Solve 0.94-3/7(.863)-4/7(.985)

$$0.94 - \frac { 3 } { 7 } ( .863 ) - \frac { 4 } { 7 } ( .985 )$$

Evaluate

$$\frac{51}{7000}\approx 0.007285714$$

Solution Steps

Convert decimal number 0.863 to fraction \frac{863}{1000}.

$$0.94-\frac{3}{7}\times \frac{863}{1000}-\frac{4}{7}\times 0.985$$

Multiply \frac{3}{7} times \frac{863}{1000} by multiplying numerator times numerator and denominator times denominator.

$$0.94-\frac{3\times 863}{7\times 1000}-\frac{4}{7}\times 0.985$$

Do the multiplications in the fraction \frac{3\times 863}{7\times 1000}.

$$0.94-\frac{2589}{7000}-\frac{4}{7}\times 0.985$$

Convert decimal number 0.94 to fraction \frac{94}{100}. Reduce the fraction \frac{94}{100} to lowest terms by extracting and canceling out 2.

$$\frac{47}{50}-\frac{2589}{7000}-\frac{4}{7}\times 0.985$$

Least common multiple of 50 and 7000 is 7000. Convert \frac{47}{50} and \frac{2589}{7000} to fractions with denominator 7000.

$$\frac{6580}{7000}-\frac{2589}{7000}-\frac{4}{7}\times 0.985$$

Since \frac{6580}{7000} and \frac{2589}{7000} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6580-2589}{7000}-\frac{4}{7}\times 0.985$$

Subtract 2589 from 6580 to get 3991.

$$\frac{3991}{7000}-\frac{4}{7}\times 0.985$$

Convert decimal number 0.985 to fraction \frac{985}{1000}. Reduce the fraction \frac{985}{1000} to lowest terms by extracting and canceling out 5.

$$\frac{3991}{7000}-\frac{4}{7}\times \frac{197}{200}$$

Multiply \frac{4}{7} times \frac{197}{200} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3991}{7000}-\frac{4\times 197}{7\times 200}$$

Do the multiplications in the fraction \frac{4\times 197}{7\times 200}.

$$\frac{3991}{7000}-\frac{788}{1400}$$

Reduce the fraction \frac{788}{1400} to lowest terms by extracting and canceling out 4.

$$\frac{3991}{7000}-\frac{197}{350}$$

Least common multiple of 7000 and 350 is 7000. Convert \frac{3991}{7000} and \frac{197}{350} to fractions with denominator 7000.

$$\frac{3991}{7000}-\frac{3940}{7000}$$

Since \frac{3991}{7000} and \frac{3940}{7000} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3991-3940}{7000}$$

Subtract 3940 from 3991 to get 51.

$$\frac{51}{7000}$$

Factor

$$\frac{3 \cdot 17}{7 \cdot 2 ^ {3} \cdot 5 ^ {3}} = 0.007285714285714286$$