1 1/4+2/7-23/28

To solve \( 1 \frac{1}{4} + \frac{2}{7} - \frac{23}{28} \), we first convert the mixed number into an improper fraction and then combine all fractions by finding a common denominator. 1. Convert \( 1 \frac{1}{4} \) to an improper fraction: \[ 1 \frac{1}{4} = \frac{4 \cdot 1 + 1}{4} = \frac{5}{4} \] 2. Now we have: \[ \frac{5}{4} + \frac{2}{7} - \frac{23}{28} \] 3. Next, we need a common denominator for the fractions \( \frac{5}{4} \), \( \frac{2}{7} \), and \( \frac{23}{28} \). The least common multiple of \( 4 \), \( 7 \), and \( 28 \) is \( 28 \). 4. Convert each fraction to have a denominator of \( 28 \): - For \( \frac{5}{4} \): \[ \frac{5}{4} = \frac{5 \cdot 7}{4 \cdot 7} = \frac{35}{28} \] - For \( \frac{2}{7} \): \[ \frac{2}{7} = \frac{2 \cdot 4}{7 \cdot 4} = \frac{8}{28} \] - \( \frac{23}{28} \) remains unchanged. 5. Now, we can combine the fractions: \[ \frac{35}{28} + \frac{8}{28} - \frac{23}{28} = \frac{35 + 8 - 23}{28} = \frac{20}{28} \] 6. Simplify \( \frac{20}{28} \): \[ \frac{20 \div 4}{28 \div 4} = \frac{5}{7} \] So, the final answer is: \[ \frac{5}{7} \]