Solve -23/5/frac{3{7}+4/10}

$$- \frac { 2 \frac { 3 } { 5 } } { \frac { 3 } { 7 } + \frac { 4 } { 10 } }$$

Evaluate

$$-\frac{91}{29}\approx -3.137931034$$

Solution Steps

Multiply 2 and 5 to get 10.

$$-\frac{\frac{10+3}{5}}{\frac{3}{7}+\frac{4}{10}}$$

Add 10 and 3 to get 13.

$$-\frac{\frac{13}{5}}{\frac{3}{7}+\frac{4}{10}}$$

Reduce the fraction \frac{4}{10} to lowest terms by extracting and canceling out 2.

$$-\frac{\frac{13}{5}}{\frac{3}{7}+\frac{2}{5}}$$

Least common multiple of 7 and 5 is 35. Convert \frac{3}{7} and \frac{2}{5} to fractions with denominator 35.

$$-\frac{\frac{13}{5}}{\frac{15}{35}+\frac{14}{35}}$$

Since \frac{15}{35} and \frac{14}{35} have the same denominator, add them by adding their numerators.

$$-\frac{\frac{13}{5}}{\frac{15+14}{35}}$$

Add 15 and 14 to get 29.

$$-\frac{\frac{13}{5}}{\frac{29}{35}}$$

Divide \frac{13}{5} by \frac{29}{35} by multiplying \frac{13}{5} by the reciprocal of \frac{29}{35}.

$$-\frac{13}{5}\times \frac{35}{29}$$

Multiply \frac{13}{5} times \frac{35}{29} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{13\times 35}{5\times 29}$$

Do the multiplications in the fraction \frac{13\times 35}{5\times 29}.

$$-\frac{455}{145}$$

Reduce the fraction \frac{455}{145} to lowest terms by extracting and canceling out 5.

$$-\frac{91}{29}$$

Factor

$$-\frac{91}{29} = -3\frac{4}{29} = -3.1379310344827585$$