Solve (12/7:2*4/7-2/5*5/6)+2frac{2}{5}:2*frac{2}{15}=

$$( 1 \frac { 2 } { 7 } : 2 \cdot \frac { 4 } { 7 } - \frac { 2 } { 5 } \cdot \frac { 5 } { 6 } ) + 2 \frac { 2 } { 5 } : 2 \cdot \frac { 2 } { 15 } =$$

Evaluate

$$\frac{713}{3675}\approx 0.194013605$$

Solution Steps

Express \frac{\frac{1\times 7+2}{7}}{2} as a single fraction.

$$\frac{1\times 7+2}{7\times 2}\times \frac{4}{7}-\frac{2}{5}\times \frac{5}{6}+\frac{\frac{2\times 5+2}{5}}{2}\times \frac{2}{15}$$

Multiply 1 and 7 to get 7.

$$\frac{7+2}{7\times 2}\times \frac{4}{7}-\frac{2}{5}\times \frac{5}{6}+\frac{\frac{2\times 5+2}{5}}{2}\times \frac{2}{15}$$

Add 7 and 2 to get 9.

$$\frac{9}{7\times 2}\times \frac{4}{7}-\frac{2}{5}\times \frac{5}{6}+\frac{\frac{2\times 5+2}{5}}{2}\times \frac{2}{15}$$

Multiply 7 and 2 to get 14.

$$\frac{9}{14}\times \frac{4}{7}-\frac{2}{5}\times \frac{5}{6}+\frac{\frac{2\times 5+2}{5}}{2}\times \frac{2}{15}$$

Multiply \frac{9}{14} times \frac{4}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9\times 4}{14\times 7}-\frac{2}{5}\times \frac{5}{6}+\frac{\frac{2\times 5+2}{5}}{2}\times \frac{2}{15}$$

Do the multiplications in the fraction \frac{9\times 4}{14\times 7}.

$$\frac{36}{98}-\frac{2}{5}\times \frac{5}{6}+\frac{\frac{2\times 5+2}{5}}{2}\times \frac{2}{15}$$

Reduce the fraction \frac{36}{98} to lowest terms by extracting and canceling out 2.

$$\frac{18}{49}-\frac{2}{5}\times \frac{5}{6}+\frac{\frac{2\times 5+2}{5}}{2}\times \frac{2}{15}$$

Multiply \frac{2}{5} times \frac{5}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{18}{49}-\frac{2\times 5}{5\times 6}+\frac{\frac{2\times 5+2}{5}}{2}\times \frac{2}{15}$$

Cancel out 5 in both numerator and denominator.

$$\frac{18}{49}-\frac{2}{6}+\frac{\frac{2\times 5+2}{5}}{2}\times \frac{2}{15}$$

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

$$\frac{18}{49}-\frac{1}{3}+\frac{\frac{2\times 5+2}{5}}{2}\times \frac{2}{15}$$

Least common multiple of 49 and 3 is 147. Convert \frac{18}{49} and \frac{1}{3} to fractions with denominator 147.

$$\frac{54}{147}-\frac{49}{147}+\frac{\frac{2\times 5+2}{5}}{2}\times \frac{2}{15}$$

Since \frac{54}{147} and \frac{49}{147} have the same denominator, subtract them by subtracting their numerators.

$$\frac{54-49}{147}+\frac{\frac{2\times 5+2}{5}}{2}\times \frac{2}{15}$$

Subtract 49 from 54 to get 5.

$$\frac{5}{147}+\frac{\frac{2\times 5+2}{5}}{2}\times \frac{2}{15}$$

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

$$\frac{5}{147}+\frac{2\times 5+2}{5\times 2}\times \frac{2}{15}$$

Multiply 2 and 5 to get 10.

$$\frac{5}{147}+\frac{10+2}{5\times 2}\times \frac{2}{15}$$

Add 10 and 2 to get 12.

$$\frac{5}{147}+\frac{12}{5\times 2}\times \frac{2}{15}$$

Multiply 5 and 2 to get 10.

$$\frac{5}{147}+\frac{12}{10}\times \frac{2}{15}$$

Reduce the fraction \frac{12}{10} to lowest terms by extracting and canceling out 2.

$$\frac{5}{147}+\frac{6}{5}\times \frac{2}{15}$$

Multiply \frac{6}{5} times \frac{2}{15} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5}{147}+\frac{6\times 2}{5\times 15}$$

Do the multiplications in the fraction \frac{6\times 2}{5\times 15}.

$$\frac{5}{147}+\frac{12}{75}$$

Reduce the fraction \frac{12}{75} to lowest terms by extracting and canceling out 3.

$$\frac{5}{147}+\frac{4}{25}$$

Least common multiple of 147 and 25 is 3675. Convert \frac{5}{147} and \frac{4}{25} to fractions with denominator 3675.

$$\frac{125}{3675}+\frac{588}{3675}$$

Since \frac{125}{3675} and \frac{588}{3675} have the same denominator, add them by adding their numerators.

$$\frac{125+588}{3675}$$

Add 125 and 588 to get 713.

$$\frac{713}{3675}$$

Factor

$$\frac{23 \cdot 31}{3 \cdot 5 ^ {2} \cdot 7 ^ {2}} = 0.19401360544217688$$