Solve 1/12+[1/5(2/3-1/3)+frac{4}{5}]divfrac{3}{7}+frac{1}{9}

$$\frac { 1 } { 12 } + [ \frac { 1 } { 5 } ( \frac { 2 } { 3 } - \frac { 1 } { 3 } ) + \frac { 4 } { 5 } ] \div \frac { 3 } { 7 } + \frac { 1 } { 9 }$$

Evaluate

$$\frac{133}{60}\approx 2.216666667$$

Solution Steps

Since \frac{2}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{12}+\frac{\frac{1}{5}\times \frac{2-1}{3}+\frac{4}{5}}{\frac{3}{7}}+\frac{1}{9}$$

Subtract 1 from 2 to get 1.

$$\frac{1}{12}+\frac{\frac{1}{5}\times \frac{1}{3}+\frac{4}{5}}{\frac{3}{7}}+\frac{1}{9}$$

Multiply \frac{1}{5} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{12}+\frac{\frac{1\times 1}{5\times 3}+\frac{4}{5}}{\frac{3}{7}}+\frac{1}{9}$$

Do the multiplications in the fraction \frac{1\times 1}{5\times 3}.

$$\frac{1}{12}+\frac{\frac{1}{15}+\frac{4}{5}}{\frac{3}{7}}+\frac{1}{9}$$

Least common multiple of 15 and 5 is 15. Convert \frac{1}{15} and \frac{4}{5} to fractions with denominator 15.

$$\frac{1}{12}+\frac{\frac{1}{15}+\frac{12}{15}}{\frac{3}{7}}+\frac{1}{9}$$

Since \frac{1}{15} and \frac{12}{15} have the same denominator, add them by adding their numerators.

$$\frac{1}{12}+\frac{\frac{1+12}{15}}{\frac{3}{7}}+\frac{1}{9}$$

Add 1 and 12 to get 13.

$$\frac{1}{12}+\frac{\frac{13}{15}}{\frac{3}{7}}+\frac{1}{9}$$

Divide \frac{13}{15} by \frac{3}{7} by multiplying \frac{13}{15} by the reciprocal of \frac{3}{7}.

$$\frac{1}{12}+\frac{13}{15}\times \frac{7}{3}+\frac{1}{9}$$

Multiply \frac{13}{15} times \frac{7}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{12}+\frac{13\times 7}{15\times 3}+\frac{1}{9}$$

Do the multiplications in the fraction \frac{13\times 7}{15\times 3}.

$$\frac{1}{12}+\frac{91}{45}+\frac{1}{9}$$

Least common multiple of 12 and 45 is 180. Convert \frac{1}{12} and \frac{91}{45} to fractions with denominator 180.

$$\frac{15}{180}+\frac{364}{180}+\frac{1}{9}$$

Since \frac{15}{180} and \frac{364}{180} have the same denominator, add them by adding their numerators.

$$\frac{15+364}{180}+\frac{1}{9}$$

Add 15 and 364 to get 379.

$$\frac{379}{180}+\frac{1}{9}$$

Least common multiple of 180 and 9 is 180. Convert \frac{379}{180} and \frac{1}{9} to fractions with denominator 180.

$$\frac{379}{180}+\frac{20}{180}$$

Since \frac{379}{180} and \frac{20}{180} have the same denominator, add them by adding their numerators.

$$\frac{379+20}{180}$$

Add 379 and 20 to get 399.

$$\frac{399}{180}$$

Reduce the fraction \frac{399}{180} to lowest terms by extracting and canceling out 3.

$$\frac{133}{60}$$

Factor

$$\frac{7 \cdot 19}{2 ^ {2} \cdot 3 \cdot 5} = 2\frac{13}{60} = 2.216666666666667$$