Solve 112000/8.314*(1/1600-1/2273)

$$\frac { 112000 } { 8.314 } \times ( \frac { 1 } { 1600 } - \frac { 1 } { 2273 } )$$

Evaluate

$$\frac{23555000}{9448861}\approx 2.492893059$$

Solution Steps

Expand \frac{112000}{8.314} by multiplying both numerator and the denominator by 1000.

$$\frac{112000000}{8314}\left(\frac{1}{1600}-\frac{1}{2273}\right)$$

Reduce the fraction \frac{112000000}{8314} to lowest terms by extracting and canceling out 2.

$$\frac{56000000}{4157}\left(\frac{1}{1600}-\frac{1}{2273}\right)$$

Least common multiple of 1600 and 2273 is 3636800. Convert \frac{1}{1600} and \frac{1}{2273} to fractions with denominator 3636800.

$$\frac{56000000}{4157}\left(\frac{2273}{3636800}-\frac{1600}{3636800}\right)$$

Since \frac{2273}{3636800} and \frac{1600}{3636800} have the same denominator, subtract them by subtracting their numerators.

$$\frac{56000000}{4157}\times \frac{2273-1600}{3636800}$$

Subtract 1600 from 2273 to get 673.

$$\frac{56000000}{4157}\times \frac{673}{3636800}$$

Multiply \frac{56000000}{4157} times \frac{673}{3636800} by multiplying numerator times numerator and denominator times denominator.

$$\frac{56000000\times 673}{4157\times 3636800}$$

Do the multiplications in the fraction \frac{56000000\times 673}{4157\times 3636800}.

$$\frac{37688000000}{15118177600}$$

Reduce the fraction \frac{37688000000}{15118177600} to lowest terms by extracting and canceling out 1600.

$$\frac{23555000}{9448861}$$

Factor

$$\frac{7 \cdot 673 \cdot 2 ^ {3} \cdot 5 ^ {4}}{2273 \cdot 4157} = 2\frac{4657278}{9448861} = 2.492893058750679$$