(7-5 1/4)-(1 4/9+4 5/9-5 1/2)
To solve the expression \((7 - 5 \frac{1}{4}) - (1 \frac{4}{9} + 4 \frac{5}{9} - 5 \frac{1}{2})\), we first need to convert all mixed numbers to improper fractions for easier calculation.
Convert mixed numbers to improper fractions:
- \(7 = \frac{7 \times 1}{1} = \frac{7}{1}\)
- \(5 \frac{1}{4} = 5 + \frac{1}{4} = \frac{20}{4} + \frac{1}{4} = \frac{21}{4}\)
- \(1 \frac{4}{9} = 1 + \frac{4}{9} = \frac{9}{9} + \frac{4}{9} = \frac{13}{9}\)
- \(4 \frac{5}{9} = 4 + \frac{5}{9} = \frac{36}{9} + \frac{5}{9} = \frac{41}{9}\)
- \(5 \frac{1}{2} = 5 + \frac{1}{2} = \frac{10}{2} + \frac{1}{2} = \frac{11}{2}\)
Substitute the improper fractions back into the expression: \[ (7 - 5 \frac{1}{4}) = \left(\frac{7}{1} - \frac{21}{4}\right) \] We need a common denominator to subtract these fractions. The least common multiple of 1 and 4 is 4. \[ = \left(\frac{7 \times 4}{4} - \frac{21}{4}\right) = \left(\frac{28}{4} - \frac{21}{4}\right) = \frac{7}{4} \]
Now calculate \((1 \frac{4}{9} + 4 \frac{5}{9} - 5 \frac{1}{2})\): \[ = \left(\frac{13}{9} + \frac{41}{9} - \frac{11}{2}\right) \] First, combine \(\frac{13}{9}\) and \(\frac{41}{9}\): \[ = \frac{54}{9} = 6 \]
Next, we need to convert \(6\) to a fraction with a common denominator with \(-\frac{11}{2}\): \[ 6 = \frac{6 \times 2}{2} = \frac{12}{2} \] Now combine: \[ = \left(\frac{12}{2} - \frac{11}{2}\right) = \frac{1}{2} \]
Combine everything back into the original expression: \[ \frac{7}{4} - \frac{1}{2} \] To subtract these fractions, convert \(\frac{1}{2}\) to have a denominator of 4: \[ \frac{1}{2} = \frac{2}{4} \] Now, perform the subtraction: \[ = \left(\frac{7}{4} - \frac{2}{4}\right) = \frac{5}{4} \]
Final Result: \[ \frac{5}{4} = 1 \frac{1}{4} \]
Therefore, the result of the expression \((7 - 5 \frac{1}{4}) - (1 \frac{4}{9} + 4 \frac{5}{9} - 5 \frac{1}{2})\) is \(\frac{5}{4}\) or \(1 \frac{1}{4}\).
