Solve 5/2+2(7-1/3)-4

$$\frac { 5 } { 2 } + 2 ( 7 - \frac { 1 } { 3 } ) - 4$$

Evaluate

$$\frac{71}{6}\approx 11.833333333$$

Solution Steps

Convert 7 to fraction \frac{21}{3}.

$$\frac{5}{2}+2\left(\frac{21}{3}-\frac{1}{3}\right)-4$$

Since \frac{21}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{2}+2\times \frac{21-1}{3}-4$$

Subtract 1 from 21 to get 20.

$$\frac{5}{2}+2\times \frac{20}{3}-4$$

Express 2\times \frac{20}{3} as a single fraction.

$$\frac{5}{2}+\frac{2\times 20}{3}-4$$

Multiply 2 and 20 to get 40.

$$\frac{5}{2}+\frac{40}{3}-4$$

Least common multiple of 2 and 3 is 6. Convert \frac{5}{2} and \frac{40}{3} to fractions with denominator 6.

$$\frac{15}{6}+\frac{80}{6}-4$$

Since \frac{15}{6} and \frac{80}{6} have the same denominator, add them by adding their numerators.

$$\frac{15+80}{6}-4$$

Add 15 and 80 to get 95.

$$\frac{95}{6}-4$$

Convert 4 to fraction \frac{24}{6}.

$$\frac{95}{6}-\frac{24}{6}$$

Since \frac{95}{6} and \frac{24}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{95-24}{6}$$

Subtract 24 from 95 to get 71.

$$\frac{71}{6}$$

Factor

$$\frac{71}{2 \cdot 3} = 11\frac{5}{6} = 11.833333333333334$$