Solve 20+273.15-(-20+213.15)/frac{0.006{0.78}+0.008/0.024+0.006/0.78}=

$$\frac { 20 + 273.15 - ( - 20 + 213.15 ) } { \frac { 0.006 } { 0.78 } + \frac { 0.008 } { 0.024 } + \frac { 0.006 } { 0.78 } } =$$

Evaluate

$$\frac{4875}{17}\approx 286.764705882$$

Solution Steps

Add 20 and 273.15 to get 293.15.

$$\frac{293.15-\left(-20+213.15\right)}{\frac{0.006}{0.78}+\frac{0.008}{0.024}+\frac{0.006}{0.78}}$$

Add -20 and 213.15 to get 193.15.

$$\frac{293.15-193.15}{\frac{0.006}{0.78}+\frac{0.008}{0.024}+\frac{0.006}{0.78}}$$

Subtract 193.15 from 293.15 to get 100.

$$\frac{100}{\frac{0.006}{0.78}+\frac{0.008}{0.024}+\frac{0.006}{0.78}}$$

Expand \frac{0.006}{0.78} by multiplying both numerator and the denominator by 1000.

$$\frac{100}{\frac{6}{780}+\frac{0.008}{0.024}+\frac{0.006}{0.78}}$$

Reduce the fraction \frac{6}{780} to lowest terms by extracting and canceling out 6.

$$\frac{100}{\frac{1}{130}+\frac{0.008}{0.024}+\frac{0.006}{0.78}}$$

Expand \frac{0.008}{0.024} by multiplying both numerator and the denominator by 1000.

$$\frac{100}{\frac{1}{130}+\frac{8}{24}+\frac{0.006}{0.78}}$$

Reduce the fraction \frac{8}{24} to lowest terms by extracting and canceling out 8.

$$\frac{100}{\frac{1}{130}+\frac{1}{3}+\frac{0.006}{0.78}}$$

Least common multiple of 130 and 3 is 390. Convert \frac{1}{130} and \frac{1}{3} to fractions with denominator 390.

$$\frac{100}{\frac{3}{390}+\frac{130}{390}+\frac{0.006}{0.78}}$$

Since \frac{3}{390} and \frac{130}{390} have the same denominator, add them by adding their numerators.

$$\frac{100}{\frac{3+130}{390}+\frac{0.006}{0.78}}$$

Add 3 and 130 to get 133.

$$\frac{100}{\frac{133}{390}+\frac{0.006}{0.78}}$$

Expand \frac{0.006}{0.78} by multiplying both numerator and the denominator by 1000.

$$\frac{100}{\frac{133}{390}+\frac{6}{780}}$$

Reduce the fraction \frac{6}{780} to lowest terms by extracting and canceling out 6.

$$\frac{100}{\frac{133}{390}+\frac{1}{130}}$$

Least common multiple of 390 and 130 is 390. Convert \frac{133}{390} and \frac{1}{130} to fractions with denominator 390.

$$\frac{100}{\frac{133}{390}+\frac{3}{390}}$$

Since \frac{133}{390} and \frac{3}{390} have the same denominator, add them by adding their numerators.

$$\frac{100}{\frac{133+3}{390}}$$

Add 133 and 3 to get 136.

$$\frac{100}{\frac{136}{390}}$$

Reduce the fraction \frac{136}{390} to lowest terms by extracting and canceling out 2.

$$\frac{100}{\frac{68}{195}}$$

Divide 100 by \frac{68}{195} by multiplying 100 by the reciprocal of \frac{68}{195}.

$$100\times \frac{195}{68}$$

Express 100\times \frac{195}{68} as a single fraction.

$$\frac{100\times 195}{68}$$

Multiply 100 and 195 to get 19500.

$$\frac{19500}{68}$$

Reduce the fraction \frac{19500}{68} to lowest terms by extracting and canceling out 4.

$$\frac{4875}{17}$$

Factor

$$\frac{3 \cdot 13 \cdot 5 ^ {3}}{17} = 286\frac{13}{17} = 286.7647058823529$$