Solve (-34/5+22/3)div(12/3*7/15)

$$( - 3 \frac { 4 } { 5 } + 2 \frac { 2 } { 3 } ) \div ( 1 \frac { 2 } { 3 } \times \frac { 7 } { 15 } )$$

Evaluate

$$-\frac{51}{35}\approx -1.457142857$$

Solution Steps

Multiply 3 and 5 to get 15.

$$\frac{-\frac{15+4}{5}+\frac{2\times 3+2}{3}}{\frac{1\times 3+2}{3}\times \frac{7}{15}}$$

Add 15 and 4 to get 19.

$$\frac{-\frac{19}{5}+\frac{2\times 3+2}{3}}{\frac{1\times 3+2}{3}\times \frac{7}{15}}$$

Multiply 2 and 3 to get 6.

$$\frac{-\frac{19}{5}+\frac{6+2}{3}}{\frac{1\times 3+2}{3}\times \frac{7}{15}}$$

Add 6 and 2 to get 8.

$$\frac{-\frac{19}{5}+\frac{8}{3}}{\frac{1\times 3+2}{3}\times \frac{7}{15}}$$

Least common multiple of 5 and 3 is 15. Convert -\frac{19}{5} and \frac{8}{3} to fractions with denominator 15.

$$\frac{-\frac{57}{15}+\frac{40}{15}}{\frac{1\times 3+2}{3}\times \frac{7}{15}}$$

Since -\frac{57}{15} and \frac{40}{15} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-57+40}{15}}{\frac{1\times 3+2}{3}\times \frac{7}{15}}$$

Add -57 and 40 to get -17.

$$\frac{-\frac{17}{15}}{\frac{1\times 3+2}{3}\times \frac{7}{15}}$$

Multiply 1 and 3 to get 3.

$$\frac{-\frac{17}{15}}{\frac{3+2}{3}\times \frac{7}{15}}$$

Add 3 and 2 to get 5.

$$\frac{-\frac{17}{15}}{\frac{5}{3}\times \frac{7}{15}}$$

Multiply \frac{5}{3} times \frac{7}{15} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\frac{17}{15}}{\frac{5\times 7}{3\times 15}}$$

Do the multiplications in the fraction \frac{5\times 7}{3\times 15}.

$$\frac{-\frac{17}{15}}{\frac{35}{45}}$$

Reduce the fraction \frac{35}{45} to lowest terms by extracting and canceling out 5.

$$\frac{-\frac{17}{15}}{\frac{7}{9}}$$

Divide -\frac{17}{15} by \frac{7}{9} by multiplying -\frac{17}{15} by the reciprocal of \frac{7}{9}.

$$-\frac{17}{15}\times \frac{9}{7}$$

Multiply -\frac{17}{15} times \frac{9}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-17\times 9}{15\times 7}$$

Do the multiplications in the fraction \frac{-17\times 9}{15\times 7}.

$$\frac{-153}{105}$$

Reduce the fraction \frac{-153}{105} to lowest terms by extracting and canceling out 3.

$$-\frac{51}{35}$$

Factor

$$-\frac{51}{35} = -1\frac{16}{35} = -1.457142857142857$$