Solve (1.67+11/30-1.8):(1.083-0.77083)/(0.816+0.583)*(0.2814-0.148+frac{8{15})}:0.26

$$\frac { ( 1.67 + \frac { 11 } { 30 } - 1.8 ) : ( 1.083 - 0.77083 ) } { ( 0.816 + 0.583 ) \times ( 0.2814 - 0.148 + \frac { 8 } { 15 } ) } : 0.26$$

Evaluate

$$\frac{17750000000000}{5678003533579}\approx 3.126098794$$

Solution Steps

Express \frac{\frac{\frac{1.67+\frac{11}{30}-1.8}{1.083-0.77083}}{\left(0.816+0.583\right)\left(0.2814-0.148+\frac{8}{15}\right)}}{0.26} as a single fraction.

$$\frac{\frac{1.67+\frac{11}{30}-1.8}{1.083-0.77083}}{\left(0.816+0.583\right)\left(0.2814-0.148+\frac{8}{15}\right)\times 0.26}$$

Convert decimal number 1.67 to fraction \frac{167}{100}.

$$\frac{\frac{\frac{167}{100}+\frac{11}{30}-1.8}{1.083-0.77083}}{\left(0.816+0.583\right)\left(0.2814-0.148+\frac{8}{15}\right)\times 0.26}$$

Least common multiple of 100 and 30 is 300. Convert \frac{167}{100} and \frac{11}{30} to fractions with denominator 300.

$$\frac{\frac{\frac{501}{300}+\frac{110}{300}-1.8}{1.083-0.77083}}{\left(0.816+0.583\right)\left(0.2814-0.148+\frac{8}{15}\right)\times 0.26}$$

Since \frac{501}{300} and \frac{110}{300} have the same denominator, add them by adding their numerators.

$$\frac{\frac{\frac{501+110}{300}-1.8}{1.083-0.77083}}{\left(0.816+0.583\right)\left(0.2814-0.148+\frac{8}{15}\right)\times 0.26}$$

Add 501 and 110 to get 611.

$$\frac{\frac{\frac{611}{300}-1.8}{1.083-0.77083}}{\left(0.816+0.583\right)\left(0.2814-0.148+\frac{8}{15}\right)\times 0.26}$$

Convert decimal number 1.8 to fraction \frac{18}{10}. Reduce the fraction \frac{18}{10} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{\frac{611}{300}-\frac{9}{5}}{1.083-0.77083}}{\left(0.816+0.583\right)\left(0.2814-0.148+\frac{8}{15}\right)\times 0.26}$$

Least common multiple of 300 and 5 is 300. Convert \frac{611}{300} and \frac{9}{5} to fractions with denominator 300.

$$\frac{\frac{\frac{611}{300}-\frac{540}{300}}{1.083-0.77083}}{\left(0.816+0.583\right)\left(0.2814-0.148+\frac{8}{15}\right)\times 0.26}$$

Since \frac{611}{300} and \frac{540}{300} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{\frac{611-540}{300}}{1.083-0.77083}}{\left(0.816+0.583\right)\left(0.2814-0.148+\frac{8}{15}\right)\times 0.26}$$

Subtract 540 from 611 to get 71.

$$\frac{\frac{\frac{71}{300}}{1.083-0.77083}}{\left(0.816+0.583\right)\left(0.2814-0.148+\frac{8}{15}\right)\times 0.26}$$

Subtract 0.77083 from 1.083 to get 0.31217.

$$\frac{\frac{\frac{71}{300}}{0.31217}}{\left(0.816+0.583\right)\left(0.2814-0.148+\frac{8}{15}\right)\times 0.26}$$

Express \frac{\frac{71}{300}}{0.31217} as a single fraction.

$$\frac{\frac{71}{300\times 0.31217}}{\left(0.816+0.583\right)\left(0.2814-0.148+\frac{8}{15}\right)\times 0.26}$$

Multiply 300 and 0.31217 to get 93.651.

$$\frac{\frac{71}{93.651}}{\left(0.816+0.583\right)\left(0.2814-0.148+\frac{8}{15}\right)\times 0.26}$$

Expand \frac{71}{93.651} by multiplying both numerator and the denominator by 1000.

$$\frac{\frac{71000}{93651}}{\left(0.816+0.583\right)\left(0.2814-0.148+\frac{8}{15}\right)\times 0.26}$$

Add 0.816 and 0.583 to get 1.399.

$$\frac{\frac{71000}{93651}}{1.399\left(0.2814-0.148+\frac{8}{15}\right)\times 0.26}$$

Subtract 0.148 from 0.2814 to get 0.1334.

$$\frac{\frac{71000}{93651}}{1.399\left(0.1334+\frac{8}{15}\right)\times 0.26}$$

Convert decimal number 0.1334 to fraction \frac{1334}{10000}. Reduce the fraction \frac{1334}{10000} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{71000}{93651}}{1.399\left(\frac{667}{5000}+\frac{8}{15}\right)\times 0.26}$$

Least common multiple of 5000 and 15 is 15000. Convert \frac{667}{5000} and \frac{8}{15} to fractions with denominator 15000.

$$\frac{\frac{71000}{93651}}{1.399\left(\frac{2001}{15000}+\frac{8000}{15000}\right)\times 0.26}$$

Since \frac{2001}{15000} and \frac{8000}{15000} have the same denominator, add them by adding their numerators.

$$\frac{\frac{71000}{93651}}{1.399\times \frac{2001+8000}{15000}\times 0.26}$$

Add 2001 and 8000 to get 10001.

$$\frac{\frac{71000}{93651}}{1.399\times \frac{10001}{15000}\times 0.26}$$

Convert decimal number 1.399 to fraction \frac{1399}{1000}.

$$\frac{\frac{71000}{93651}}{\frac{1399}{1000}\times \frac{10001}{15000}\times 0.26}$$

Multiply \frac{1399}{1000} times \frac{10001}{15000} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{71000}{93651}}{\frac{1399\times 10001}{1000\times 15000}\times 0.26}$$

Do the multiplications in the fraction \frac{1399\times 10001}{1000\times 15000}.

$$\frac{\frac{71000}{93651}}{\frac{13991399}{15000000}\times 0.26}$$

Convert decimal number 0.26 to fraction \frac{26}{100}. Reduce the fraction \frac{26}{100} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{71000}{93651}}{\frac{13991399}{15000000}\times \frac{13}{50}}$$

Multiply \frac{13991399}{15000000} times \frac{13}{50} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{71000}{93651}}{\frac{13991399\times 13}{15000000\times 50}}$$

Do the multiplications in the fraction \frac{13991399\times 13}{15000000\times 50}.

$$\frac{\frac{71000}{93651}}{\frac{181888187}{750000000}}$$

Divide \frac{71000}{93651} by \frac{181888187}{750000000} by multiplying \frac{71000}{93651} by the reciprocal of \frac{181888187}{750000000}.

$$\frac{71000}{93651}\times \frac{750000000}{181888187}$$

Multiply \frac{71000}{93651} times \frac{750000000}{181888187} by multiplying numerator times numerator and denominator times denominator.

$$\frac{71000\times 750000000}{93651\times 181888187}$$

Do the multiplications in the fraction \frac{71000\times 750000000}{93651\times 181888187}.

$$\frac{53250000000000}{17034010600737}$$

Reduce the fraction \frac{53250000000000}{17034010600737} to lowest terms by extracting and canceling out 3.

$$\frac{17750000000000}{5678003533579}$$

Factor

$$\frac{71 \cdot 2 ^ {10} \cdot 5 ^ {12}}{13 \cdot 19 \cdot 31 \cdot 53 \cdot 73 \cdot 137 \cdot 1399} = 3\frac{715989399263}{5678003533579} = 3.126098794237927$$