(2/7 + (1/2)+3/4) :1 1/7

To solve the expression \((\frac{2}{7} + \frac{1}{2} + \frac{3}{4}) : 1 \frac{1}{7}\), we first need to convert the mixed number \(1 \frac{1}{7}\) into an improper fraction. 1. Convert \(1 \frac{1}{7}\) to an improper fraction: \[ 1 \frac{1}{7} = \frac{7 \cdot 1 + 1}{7} = \frac{8}{7} \] 2. Now, we will calculate \(\frac{2}{7} + \frac{1}{2} + \frac{3}{4}\): - First, find a common denominator for the fractions. The denominators are 7, 2, and 4. The least common multiple (LCM) of these numbers is 28. 3. Convert each fraction to have a denominator of 28: - For \(\frac{2}{7}\): \[ \frac{2}{7} = \frac{2 \cdot 4}{7 \cdot 4} = \frac{8}{28} \] - For \(\frac{1}{2}\): \[ \frac{1}{2} = \frac{1 \cdot 14}{2 \cdot 14} = \frac{14}{28} \] - For \(\frac{3}{4}\): \[ \frac{3}{4} = \frac{3 \cdot 7}{4 \cdot 7} = \frac{21}{28} \] 4. Now, add the fractions: \[ \frac{8}{28} + \frac{14}{28} + \frac{21}{28} = \frac{8 + 14 + 21}{28} = \frac{43}{28} \] 5. Now, divide \(\frac{43}{28}\) by \(\frac{8}{7}\) (the improper fraction we converted earlier): \[ \frac{43}{28} \div \frac{8}{7} = \frac{43}{28} \cdot \frac{7}{8} = \frac{43 \cdot 7}{28 \cdot 8} = \frac{301}{224} \] Thus, the final result is: \[ \frac{301}{224} \] If you would like to convert it back to a mixed number: \[ 301 \div 224 = 1 \quad \text{(remainder } 77\text{)} \] So, \[ \frac{301}{224} = 1 \frac{77}{224} \] The final answer is: \[ \frac{301}{224} \quad \text{or} \quad 1 \frac{77}{224} \]