Solve 95/6+995/6+9995/6+99995/6+99999frac{5}{6}+frac{1}{6}*5

$$9 \frac { 5 } { 6 } + 99 \frac { 5 } { 6 } + 999 \frac { 5 } { 6 } + 9999 \frac { 5 } { 6 } + 99999 \frac { 5 } { 6 } + \frac { 1 } { 6 } \times 5$$

Evaluate

$$\frac{327659}{3}\approx 109219.666666667$$

Solution Steps

Multiply 9 and 6 to get 54.

$$\frac{54+5}{6}+9\times \frac{9\times 6+5}{6}+99\times \frac{9\times 6+5}{6}+999\times \frac{9\times 6+5}{6}+9999\times \frac{9\times 6+5}{6}+\frac{1}{6}\times 5$$

Add 54 and 5 to get 59.

$$\frac{59}{6}+9\times \frac{9\times 6+5}{6}+99\times \frac{9\times 6+5}{6}+999\times \frac{9\times 6+5}{6}+9999\times \frac{9\times 6+5}{6}+\frac{1}{6}\times 5$$

Multiply 9 and 6 to get 54.

$$\frac{59}{6}+9\times \frac{54+5}{6}+99\times \frac{9\times 6+5}{6}+999\times \frac{9\times 6+5}{6}+9999\times \frac{9\times 6+5}{6}+\frac{1}{6}\times 5$$

Add 54 and 5 to get 59.

$$\frac{59}{6}+9\times \frac{59}{6}+99\times \frac{9\times 6+5}{6}+999\times \frac{9\times 6+5}{6}+9999\times \frac{9\times 6+5}{6}+\frac{1}{6}\times 5$$

Express 9\times \frac{59}{6} as a single fraction.

$$\frac{59}{6}+\frac{9\times 59}{6}+99\times \frac{9\times 6+5}{6}+999\times \frac{9\times 6+5}{6}+9999\times \frac{9\times 6+5}{6}+\frac{1}{6}\times 5$$

Multiply 9 and 59 to get 531.

$$\frac{59}{6}+\frac{531}{6}+99\times \frac{9\times 6+5}{6}+999\times \frac{9\times 6+5}{6}+9999\times \frac{9\times 6+5}{6}+\frac{1}{6}\times 5$$

Since \frac{59}{6} and \frac{531}{6} have the same denominator, add them by adding their numerators.

$$\frac{59+531}{6}+99\times \frac{9\times 6+5}{6}+999\times \frac{9\times 6+5}{6}+9999\times \frac{9\times 6+5}{6}+\frac{1}{6}\times 5$$

Add 59 and 531 to get 590.

$$\frac{590}{6}+99\times \frac{9\times 6+5}{6}+999\times \frac{9\times 6+5}{6}+9999\times \frac{9\times 6+5}{6}+\frac{1}{6}\times 5$$

Reduce the fraction \frac{590}{6} to lowest terms by extracting and canceling out 2.

$$\frac{295}{3}+99\times \frac{9\times 6+5}{6}+999\times \frac{9\times 6+5}{6}+9999\times \frac{9\times 6+5}{6}+\frac{1}{6}\times 5$$

Multiply 9 and 6 to get 54.

$$\frac{295}{3}+99\times \frac{54+5}{6}+999\times \frac{9\times 6+5}{6}+9999\times \frac{9\times 6+5}{6}+\frac{1}{6}\times 5$$

Add 54 and 5 to get 59.

$$\frac{295}{3}+99\times \frac{59}{6}+999\times \frac{9\times 6+5}{6}+9999\times \frac{9\times 6+5}{6}+\frac{1}{6}\times 5$$

Express 99\times \frac{59}{6} as a single fraction.

$$\frac{295}{3}+\frac{99\times 59}{6}+999\times \frac{9\times 6+5}{6}+9999\times \frac{9\times 6+5}{6}+\frac{1}{6}\times 5$$

Multiply 99 and 59 to get 5841.

$$\frac{295}{3}+\frac{5841}{6}+999\times \frac{9\times 6+5}{6}+9999\times \frac{9\times 6+5}{6}+\frac{1}{6}\times 5$$

Reduce the fraction \frac{5841}{6} to lowest terms by extracting and canceling out 3.

$$\frac{295}{3}+\frac{1947}{2}+999\times \frac{9\times 6+5}{6}+9999\times \frac{9\times 6+5}{6}+\frac{1}{6}\times 5$$

Least common multiple of 3 and 2 is 6. Convert \frac{295}{3} and \frac{1947}{2} to fractions with denominator 6.

$$\frac{590}{6}+\frac{5841}{6}+999\times \frac{9\times 6+5}{6}+9999\times \frac{9\times 6+5}{6}+\frac{1}{6}\times 5$$

Since \frac{590}{6} and \frac{5841}{6} have the same denominator, add them by adding their numerators.

$$\frac{590+5841}{6}+999\times \frac{9\times 6+5}{6}+9999\times \frac{9\times 6+5}{6}+\frac{1}{6}\times 5$$

Add 590 and 5841 to get 6431.

$$\frac{6431}{6}+999\times \frac{9\times 6+5}{6}+9999\times \frac{9\times 6+5}{6}+\frac{1}{6}\times 5$$

Multiply 9 and 6 to get 54.

$$\frac{6431}{6}+999\times \frac{54+5}{6}+9999\times \frac{9\times 6+5}{6}+\frac{1}{6}\times 5$$

Add 54 and 5 to get 59.

$$\frac{6431}{6}+999\times \frac{59}{6}+9999\times \frac{9\times 6+5}{6}+\frac{1}{6}\times 5$$

Express 999\times \frac{59}{6} as a single fraction.

$$\frac{6431}{6}+\frac{999\times 59}{6}+9999\times \frac{9\times 6+5}{6}+\frac{1}{6}\times 5$$

Multiply 999 and 59 to get 58941.

$$\frac{6431}{6}+\frac{58941}{6}+9999\times \frac{9\times 6+5}{6}+\frac{1}{6}\times 5$$

Since \frac{6431}{6} and \frac{58941}{6} have the same denominator, add them by adding their numerators.

$$\frac{6431+58941}{6}+9999\times \frac{9\times 6+5}{6}+\frac{1}{6}\times 5$$

Add 6431 and 58941 to get 65372.

$$\frac{65372}{6}+9999\times \frac{9\times 6+5}{6}+\frac{1}{6}\times 5$$

Reduce the fraction \frac{65372}{6} to lowest terms by extracting and canceling out 2.

$$\frac{32686}{3}+9999\times \frac{9\times 6+5}{6}+\frac{1}{6}\times 5$$

Multiply 9 and 6 to get 54.

$$\frac{32686}{3}+9999\times \frac{54+5}{6}+\frac{1}{6}\times 5$$

Add 54 and 5 to get 59.

$$\frac{32686}{3}+9999\times \frac{59}{6}+\frac{1}{6}\times 5$$

Express 9999\times \frac{59}{6} as a single fraction.

$$\frac{32686}{3}+\frac{9999\times 59}{6}+\frac{1}{6}\times 5$$

Multiply 9999 and 59 to get 589941.

$$\frac{32686}{3}+\frac{589941}{6}+\frac{1}{6}\times 5$$

Reduce the fraction \frac{589941}{6} to lowest terms by extracting and canceling out 3.

$$\frac{32686}{3}+\frac{196647}{2}+\frac{1}{6}\times 5$$

Least common multiple of 3 and 2 is 6. Convert \frac{32686}{3} and \frac{196647}{2} to fractions with denominator 6.

$$\frac{65372}{6}+\frac{589941}{6}+\frac{1}{6}\times 5$$

Since \frac{65372}{6} and \frac{589941}{6} have the same denominator, add them by adding their numerators.

$$\frac{65372+589941}{6}+\frac{1}{6}\times 5$$

Add 65372 and 589941 to get 655313.

$$\frac{655313}{6}+\frac{1}{6}\times 5$$

Multiply \frac{1}{6} and 5 to get \frac{5}{6}.

$$\frac{655313}{6}+\frac{5}{6}$$

Since \frac{655313}{6} and \frac{5}{6} have the same denominator, add them by adding their numerators.

$$\frac{655313+5}{6}$$

Add 655313 and 5 to get 655318.

$$\frac{655318}{6}$$

Reduce the fraction \frac{655318}{6} to lowest terms by extracting and canceling out 2.

$$\frac{327659}{3}$$

Factor

$$\frac{157 \cdot 2087}{3} = 109219\frac{2}{3} = 109219.66666666667$$