Solve 180-31/5-(21/3+7/6-7/9)

$$180 - 3 \frac { 1 } { 5 } - ( 2 \frac { 1 } { 3 } + \frac { 7 } { 6 } - \frac { 7 } { 9 } )$$

Evaluate

$$\frac{15667}{90}\approx 174.077777778$$

Solution Steps

Multiply 3 and 5 to get 15.

$$180-\frac{15+1}{5}-\left(\frac{2\times 3+1}{3}+\frac{7}{6}-\frac{7}{9}\right)$$

Add 15 and 1 to get 16.

$$180-\frac{16}{5}-\left(\frac{2\times 3+1}{3}+\frac{7}{6}-\frac{7}{9}\right)$$

Convert 180 to fraction \frac{900}{5}.

$$\frac{900}{5}-\frac{16}{5}-\left(\frac{2\times 3+1}{3}+\frac{7}{6}-\frac{7}{9}\right)$$

Since \frac{900}{5} and \frac{16}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{900-16}{5}-\left(\frac{2\times 3+1}{3}+\frac{7}{6}-\frac{7}{9}\right)$$

Subtract 16 from 900 to get 884.

$$\frac{884}{5}-\left(\frac{2\times 3+1}{3}+\frac{7}{6}-\frac{7}{9}\right)$$

Multiply 2 and 3 to get 6.

$$\frac{884}{5}-\left(\frac{6+1}{3}+\frac{7}{6}-\frac{7}{9}\right)$$

Add 6 and 1 to get 7.

$$\frac{884}{5}-\left(\frac{7}{3}+\frac{7}{6}-\frac{7}{9}\right)$$

Least common multiple of 3 and 6 is 6. Convert \frac{7}{3} and \frac{7}{6} to fractions with denominator 6.

$$\frac{884}{5}-\left(\frac{14}{6}+\frac{7}{6}-\frac{7}{9}\right)$$

Since \frac{14}{6} and \frac{7}{6} have the same denominator, add them by adding their numerators.

$$\frac{884}{5}-\left(\frac{14+7}{6}-\frac{7}{9}\right)$$

Add 14 and 7 to get 21.

$$\frac{884}{5}-\left(\frac{21}{6}-\frac{7}{9}\right)$$

Reduce the fraction \frac{21}{6} to lowest terms by extracting and canceling out 3.

$$\frac{884}{5}-\left(\frac{7}{2}-\frac{7}{9}\right)$$

Least common multiple of 2 and 9 is 18. Convert \frac{7}{2} and \frac{7}{9} to fractions with denominator 18.

$$\frac{884}{5}-\left(\frac{63}{18}-\frac{14}{18}\right)$$

Since \frac{63}{18} and \frac{14}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{884}{5}-\frac{63-14}{18}$$

Subtract 14 from 63 to get 49.

$$\frac{884}{5}-\frac{49}{18}$$

Least common multiple of 5 and 18 is 90. Convert \frac{884}{5} and \frac{49}{18} to fractions with denominator 90.

$$\frac{15912}{90}-\frac{245}{90}$$

Since \frac{15912}{90} and \frac{245}{90} have the same denominator, subtract them by subtracting their numerators.

$$\frac{15912-245}{90}$$

Subtract 245 from 15912 to get 15667.

$$\frac{15667}{90}$$

Factor

$$\frac{15667}{2 \cdot 3 ^ {2} \cdot 5} = 174\frac{7}{90} = 174.07777777777778$$