Solve 71/2div12-{12*(1/3-03)-3/20}

$$7 \frac { 1 } { 2 } \div 12 - \{ 12 \times ( \frac { 1 } { 3 } - 03 ) - \frac { 3 } { 20 } \}$$

Evaluate

$$-\frac{129}{40}=-3.225$$

Solution Steps

Express \frac{\frac{7\times 2+1}{2}}{12} as a single fraction.

$$\frac{7\times 2+1}{2\times 12}-\left(12\left(\frac{1}{3}-0\times 3\right)-\frac{3}{20}\right)$$

Multiply 7 and 2 to get 14.

$$\frac{14+1}{2\times 12}-\left(12\left(\frac{1}{3}-0\times 3\right)-\frac{3}{20}\right)$$

Add 14 and 1 to get 15.

$$\frac{15}{2\times 12}-\left(12\left(\frac{1}{3}-0\times 3\right)-\frac{3}{20}\right)$$

Multiply 2 and 12 to get 24.

$$\frac{15}{24}-\left(12\left(\frac{1}{3}-0\times 3\right)-\frac{3}{20}\right)$$

Reduce the fraction \frac{15}{24} to lowest terms by extracting and canceling out 3.

$$\frac{5}{8}-\left(12\left(\frac{1}{3}-0\times 3\right)-\frac{3}{20}\right)$$

Multiply 0 and 3 to get 0.

$$\frac{5}{8}-\left(12\left(\frac{1}{3}-0\right)-\frac{3}{20}\right)$$

Subtract 0 from \frac{1}{3} to get \frac{1}{3}.

$$\frac{5}{8}-\left(12\times \frac{1}{3}-\frac{3}{20}\right)$$

Multiply 12 and \frac{1}{3} to get \frac{12}{3}.

$$\frac{5}{8}-\left(\frac{12}{3}-\frac{3}{20}\right)$$

Divide 12 by 3 to get 4.

$$\frac{5}{8}-\left(4-\frac{3}{20}\right)$$

Convert 4 to fraction \frac{80}{20}.

$$\frac{5}{8}-\left(\frac{80}{20}-\frac{3}{20}\right)$$

Since \frac{80}{20} and \frac{3}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{8}-\frac{80-3}{20}$$

Subtract 3 from 80 to get 77.

$$\frac{5}{8}-\frac{77}{20}$$

Least common multiple of 8 and 20 is 40. Convert \frac{5}{8} and \frac{77}{20} to fractions with denominator 40.

$$\frac{25}{40}-\frac{154}{40}$$

Since \frac{25}{40} and \frac{154}{40} have the same denominator, subtract them by subtracting their numerators.

$$\frac{25-154}{40}$$

Subtract 154 from 25 to get -129.

$$-\frac{129}{40}$$

Factor

$$-\frac{129}{40} = -3\frac{9}{40} = -3.225$$