To subtract the fractions \(2 \frac{3}{5} - 1 \frac{1}{4}\), we can follow these steps:
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Convert the mixed numbers to improper fractions.
- \(2 \frac{3}{5} = \frac{2 \times 5 + 3}{5} = \frac{10 + 3}{5} = \frac{13}{5}\)
- \(1 \frac{1}{4} = \frac{1 \times 4 + 1}{4} = \frac{4 + 1}{4} = \frac{5}{4}\)
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Subtract the improper fractions:
- To subtract the fractions, we need a common denominator. The least common multiple of 5 and 4 is 20.
- Convert \(\frac{13}{5}\) to have a denominator of 20: \[ \frac{13}{5} = \frac{13 \times 4}{5 \times 4} = \frac{52}{20} \]
- Convert \(\frac{5}{4}\) to have a denominator of 20: \[ \frac{5}{4} = \frac{5 \times 5}{4 \times 5} = \frac{25}{20} \]
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Now, subtract the fractions: \[ \frac{52}{20} - \frac{25}{20} = \frac{52 - 25}{20} = \frac{27}{20} \]
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Convert back to a mixed number:
- \(\frac{27}{20} = 1 \frac{7}{20}\) (since 27 divided by 20 gives 1 with a remainder of 7)
So, \(2 \frac{3}{5} - 1 \frac{1}{4} = 1 \frac{7}{20}\).
The final answer is \(1 \frac{7}{20}\).
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