To convert \(\frac{1923}{40}\) to a mixed number:
- Divide 1923 by 40.
Calculating \(1923 \div 40 = 48\) remainder \(3\).
Thus, we can write:
\[ \frac{1923}{40} = 48 \frac{3}{40} \]
To summarize: \[ 73 \frac{7}{10} - 25 \frac{5}{8} = 48 \frac{3}{40} \]