Solve 64/5-34/5div(2/3+3/5)

$$6 \frac { 4 } { 5 } - 3 \frac { 4 } { 5 } \div ( \frac { 2 } { 3 } + \frac { 3 } { 5 } )$$

Evaluate

$$\frac{19}{5}=3.8$$

Solution Steps

Multiply 6 and 5 to get 30.

$$\frac{30+4}{5}-\frac{\frac{3\times 5+4}{5}}{\frac{2}{3}+\frac{3}{5}}$$

Add 30 and 4 to get 34.

$$\frac{34}{5}-\frac{\frac{3\times 5+4}{5}}{\frac{2}{3}+\frac{3}{5}}$$

Multiply 3 and 5 to get 15.

$$\frac{34}{5}-\frac{\frac{15+4}{5}}{\frac{2}{3}+\frac{3}{5}}$$

Add 15 and 4 to get 19.

$$\frac{34}{5}-\frac{\frac{19}{5}}{\frac{2}{3}+\frac{3}{5}}$$

Least common multiple of 3 and 5 is 15. Convert \frac{2}{3} and \frac{3}{5} to fractions with denominator 15.

$$\frac{34}{5}-\frac{\frac{19}{5}}{\frac{10}{15}+\frac{9}{15}}$$

Since \frac{10}{15} and \frac{9}{15} have the same denominator, add them by adding their numerators.

$$\frac{34}{5}-\frac{\frac{19}{5}}{\frac{10+9}{15}}$$

Add 10 and 9 to get 19.

$$\frac{34}{5}-\frac{\frac{19}{5}}{\frac{19}{15}}$$

Divide \frac{19}{5} by \frac{19}{15} by multiplying \frac{19}{5} by the reciprocal of \frac{19}{15}.

$$\frac{34}{5}-\frac{19}{5}\times \frac{15}{19}$$

Multiply \frac{19}{5} times \frac{15}{19} by multiplying numerator times numerator and denominator times denominator.

$$\frac{34}{5}-\frac{19\times 15}{5\times 19}$$

Cancel out 19 in both numerator and denominator.

$$\frac{34}{5}-\frac{15}{5}$$

Since \frac{34}{5} and \frac{15}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{34-15}{5}$$

Subtract 15 from 34 to get 19.

$$\frac{19}{5}$$

Factor

$$\frac{19}{5} = 3\frac{4}{5} = 3.8$$