Solve 3/4/1/6+5^2/3/1/12/6+(8-1/4)+3

$$\frac { \frac { 3 / 4 } { 1 / 6 } + \frac { 5 ^ { 2 } / 3 } { 1 / 12 } } { 6 + ( 8 - 1 / 4 ) } + 3$$

Evaluate

$$\frac{53}{5}=10.6$$

Solution Steps

Divide \frac{3}{4} by \frac{1}{6} by multiplying \frac{3}{4} by the reciprocal of \frac{1}{6}.

$$\frac{\frac{3}{4}\times 6+\frac{\frac{5^{2}}{3}}{\frac{1}{12}}}{6+8-\frac{1}{4}}+3$$

Express \frac{3}{4}\times 6 as a single fraction.

$$\frac{\frac{3\times 6}{4}+\frac{\frac{5^{2}}{3}}{\frac{1}{12}}}{6+8-\frac{1}{4}}+3$$

Multiply 3 and 6 to get 18.

$$\frac{\frac{18}{4}+\frac{\frac{5^{2}}{3}}{\frac{1}{12}}}{6+8-\frac{1}{4}}+3$$

Reduce the fraction \frac{18}{4} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{9}{2}+\frac{\frac{5^{2}}{3}}{\frac{1}{12}}}{6+8-\frac{1}{4}}+3$$

Divide \frac{5^{2}}{3} by \frac{1}{12} by multiplying \frac{5^{2}}{3} by the reciprocal of \frac{1}{12}.

$$\frac{\frac{9}{2}+\frac{5^{2}\times 12}{3}}{6+8-\frac{1}{4}}+3$$

Calculate 5 to the power of 2 and get 25.

$$\frac{\frac{9}{2}+\frac{25\times 12}{3}}{6+8-\frac{1}{4}}+3$$

Multiply 25 and 12 to get 300.

$$\frac{\frac{9}{2}+\frac{300}{3}}{6+8-\frac{1}{4}}+3$$

Divide 300 by 3 to get 100.

$$\frac{\frac{9}{2}+100}{6+8-\frac{1}{4}}+3$$

Convert 100 to fraction \frac{200}{2}.

$$\frac{\frac{9}{2}+\frac{200}{2}}{6+8-\frac{1}{4}}+3$$

Since \frac{9}{2} and \frac{200}{2} have the same denominator, add them by adding their numerators.

$$\frac{\frac{9+200}{2}}{6+8-\frac{1}{4}}+3$$

Add 9 and 200 to get 209.

$$\frac{\frac{209}{2}}{6+8-\frac{1}{4}}+3$$

Add 6 and 8 to get 14.

$$\frac{\frac{209}{2}}{14-\frac{1}{4}}+3$$

Convert 14 to fraction \frac{56}{4}.

$$\frac{\frac{209}{2}}{\frac{56}{4}-\frac{1}{4}}+3$$

Since \frac{56}{4} and \frac{1}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{209}{2}}{\frac{56-1}{4}}+3$$

Subtract 1 from 56 to get 55.

$$\frac{\frac{209}{2}}{\frac{55}{4}}+3$$

Divide \frac{209}{2} by \frac{55}{4} by multiplying \frac{209}{2} by the reciprocal of \frac{55}{4}.

$$\frac{209}{2}\times \frac{4}{55}+3$$

Multiply \frac{209}{2} times \frac{4}{55} by multiplying numerator times numerator and denominator times denominator.

$$\frac{209\times 4}{2\times 55}+3$$

Do the multiplications in the fraction \frac{209\times 4}{2\times 55}.

$$\frac{836}{110}+3$$

Reduce the fraction \frac{836}{110} to lowest terms by extracting and canceling out 22.

$$\frac{38}{5}+3$$

Convert 3 to fraction \frac{15}{5}.

$$\frac{38}{5}+\frac{15}{5}$$

Since \frac{38}{5} and \frac{15}{5} have the same denominator, add them by adding their numerators.

$$\frac{38+15}{5}$$

Add 38 and 15 to get 53.

$$\frac{53}{5}$$

Factor

$$\frac{53}{5} = 10\frac{3}{5} = 10.6$$