Solve =(3-2*1/4):1/6+1/9:4/3+(frac{3}{4}+frac{1}{6})

$$= ( 3 - 2 \times \frac { 1 } { 4 } ) : \frac { 1 } { 6 } + \frac { 1 } { 9 } : \frac { 4 } { 3 } + ( \frac { 3 } { 4 } + \frac { 1 } { 6 } )$$

Evaluate

$$16$$

Solution Steps

Multiply 2 and \frac{1}{4} to get \frac{2}{4}.

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

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

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

Convert 3 to fraction \frac{6}{2}.

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

Since \frac{6}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 1 from 6 to get 5.

$$\frac{\frac{5}{2}}{\frac{1}{6}}+\frac{\frac{1}{9}}{\frac{4}{3}}+\frac{3}{4}+\frac{1}{6}$$

Divide \frac{5}{2} by \frac{1}{6} by multiplying \frac{5}{2} by the reciprocal of \frac{1}{6}.

$$\frac{5}{2}\times 6+\frac{\frac{1}{9}}{\frac{4}{3}}+\frac{3}{4}+\frac{1}{6}$$

Express \frac{5}{2}\times 6 as a single fraction.

$$\frac{5\times 6}{2}+\frac{\frac{1}{9}}{\frac{4}{3}}+\frac{3}{4}+\frac{1}{6}$$

Multiply 5 and 6 to get 30.

$$\frac{30}{2}+\frac{\frac{1}{9}}{\frac{4}{3}}+\frac{3}{4}+\frac{1}{6}$$

Divide 30 by 2 to get 15.

$$15+\frac{\frac{1}{9}}{\frac{4}{3}}+\frac{3}{4}+\frac{1}{6}$$

Divide \frac{1}{9} by \frac{4}{3} by multiplying \frac{1}{9} by the reciprocal of \frac{4}{3}.

$$15+\frac{1}{9}\times \frac{3}{4}+\frac{3}{4}+\frac{1}{6}$$

Multiply \frac{1}{9} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$15+\frac{1\times 3}{9\times 4}+\frac{3}{4}+\frac{1}{6}$$

Do the multiplications in the fraction \frac{1\times 3}{9\times 4}.

$$15+\frac{3}{36}+\frac{3}{4}+\frac{1}{6}$$

Reduce the fraction \frac{3}{36} to lowest terms by extracting and canceling out 3.

$$15+\frac{1}{12}+\frac{3}{4}+\frac{1}{6}$$

Convert 15 to fraction \frac{180}{12}.

$$\frac{180}{12}+\frac{1}{12}+\frac{3}{4}+\frac{1}{6}$$

Since \frac{180}{12} and \frac{1}{12} have the same denominator, add them by adding their numerators.

$$\frac{180+1}{12}+\frac{3}{4}+\frac{1}{6}$$

Add 180 and 1 to get 181.

$$\frac{181}{12}+\frac{3}{4}+\frac{1}{6}$$

Least common multiple of 12 and 4 is 12. Convert \frac{181}{12} and \frac{3}{4} to fractions with denominator 12.

$$\frac{181}{12}+\frac{9}{12}+\frac{1}{6}$$

Since \frac{181}{12} and \frac{9}{12} have the same denominator, add them by adding their numerators.

$$\frac{181+9}{12}+\frac{1}{6}$$

Add 181 and 9 to get 190.

$$\frac{190}{12}+\frac{1}{6}$$

Reduce the fraction \frac{190}{12} to lowest terms by extracting and canceling out 2.

$$\frac{95}{6}+\frac{1}{6}$$

Since \frac{95}{6} and \frac{1}{6} have the same denominator, add them by adding their numerators.

$$\frac{95+1}{6}$$

Add 95 and 1 to get 96.

$$\frac{96}{6}$$

Divide 96 by 6 to get 16.

$$16$$

Factor

$$2^{4}$$