Solve (-1-3/7):0,2*7/9-(-5/3)*0,125

$$( - 1 - \frac { 3 } { 7 } ) : 0,2 \cdot \frac { 7 } { 9 } - ( - \frac { 5 } { 3 } ) \cdot 0,125$$

Evaluate

$$-\frac{385}{72}\approx -5,347222222$$

Solution Steps

Convert -1 to fraction -\frac{7}{7}.

$$\frac{-\frac{7}{7}-\frac{3}{7}}{0,2}\times \frac{7}{9}-\left(-\frac{5}{3}\times 0,125\right)$$

Since -\frac{7}{7} and \frac{3}{7} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{-7-3}{7}}{0,2}\times \frac{7}{9}-\left(-\frac{5}{3}\times 0,125\right)$$

Subtract 3 from -7 to get -10.

$$\frac{-\frac{10}{7}}{0,2}\times \frac{7}{9}-\left(-\frac{5}{3}\times 0,125\right)$$

Express \frac{-\frac{10}{7}}{0,2} as a single fraction.

$$\frac{-10}{7\times 0,2}\times \frac{7}{9}-\left(-\frac{5}{3}\times 0,125\right)$$

Multiply 7 and 0,2 to get 1,4.

$$\frac{-10}{1,4}\times \frac{7}{9}-\left(-\frac{5}{3}\times 0,125\right)$$

Expand \frac{-10}{1,4} by multiplying both numerator and the denominator by 10.

$$\frac{-100}{14}\times \frac{7}{9}-\left(-\frac{5}{3}\times 0,125\right)$$

Reduce the fraction \frac{-100}{14} to lowest terms by extracting and canceling out 2.

$$-\frac{50}{7}\times \frac{7}{9}-\left(-\frac{5}{3}\times 0,125\right)$$

Multiply -\frac{50}{7} times \frac{7}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-50\times 7}{7\times 9}-\left(-\frac{5}{3}\times 0,125\right)$$

Cancel out 7 in both numerator and denominator.

$$\frac{-50}{9}-\left(-\frac{5}{3}\times 0,125\right)$$

Fraction \frac{-50}{9} can be rewritten as -\frac{50}{9} by extracting the negative sign.

$$-\frac{50}{9}-\left(-\frac{5}{3}\times 0,125\right)$$

Convert decimal number 0,125 to fraction \frac{125}{1000}. Reduce the fraction \frac{125}{1000} to lowest terms by extracting and canceling out 125.

$$-\frac{50}{9}-\left(-\frac{5}{3}\times \frac{1}{8}\right)$$

Multiply -\frac{5}{3} times \frac{1}{8} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{50}{9}-\frac{-5}{3\times 8}$$

Do the multiplications in the fraction \frac{-5}{3\times 8}.

$$-\frac{50}{9}-\frac{-5}{24}$$

Fraction \frac{-5}{24} can be rewritten as -\frac{5}{24} by extracting the negative sign.

$$-\frac{50}{9}-\left(-\frac{5}{24}\right)$$

The opposite of -\frac{5}{24} is \frac{5}{24}.

$$-\frac{50}{9}+\frac{5}{24}$$

Least common multiple of 9 and 24 is 72. Convert -\frac{50}{9} and \frac{5}{24} to fractions with denominator 72.

$$-\frac{400}{72}+\frac{15}{72}$$

Since -\frac{400}{72} and \frac{15}{72} have the same denominator, add them by adding their numerators.

$$\frac{-400+15}{72}$$

Add -400 and 15 to get -385.

$$-\frac{385}{72}$$

Factor

$$-\frac{385}{72} = -5\frac{25}{72} = -5.347222222222222$$