Solve 34/5div(3-2.4*14/15)-31/3

$$3 \frac { 4 } { 5 } \div ( 3 - 2.4 \times \frac { 14 } { 15 } ) - 3 \frac { 1 } { 3 }$$

Evaluate

$$\frac{5}{3}\approx 1.666666667$$

Solution Steps

Multiply 3 and 5 to get 15.

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

Add 15 and 4 to get 19.

$$\frac{\frac{19}{5}}{3-2.4\times \frac{14}{15}}-\frac{3\times 3+1}{3}$$

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.

$$\frac{\frac{19}{5}}{3-\frac{12}{5}\times \frac{14}{15}}-\frac{3\times 3+1}{3}$$

Multiply \frac{12}{5} times \frac{14}{15} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{19}{5}}{3-\frac{12\times 14}{5\times 15}}-\frac{3\times 3+1}{3}$$

Do the multiplications in the fraction \frac{12\times 14}{5\times 15}.

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

Reduce the fraction \frac{168}{75} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{19}{5}}{3-\frac{56}{25}}-\frac{3\times 3+1}{3}$$

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

$$\frac{\frac{19}{5}}{\frac{75}{25}-\frac{56}{25}}-\frac{3\times 3+1}{3}$$

Since \frac{75}{25} and \frac{56}{25} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{19}{5}}{\frac{75-56}{25}}-\frac{3\times 3+1}{3}$$

Subtract 56 from 75 to get 19.

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

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

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

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

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

Cancel out 19 in both numerator and denominator.

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

Divide 25 by 5 to get 5.

$$5-\frac{3\times 3+1}{3}$$

Multiply 3 and 3 to get 9.

$$5-\frac{9+1}{3}$$

Add 9 and 1 to get 10.

$$5-\frac{10}{3}$$

Convert 5 to fraction \frac{15}{3}.

$$\frac{15}{3}-\frac{10}{3}$$

Since \frac{15}{3} and \frac{10}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{15-10}{3}$$

Subtract 10 from 15 to get 5.

$$\frac{5}{3}$$

Factor

$$\frac{5}{3} = 1\frac{2}{3} = 1.6666666666666667$$