Solve (65/18-511/15)div[22/7+(12-82/3)div14]

$$( 6 \frac { 5 } { 18 } - 5 \frac { 11 } { 15 } ) \div [ 2 \frac { 2 } { 7 } + ( 12 - 8 \frac { 2 } { 3 } ) \div 14 ]$$

Evaluate

$$\frac{343}{1590}\approx 0.21572327$$

Solution Steps

Multiply 6 and 18 to get 108.

$$\frac{\frac{108+5}{18}-\frac{5\times 15+11}{15}}{\frac{2\times 7+2}{7}+\frac{12-\frac{8\times 3+2}{3}}{14}}$$

Add 108 and 5 to get 113.

$$\frac{\frac{113}{18}-\frac{5\times 15+11}{15}}{\frac{2\times 7+2}{7}+\frac{12-\frac{8\times 3+2}{3}}{14}}$$

Multiply 5 and 15 to get 75.

$$\frac{\frac{113}{18}-\frac{75+11}{15}}{\frac{2\times 7+2}{7}+\frac{12-\frac{8\times 3+2}{3}}{14}}$$

Add 75 and 11 to get 86.

$$\frac{\frac{113}{18}-\frac{86}{15}}{\frac{2\times 7+2}{7}+\frac{12-\frac{8\times 3+2}{3}}{14}}$$

Least common multiple of 18 and 15 is 90. Convert \frac{113}{18} and \frac{86}{15} to fractions with denominator 90.

$$\frac{\frac{565}{90}-\frac{516}{90}}{\frac{2\times 7+2}{7}+\frac{12-\frac{8\times 3+2}{3}}{14}}$$

Since \frac{565}{90} and \frac{516}{90} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{565-516}{90}}{\frac{2\times 7+2}{7}+\frac{12-\frac{8\times 3+2}{3}}{14}}$$

Subtract 516 from 565 to get 49.

$$\frac{\frac{49}{90}}{\frac{2\times 7+2}{7}+\frac{12-\frac{8\times 3+2}{3}}{14}}$$

Multiply 2 and 7 to get 14.

$$\frac{\frac{49}{90}}{\frac{14+2}{7}+\frac{12-\frac{8\times 3+2}{3}}{14}}$$

Add 14 and 2 to get 16.

$$\frac{\frac{49}{90}}{\frac{16}{7}+\frac{12-\frac{8\times 3+2}{3}}{14}}$$

Multiply 8 and 3 to get 24.

$$\frac{\frac{49}{90}}{\frac{16}{7}+\frac{12-\frac{24+2}{3}}{14}}$$

Add 24 and 2 to get 26.

$$\frac{\frac{49}{90}}{\frac{16}{7}+\frac{12-\frac{26}{3}}{14}}$$

Convert 12 to fraction \frac{36}{3}.

$$\frac{\frac{49}{90}}{\frac{16}{7}+\frac{\frac{36}{3}-\frac{26}{3}}{14}}$$

Since \frac{36}{3} and \frac{26}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{49}{90}}{\frac{16}{7}+\frac{\frac{36-26}{3}}{14}}$$

Subtract 26 from 36 to get 10.

$$\frac{\frac{49}{90}}{\frac{16}{7}+\frac{\frac{10}{3}}{14}}$$

Express \frac{\frac{10}{3}}{14} as a single fraction.

$$\frac{\frac{49}{90}}{\frac{16}{7}+\frac{10}{3\times 14}}$$

Multiply 3 and 14 to get 42.

$$\frac{\frac{49}{90}}{\frac{16}{7}+\frac{10}{42}}$$

Reduce the fraction \frac{10}{42} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{49}{90}}{\frac{16}{7}+\frac{5}{21}}$$

Least common multiple of 7 and 21 is 21. Convert \frac{16}{7} and \frac{5}{21} to fractions with denominator 21.

$$\frac{\frac{49}{90}}{\frac{48}{21}+\frac{5}{21}}$$

Since \frac{48}{21} and \frac{5}{21} have the same denominator, add them by adding their numerators.

$$\frac{\frac{49}{90}}{\frac{48+5}{21}}$$

Add 48 and 5 to get 53.

$$\frac{\frac{49}{90}}{\frac{53}{21}}$$

Divide \frac{49}{90} by \frac{53}{21} by multiplying \frac{49}{90} by the reciprocal of \frac{53}{21}.

$$\frac{49}{90}\times \frac{21}{53}$$

Multiply \frac{49}{90} times \frac{21}{53} by multiplying numerator times numerator and denominator times denominator.

$$\frac{49\times 21}{90\times 53}$$

Do the multiplications in the fraction \frac{49\times 21}{90\times 53}.

$$\frac{1029}{4770}$$

Reduce the fraction \frac{1029}{4770} to lowest terms by extracting and canceling out 3.

$$\frac{343}{1590}$$

Factor

$$\frac{7 ^ {3}}{2 \cdot 3 \cdot 5 \cdot 53} = 0.21572327044025158$$