Solve 60/1*6/1000+60/1*6^2/1000+frac{frac{1060}{1*6^3}}{1000}*3

$$\frac { \frac { 60 } { 1 \cdot 6 } } { 1000 } + \frac { \frac { 60 } { 1 \cdot 6 ^ { 2 } } } { 1000 } + \frac { \frac { 1060 } { 1 \cdot 6 ^ { 3 } } } { 1000 } \times 3$$

Evaluate

$$\frac{19}{720}\approx 0.026388889$$

Solution Steps

Express \frac{\frac{60}{1\times 6}}{1000} as a single fraction.

$$\frac{60}{1\times 6\times 1000}+\frac{\frac{60}{1\times 6^{2}}}{1000}+\frac{\frac{1060}{1\times 6^{3}}}{1000}\times 3$$

Multiply 1 and 6 to get 6.

$$\frac{60}{6\times 1000}+\frac{\frac{60}{1\times 6^{2}}}{1000}+\frac{\frac{1060}{1\times 6^{3}}}{1000}\times 3$$

Multiply 6 and 1000 to get 6000.

$$\frac{60}{6000}+\frac{\frac{60}{1\times 6^{2}}}{1000}+\frac{\frac{1060}{1\times 6^{3}}}{1000}\times 3$$

Reduce the fraction \frac{60}{6000} to lowest terms by extracting and canceling out 60.

$$\frac{1}{100}+\frac{\frac{60}{1\times 6^{2}}}{1000}+\frac{\frac{1060}{1\times 6^{3}}}{1000}\times 3$$

Express \frac{\frac{60}{1\times 6^{2}}}{1000} as a single fraction.

$$\frac{1}{100}+\frac{60}{1\times 6^{2}\times 1000}+\frac{\frac{1060}{1\times 6^{3}}}{1000}\times 3$$

Calculate 6 to the power of 2 and get 36.

$$\frac{1}{100}+\frac{60}{1\times 36\times 1000}+\frac{\frac{1060}{1\times 6^{3}}}{1000}\times 3$$

Multiply 1 and 36 to get 36.

$$\frac{1}{100}+\frac{60}{36\times 1000}+\frac{\frac{1060}{1\times 6^{3}}}{1000}\times 3$$

Multiply 36 and 1000 to get 36000.

$$\frac{1}{100}+\frac{60}{36000}+\frac{\frac{1060}{1\times 6^{3}}}{1000}\times 3$$

Reduce the fraction \frac{60}{36000} to lowest terms by extracting and canceling out 60.

$$\frac{1}{100}+\frac{1}{600}+\frac{\frac{1060}{1\times 6^{3}}}{1000}\times 3$$

Least common multiple of 100 and 600 is 600. Convert \frac{1}{100} and \frac{1}{600} to fractions with denominator 600.

$$\frac{6}{600}+\frac{1}{600}+\frac{\frac{1060}{1\times 6^{3}}}{1000}\times 3$$

Since \frac{6}{600} and \frac{1}{600} have the same denominator, add them by adding their numerators.

$$\frac{6+1}{600}+\frac{\frac{1060}{1\times 6^{3}}}{1000}\times 3$$

Add 6 and 1 to get 7.

$$\frac{7}{600}+\frac{\frac{1060}{1\times 6^{3}}}{1000}\times 3$$

Express \frac{\frac{1060}{1\times 6^{3}}}{1000} as a single fraction.

$$\frac{7}{600}+\frac{1060}{1\times 6^{3}\times 1000}\times 3$$

Calculate 6 to the power of 3 and get 216.

$$\frac{7}{600}+\frac{1060}{1\times 216\times 1000}\times 3$$

Multiply 1 and 216 to get 216.

$$\frac{7}{600}+\frac{1060}{216\times 1000}\times 3$$

Multiply 216 and 1000 to get 216000.

$$\frac{7}{600}+\frac{1060}{216000}\times 3$$

Reduce the fraction \frac{1060}{216000} to lowest terms by extracting and canceling out 20.

$$\frac{7}{600}+\frac{53}{10800}\times 3$$

Express \frac{53}{10800}\times 3 as a single fraction.

$$\frac{7}{600}+\frac{53\times 3}{10800}$$

Multiply 53 and 3 to get 159.

$$\frac{7}{600}+\frac{159}{10800}$$

Reduce the fraction \frac{159}{10800} to lowest terms by extracting and canceling out 3.

$$\frac{7}{600}+\frac{53}{3600}$$

Least common multiple of 600 and 3600 is 3600. Convert \frac{7}{600} and \frac{53}{3600} to fractions with denominator 3600.

$$\frac{42}{3600}+\frac{53}{3600}$$

Since \frac{42}{3600} and \frac{53}{3600} have the same denominator, add them by adding their numerators.

$$\frac{42+53}{3600}$$

Add 42 and 53 to get 95.

$$\frac{95}{3600}$$

Reduce the fraction \frac{95}{3600} to lowest terms by extracting and canceling out 5.

$$\frac{19}{720}$$

Factor

$$\frac{19}{2 ^ {4} \cdot 3 ^ {2} \cdot 5} = 0.02638888888888889$$