3:3

To solve these expressions, we need to perform arithmetic operations on fractions. Let's tackle them one by one: 1) \( \frac{3}{4} - 8 - \frac{2}{3} \left( -\frac{1}{4} - \frac{1}{37} \right) - \frac{2}{48} \) First, calculate \( -\frac{1}{4} - \frac{1}{37} \): \[ -\frac{1}{4} - \frac{1}{37} = -\frac{37}{148} - \frac{4}{148} = -\frac{41}{148} \] Now, multiply by \(-\frac{2}{3}\): \[ \frac{2}{3} \times \frac{41}{148} = \frac{82}{444} = \frac{41}{222} \] So the expression becomes: \[ \frac{3}{4} - 8 + \frac{41}{222} - \frac{1}{24} \] Find a common denominator (e.g., 444): \[ \frac{3}{4} = \frac{333}{444}, \quad \frac{41}{222} = \frac{82}{444}, \quad \frac{1}{24} = \frac{37}{888} = \frac{18.5}{444} \] Combine and subtract: \[ \frac{333}{444} + \frac{82}{444} - \frac{18.5}{444} - 8 \] Calculate: \[ \frac{396.5}{444} - 8 = \frac{396.5}{444} - \frac{3552}{444} = -\frac{3155.5}{444} \] Simplify if needed. 2) \( \frac{3}{22} - \frac{14}{15} \left( \frac{5}{8} + \frac{11}{17} \right) \times \frac{3}{7} \) Calculate inside the brackets first: \[ \frac{5}{8} + \frac{11}{17} = \frac{85}{136} + \frac{88}{136} = \frac{173}{136} \] Multiply by \(-\frac{14}{15}\): \[ \frac{14}{15} \times \frac{173}{136} = \frac{2422}{2040} = \frac{1211}{1020} \] Now multiply by \(\frac{3}{7}\): \[ \frac{1211}{1020} \times \frac{3}{7} = \frac{3633}{7140} \] Subtract from \(\frac{3}{22}\): Convert \(\frac{3}{22}\): \[ \frac{3}{22} = \frac{150}{110}, \quad \frac{3633}{7140} = \frac{163.5}{110} \] Combine and subtract: \[ \frac{150}{110} - \frac{163.5}{110} = -\frac{13.5}{110} \] 3) \( 6 \cdot \frac{2}{5} - \frac{9}{16} \left( \frac{2}{1} \right)^2 \): Square the parentheses: \[ \left( \frac{2}{1} \right)^2 = \frac{4}{1} = 4 \] Multiply by \(-\frac{9}{16}\): \[ -\frac{9}{16} \times 4 = -\frac{36}{16} = -\frac{9}{4} \] The expression becomes: \[ 6 \cdot \frac{2}{5} - \frac{9}{4} = \frac{12}{5} - \frac{9}{4} \] Convert to a common denominator and subtract. 4) \( \left( \frac{2}{7} - \frac{10}{15} \times \frac{8}{9} \right)^{\frac{9}{14}} \): Calculate inside the parentheses: \[ \frac{10}{15} \times \frac{8}{9} = \frac{80}{135} = \frac{16}{27} \] Subtract: \[ \frac{2}{7} - \frac{16}{27} \] Find a common denominator and subtract: \[ \frac{54}{189} - \frac{112}{189} = -\frac{58}{189} \] Raise to the power \(\frac{9}{14}\). You may need a calculator to simplify or approximate results for some expressions.