Solve 1.9191+1/3(1.9638)-2.1038-1/5(2.3909)

$$1.9191 + \frac { 1 } { 3 } ( 1.9638 ) - 2.1038 - \frac { 1 } { 5 } ( 2.3909 )$$

Evaluate

$$-0.00828$$

Solution Steps

Convert decimal number 1.9638 to fraction \frac{19638}{10000}. Reduce the fraction \frac{19638}{10000} to lowest terms by extracting and canceling out 2.

$$1.9191+\frac{1}{3}\times \frac{9819}{5000}-2.1038-\frac{1}{5}\times 2.3909$$

Multiply \frac{1}{3} times \frac{9819}{5000} by multiplying numerator times numerator and denominator times denominator.

$$1.9191+\frac{1\times 9819}{3\times 5000}-2.1038-\frac{1}{5}\times 2.3909$$

Do the multiplications in the fraction \frac{1\times 9819}{3\times 5000}.

$$1.9191+\frac{9819}{15000}-2.1038-\frac{1}{5}\times 2.3909$$

Reduce the fraction \frac{9819}{15000} to lowest terms by extracting and canceling out 3.

$$1.9191+\frac{3273}{5000}-2.1038-\frac{1}{5}\times 2.3909$$

Convert decimal number 1.9191 to fraction \frac{19191}{10000}.

$$\frac{19191}{10000}+\frac{3273}{5000}-2.1038-\frac{1}{5}\times 2.3909$$

Least common multiple of 10000 and 5000 is 10000. Convert \frac{19191}{10000} and \frac{3273}{5000} to fractions with denominator 10000.

$$\frac{19191}{10000}+\frac{6546}{10000}-2.1038-\frac{1}{5}\times 2.3909$$

Since \frac{19191}{10000} and \frac{6546}{10000} have the same denominator, add them by adding their numerators.

$$\frac{19191+6546}{10000}-2.1038-\frac{1}{5}\times 2.3909$$

Add 19191 and 6546 to get 25737.

$$\frac{25737}{10000}-2.1038-\frac{1}{5}\times 2.3909$$

Convert decimal number 2.1038 to fraction \frac{21038}{10000}. Reduce the fraction \frac{21038}{10000} to lowest terms by extracting and canceling out 2.

$$\frac{25737}{10000}-\frac{10519}{5000}-\frac{1}{5}\times 2.3909$$

Least common multiple of 10000 and 5000 is 10000. Convert \frac{25737}{10000} and \frac{10519}{5000} to fractions with denominator 10000.

$$\frac{25737}{10000}-\frac{21038}{10000}-\frac{1}{5}\times 2.3909$$

Since \frac{25737}{10000} and \frac{21038}{10000} have the same denominator, subtract them by subtracting their numerators.

$$\frac{25737-21038}{10000}-\frac{1}{5}\times 2.3909$$

Subtract 21038 from 25737 to get 4699.

$$\frac{4699}{10000}-\frac{1}{5}\times 2.3909$$

Convert decimal number 2.3909 to fraction \frac{23909}{10000}.

$$\frac{4699}{10000}-\frac{1}{5}\times \frac{23909}{10000}$$

Multiply \frac{1}{5} times \frac{23909}{10000} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4699}{10000}-\frac{1\times 23909}{5\times 10000}$$

Do the multiplications in the fraction \frac{1\times 23909}{5\times 10000}.

$$\frac{4699}{10000}-\frac{23909}{50000}$$

Least common multiple of 10000 and 50000 is 50000. Convert \frac{4699}{10000} and \frac{23909}{50000} to fractions with denominator 50000.

$$\frac{23495}{50000}-\frac{23909}{50000}$$

Since \frac{23495}{50000} and \frac{23909}{50000} have the same denominator, subtract them by subtracting their numerators.

$$\frac{23495-23909}{50000}$$

Subtract 23909 from 23495 to get -414.

$$\frac{-414}{50000}$$

Reduce the fraction \frac{-414}{50000} to lowest terms by extracting and canceling out 2.

$$-\frac{207}{25000}$$

Factor

$$-0.00828$$