Solve 34/5div(3-2.4*14/5)-31/3

$$3 \frac { 4 } { 5 } \div ( 3 - 2.4 \times \frac { 14 } { 5 } ) - 3 \frac { 1 } { 3 }$$

Evaluate

$$-\frac{135}{31}\approx -4.35483871$$

Solution Steps

Multiply 3 and 5 to get 15.

$$\frac{\frac{15+4}{5}}{3-2.4\times \frac{14}{5}}-\frac{3\times 3+1}{3}$$

Add 15 and 4 to get 19.

$$\frac{\frac{19}{5}}{3-2.4\times \frac{14}{5}}-\frac{3\times 3+1}{3}$$

Convert decimal number 2.4 to fraction \frac{24}{10}. Reduce the fraction \frac{24}{10} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{19}{5}}{3-\frac{12}{5}\times \frac{14}{5}}-\frac{3\times 3+1}{3}$$

Multiply \frac{12}{5} times \frac{14}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{19}{5}}{3-\frac{12\times 14}{5\times 5}}-\frac{3\times 3+1}{3}$$

Do the multiplications in the fraction \frac{12\times 14}{5\times 5}.

$$\frac{\frac{19}{5}}{3-\frac{168}{25}}-\frac{3\times 3+1}{3}$$

Convert 3 to fraction \frac{75}{25}.

$$\frac{\frac{19}{5}}{\frac{75}{25}-\frac{168}{25}}-\frac{3\times 3+1}{3}$$

Since \frac{75}{25} and \frac{168}{25} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{19}{5}}{\frac{75-168}{25}}-\frac{3\times 3+1}{3}$$

Subtract 168 from 75 to get -93.

$$\frac{\frac{19}{5}}{-\frac{93}{25}}-\frac{3\times 3+1}{3}$$

Divide \frac{19}{5} by -\frac{93}{25} by multiplying \frac{19}{5} by the reciprocal of -\frac{93}{25}.

$$\frac{19}{5}\left(-\frac{25}{93}\right)-\frac{3\times 3+1}{3}$$

Multiply \frac{19}{5} times -\frac{25}{93} by multiplying numerator times numerator and denominator times denominator.

$$\frac{19\left(-25\right)}{5\times 93}-\frac{3\times 3+1}{3}$$

Do the multiplications in the fraction \frac{19\left(-25\right)}{5\times 93}.

$$\frac{-475}{465}-\frac{3\times 3+1}{3}$$

Reduce the fraction \frac{-475}{465} to lowest terms by extracting and canceling out 5.

$$-\frac{95}{93}-\frac{3\times 3+1}{3}$$

Multiply 3 and 3 to get 9.

$$-\frac{95}{93}-\frac{9+1}{3}$$

Add 9 and 1 to get 10.

$$-\frac{95}{93}-\frac{10}{3}$$

Least common multiple of 93 and 3 is 93. Convert -\frac{95}{93} and \frac{10}{3} to fractions with denominator 93.

$$-\frac{95}{93}-\frac{310}{93}$$

Since -\frac{95}{93} and \frac{310}{93} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-95-310}{93}$$

Subtract 310 from -95 to get -405.

$$\frac{-405}{93}$$

Reduce the fraction \frac{-405}{93} to lowest terms by extracting and canceling out 3.

$$-\frac{135}{31}$$

Factor

$$-\frac{135}{31} = -4\frac{11}{31} = -4.354838709677419$$