Solve (42/7+15/6)-(42/7-1frac{5/6)}{30}=

$$\frac { ( 4 \frac { 2 } { 7 } + 1 \frac { 5 } { 6 } ) - ( 4 \frac { 2 } { 7 } - 1 \frac { 5 } { 6 } ) } { 30 } =$$

Evaluate

$$\frac{11}{90}\approx 0.122222222$$

Solution Steps

Multiply 4 and 7 to get 28.

$$\frac{\frac{28+2}{7}+\frac{1\times 6+5}{6}-\left(\frac{4\times 7+2}{7}-\frac{1\times 6+5}{6}\right)}{30}$$

Add 28 and 2 to get 30.

$$\frac{\frac{30}{7}+\frac{1\times 6+5}{6}-\left(\frac{4\times 7+2}{7}-\frac{1\times 6+5}{6}\right)}{30}$$

Multiply 1 and 6 to get 6.

$$\frac{\frac{30}{7}+\frac{6+5}{6}-\left(\frac{4\times 7+2}{7}-\frac{1\times 6+5}{6}\right)}{30}$$

Add 6 and 5 to get 11.

$$\frac{\frac{30}{7}+\frac{11}{6}-\left(\frac{4\times 7+2}{7}-\frac{1\times 6+5}{6}\right)}{30}$$

Least common multiple of 7 and 6 is 42. Convert \frac{30}{7} and \frac{11}{6} to fractions with denominator 42.

$$\frac{\frac{180}{42}+\frac{77}{42}-\left(\frac{4\times 7+2}{7}-\frac{1\times 6+5}{6}\right)}{30}$$

Since \frac{180}{42} and \frac{77}{42} have the same denominator, add them by adding their numerators.

$$\frac{\frac{180+77}{42}-\left(\frac{4\times 7+2}{7}-\frac{1\times 6+5}{6}\right)}{30}$$

Add 180 and 77 to get 257.

$$\frac{\frac{257}{42}-\left(\frac{4\times 7+2}{7}-\frac{1\times 6+5}{6}\right)}{30}$$

Multiply 4 and 7 to get 28.

$$\frac{\frac{257}{42}-\left(\frac{28+2}{7}-\frac{1\times 6+5}{6}\right)}{30}$$

Add 28 and 2 to get 30.

$$\frac{\frac{257}{42}-\left(\frac{30}{7}-\frac{1\times 6+5}{6}\right)}{30}$$

Multiply 1 and 6 to get 6.

$$\frac{\frac{257}{42}-\left(\frac{30}{7}-\frac{6+5}{6}\right)}{30}$$

Add 6 and 5 to get 11.

$$\frac{\frac{257}{42}-\left(\frac{30}{7}-\frac{11}{6}\right)}{30}$$

Least common multiple of 7 and 6 is 42. Convert \frac{30}{7} and \frac{11}{6} to fractions with denominator 42.

$$\frac{\frac{257}{42}-\left(\frac{180}{42}-\frac{77}{42}\right)}{30}$$

Since \frac{180}{42} and \frac{77}{42} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{257}{42}-\frac{180-77}{42}}{30}$$

Subtract 77 from 180 to get 103.

$$\frac{\frac{257}{42}-\frac{103}{42}}{30}$$

Since \frac{257}{42} and \frac{103}{42} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{257-103}{42}}{30}$$

Subtract 103 from 257 to get 154.

$$\frac{\frac{154}{42}}{30}$$

Reduce the fraction \frac{154}{42} to lowest terms by extracting and canceling out 14.

$$\frac{\frac{11}{3}}{30}$$

Express \frac{\frac{11}{3}}{30} as a single fraction.

$$\frac{11}{3\times 30}$$

Multiply 3 and 30 to get 90.

$$\frac{11}{90}$$

Factor

$$\frac{11}{2 \cdot 3 ^ {2} \cdot 5} = 0.12222222222222222$$