Solve 3/2-64/6+117/4-2sqrt{3}

$$3 / 2 - 6 \frac { 4 } { 6 } + 11 \frac { 7 } { 4 } - 2 \sqrt { 3 }$$

Evaluate

$$\frac{91}{12}-2\sqrt{3}\approx 4.119231718$$

Solution Steps

Multiply 6 and 6 to get 36.

$$\frac{3}{2}-\frac{36+4}{6}+\frac{11\times 4+7}{4}-2\sqrt{3}$$

Add 36 and 4 to get 40.

$$\frac{3}{2}-\frac{40}{6}+\frac{11\times 4+7}{4}-2\sqrt{3}$$

Reduce the fraction \frac{40}{6} to lowest terms by extracting and canceling out 2.

$$\frac{3}{2}-\frac{20}{3}+\frac{11\times 4+7}{4}-2\sqrt{3}$$

Least common multiple of 2 and 3 is 6. Convert \frac{3}{2} and \frac{20}{3} to fractions with denominator 6.

$$\frac{9}{6}-\frac{40}{6}+\frac{11\times 4+7}{4}-2\sqrt{3}$$

Since \frac{9}{6} and \frac{40}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9-40}{6}+\frac{11\times 4+7}{4}-2\sqrt{3}$$

Subtract 40 from 9 to get -31.

$$-\frac{31}{6}+\frac{11\times 4+7}{4}-2\sqrt{3}$$

Multiply 11 and 4 to get 44.

$$-\frac{31}{6}+\frac{44+7}{4}-2\sqrt{3}$$

Add 44 and 7 to get 51.

$$-\frac{31}{6}+\frac{51}{4}-2\sqrt{3}$$

Least common multiple of 6 and 4 is 12. Convert -\frac{31}{6} and \frac{51}{4} to fractions with denominator 12.

$$-\frac{62}{12}+\frac{153}{12}-2\sqrt{3}$$

Since -\frac{62}{12} and \frac{153}{12} have the same denominator, add them by adding their numerators.

$$\frac{-62+153}{12}-2\sqrt{3}$$

Add -62 and 153 to get 91.

$$\frac{91}{12}-2\sqrt{3}$$

Factor

$$\frac{91 - 24 \sqrt{3}}{12} = 4.119231718195579$$