Solve |-(1/24+1/30)*1|/7+1/24+frac{1}{30}

$$\frac { | - ( \frac { 1 } { 24 } + \frac { 1 } { 30 } ) \times 1 | } { 7 } + \frac { 1 } { 24 } + \frac { 1 } { 30 }$$

Evaluate

$$\frac{3}{35}\approx 0.085714286$$

Solution Steps

Least common multiple of 24 and 30 is 120. Convert \frac{1}{24} and \frac{1}{30} to fractions with denominator 120.

$$\frac{|\left(-\left(\frac{5}{120}+\frac{4}{120}\right)\right)\times 1|}{7}+\frac{1}{24}+\frac{1}{30}$$

Since \frac{5}{120} and \frac{4}{120} have the same denominator, add them by adding their numerators.

$$\frac{|\left(-\frac{5+4}{120}\right)\times 1|}{7}+\frac{1}{24}+\frac{1}{30}$$

Add 5 and 4 to get 9.

$$\frac{|\left(-\frac{9}{120}\right)\times 1|}{7}+\frac{1}{24}+\frac{1}{30}$$

Reduce the fraction \frac{9}{120} to lowest terms by extracting and canceling out 3.

$$\frac{|-\frac{3}{40}|}{7}+\frac{1}{24}+\frac{1}{30}$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -\frac{3}{40} is \frac{3}{40}.

$$\frac{\frac{3}{40}}{7}+\frac{1}{24}+\frac{1}{30}$$

Express \frac{\frac{3}{40}}{7} as a single fraction.

$$\frac{3}{40\times 7}+\frac{1}{24}+\frac{1}{30}$$

Multiply 40 and 7 to get 280.

$$\frac{3}{280}+\frac{1}{24}+\frac{1}{30}$$

Least common multiple of 280 and 24 is 840. Convert \frac{3}{280} and \frac{1}{24} to fractions with denominator 840.

$$\frac{9}{840}+\frac{35}{840}+\frac{1}{30}$$

Since \frac{9}{840} and \frac{35}{840} have the same denominator, add them by adding their numerators.

$$\frac{9+35}{840}+\frac{1}{30}$$

Add 9 and 35 to get 44.

$$\frac{44}{840}+\frac{1}{30}$$

Reduce the fraction \frac{44}{840} to lowest terms by extracting and canceling out 4.

$$\frac{11}{210}+\frac{1}{30}$$

Least common multiple of 210 and 30 is 210. Convert \frac{11}{210} and \frac{1}{30} to fractions with denominator 210.

$$\frac{11}{210}+\frac{7}{210}$$

Since \frac{11}{210} and \frac{7}{210} have the same denominator, add them by adding their numerators.

$$\frac{11+7}{210}$$

Add 11 and 7 to get 18.

$$\frac{18}{210}$$

Reduce the fraction \frac{18}{210} to lowest terms by extracting and canceling out 6.

$$\frac{3}{35}$$

Factor

$$\frac{3}{5 \cdot 7} = 0.08571428571428572$$