Solve 5/2+2*(7-1/3)-8

$$\frac { 5 } { 2 } + 2 \cdot ( 7 - \frac { 1 } { 3 } ) - 8$$

Evaluate

$$\frac{47}{6}\approx 7.833333333$$

Solution Steps

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

$$\frac{5}{2}+2\left(\frac{21}{3}-\frac{1}{3}\right)-8$$

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

$$\frac{5}{2}+2\times \frac{21-1}{3}-8$$

Subtract 1 from 21 to get 20.

$$\frac{5}{2}+2\times \frac{20}{3}-8$$

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

$$\frac{5}{2}+\frac{2\times 20}{3}-8$$

Multiply 2 and 20 to get 40.

$$\frac{5}{2}+\frac{40}{3}-8$$

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

$$\frac{15}{6}+\frac{80}{6}-8$$

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

$$\frac{15+80}{6}-8$$

Add 15 and 80 to get 95.

$$\frac{95}{6}-8$$

Convert 8 to fraction \frac{48}{6}.

$$\frac{95}{6}-\frac{48}{6}$$

Since \frac{95}{6} and \frac{48}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{95-48}{6}$$

Subtract 48 from 95 to get 47.

$$\frac{47}{6}$$

Factor

$$\frac{47}{2 \cdot 3} = 7\frac{5}{6} = 7.833333333333333$$