Solve 44/8314(0.4*10^6*3/70+273.15-(0.1*10^6+30*10^3)*3/45+273.15)

$$\frac { 44 } { 8314 } ( \frac { 0.4 \times 10 ^ { 6 } \times 3 } { 70 + 273.15 } - \frac { ( 0.1 \times 10 ^ { 6 } + 30 \times 10 ^ { 3 } ) \times 3 } { 45 + 273.15 } )$$

Evaluate

$$\frac{727324400000}{60511050411}\approx 12.019695495$$

Solution Steps

Reduce the fraction \frac{44}{8314} to lowest terms by extracting and canceling out 2.

$$\frac{22}{4157}\left(\frac{0.4\times 10^{6}\times 3}{70+273.15}-\frac{\left(0.1\times 10^{6}+30\times 10^{3}\right)\times 3}{45+273.15}\right)$$

Calculate 10 to the power of 6 and get 1000000.

$$\frac{22}{4157}\left(\frac{0.4\times 1000000\times 3}{70+273.15}-\frac{\left(0.1\times 10^{6}+30\times 10^{3}\right)\times 3}{45+273.15}\right)$$

Multiply 0.4 and 1000000 to get 400000.

$$\frac{22}{4157}\left(\frac{400000\times 3}{70+273.15}-\frac{\left(0.1\times 10^{6}+30\times 10^{3}\right)\times 3}{45+273.15}\right)$$

Multiply 400000 and 3 to get 1200000.

$$\frac{22}{4157}\left(\frac{1200000}{70+273.15}-\frac{\left(0.1\times 10^{6}+30\times 10^{3}\right)\times 3}{45+273.15}\right)$$

Add 70 and 273.15 to get 343.15.

$$\frac{22}{4157}\left(\frac{1200000}{343.15}-\frac{\left(0.1\times 10^{6}+30\times 10^{3}\right)\times 3}{45+273.15}\right)$$

Expand \frac{1200000}{343.15} by multiplying both numerator and the denominator by 100.

$$\frac{22}{4157}\left(\frac{120000000}{34315}-\frac{\left(0.1\times 10^{6}+30\times 10^{3}\right)\times 3}{45+273.15}\right)$$

Reduce the fraction \frac{120000000}{34315} to lowest terms by extracting and canceling out 5.

$$\frac{22}{4157}\left(\frac{24000000}{6863}-\frac{\left(0.1\times 10^{6}+30\times 10^{3}\right)\times 3}{45+273.15}\right)$$

Calculate 10 to the power of 6 and get 1000000.

$$\frac{22}{4157}\left(\frac{24000000}{6863}-\frac{\left(0.1\times 1000000+30\times 10^{3}\right)\times 3}{45+273.15}\right)$$

Multiply 0.1 and 1000000 to get 100000.

$$\frac{22}{4157}\left(\frac{24000000}{6863}-\frac{\left(100000+30\times 10^{3}\right)\times 3}{45+273.15}\right)$$

Calculate 10 to the power of 3 and get 1000.

$$\frac{22}{4157}\left(\frac{24000000}{6863}-\frac{\left(100000+30\times 1000\right)\times 3}{45+273.15}\right)$$

Multiply 30 and 1000 to get 30000.

$$\frac{22}{4157}\left(\frac{24000000}{6863}-\frac{\left(100000+30000\right)\times 3}{45+273.15}\right)$$

Add 100000 and 30000 to get 130000.

$$\frac{22}{4157}\left(\frac{24000000}{6863}-\frac{130000\times 3}{45+273.15}\right)$$

Multiply 130000 and 3 to get 390000.

$$\frac{22}{4157}\left(\frac{24000000}{6863}-\frac{390000}{45+273.15}\right)$$

Add 45 and 273.15 to get 318.15.

$$\frac{22}{4157}\left(\frac{24000000}{6863}-\frac{390000}{318.15}\right)$$

Expand \frac{390000}{318.15} by multiplying both numerator and the denominator by 100.

$$\frac{22}{4157}\left(\frac{24000000}{6863}-\frac{39000000}{31815}\right)$$

Reduce the fraction \frac{39000000}{31815} to lowest terms by extracting and canceling out 15.

$$\frac{22}{4157}\left(\frac{24000000}{6863}-\frac{2600000}{2121}\right)$$

Least common multiple of 6863 and 2121 is 14556423. Convert \frac{24000000}{6863} and \frac{2600000}{2121} to fractions with denominator 14556423.

$$\frac{22}{4157}\left(\frac{50904000000}{14556423}-\frac{17843800000}{14556423}\right)$$

Since \frac{50904000000}{14556423} and \frac{17843800000}{14556423} have the same denominator, subtract them by subtracting their numerators.

$$\frac{22}{4157}\times \frac{50904000000-17843800000}{14556423}$$

Subtract 17843800000 from 50904000000 to get 33060200000.

$$\frac{22}{4157}\times \frac{33060200000}{14556423}$$

Multiply \frac{22}{4157} times \frac{33060200000}{14556423} by multiplying numerator times numerator and denominator times denominator.

$$\frac{22\times 33060200000}{4157\times 14556423}$$

Do the multiplications in the fraction \frac{22\times 33060200000}{4157\times 14556423}.

$$\frac{727324400000}{60511050411}$$

Factor

$$\frac{11 \cdot 23 \cdot 7187 \cdot 2 ^ {7} \cdot 5 ^ {5}}{3 \cdot 7 \cdot 101 \cdot 4157 \cdot 6863} = 12\frac{1191795068}{60511050411} = 12.019695494622969$$