Solve 5(3/2)+3/7(frac{3{2})-2}

$$\frac { 5 ( \frac { 3 } { 2 } ) + 3 } { 7 ( \frac { 3 } { 2 } ) - 2 }$$

Evaluate

$$\frac{21}{17}\approx 1.235294118$$

Solution Steps

Express 5\times \frac{3}{2} as a single fraction.

$$\frac{\frac{5\times 3}{2}+3}{7\times \frac{3}{2}-2}$$

Multiply 5 and 3 to get 15.

$$\frac{\frac{15}{2}+3}{7\times \frac{3}{2}-2}$$

Convert 3 to fraction \frac{6}{2}.

$$\frac{\frac{15}{2}+\frac{6}{2}}{7\times \frac{3}{2}-2}$$

Since \frac{15}{2} and \frac{6}{2} have the same denominator, add them by adding their numerators.

$$\frac{\frac{15+6}{2}}{7\times \frac{3}{2}-2}$$

Add 15 and 6 to get 21.

$$\frac{\frac{21}{2}}{7\times \frac{3}{2}-2}$$

Express 7\times \frac{3}{2} as a single fraction.

$$\frac{\frac{21}{2}}{\frac{7\times 3}{2}-2}$$

Multiply 7 and 3 to get 21.

$$\frac{\frac{21}{2}}{\frac{21}{2}-2}$$

Convert 2 to fraction \frac{4}{2}.

$$\frac{\frac{21}{2}}{\frac{21}{2}-\frac{4}{2}}$$

Since \frac{21}{2} and \frac{4}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{21}{2}}{\frac{21-4}{2}}$$

Subtract 4 from 21 to get 17.

$$\frac{\frac{21}{2}}{\frac{17}{2}}$$

Divide \frac{21}{2} by \frac{17}{2} by multiplying \frac{21}{2} by the reciprocal of \frac{17}{2}.

$$\frac{21}{2}\times \frac{2}{17}$$

Multiply \frac{21}{2} times \frac{2}{17} by multiplying numerator times numerator and denominator times denominator.

$$\frac{21\times 2}{2\times 17}$$

Cancel out 2 in both numerator and denominator.

$$\frac{21}{17}$$

Factor

$$\frac{3 \cdot 7}{17} = 1\frac{4}{17} = 1.2352941176470589$$