Solve [(-71/9)-(-214/15)]div(22/3-(-13/5))

$$[ ( - 7 \frac { 1 } { 9 } ) - ( - 2 \frac { 14 } { 15 } ) ] \div ( 2 \frac { 2 } { 3 } - ( - 1 \frac { 3 } { 5 } ) )$$

Evaluate

$$-\frac{47}{48}\approx -0.979166667$$

Solution Steps

Multiply 7 and 9 to get 63.

$$\frac{-\frac{63+1}{9}-\left(-\frac{2\times 15+14}{15}\right)}{\frac{2\times 3+2}{3}-\left(-\frac{1\times 5+3}{5}\right)}$$

Add 63 and 1 to get 64.

$$\frac{-\frac{64}{9}-\left(-\frac{2\times 15+14}{15}\right)}{\frac{2\times 3+2}{3}-\left(-\frac{1\times 5+3}{5}\right)}$$

Multiply 2 and 15 to get 30.

$$\frac{-\frac{64}{9}-\left(-\frac{30+14}{15}\right)}{\frac{2\times 3+2}{3}-\left(-\frac{1\times 5+3}{5}\right)}$$

Add 30 and 14 to get 44.

$$\frac{-\frac{64}{9}-\left(-\frac{44}{15}\right)}{\frac{2\times 3+2}{3}-\left(-\frac{1\times 5+3}{5}\right)}$$

The opposite of -\frac{44}{15} is \frac{44}{15}.

$$\frac{-\frac{64}{9}+\frac{44}{15}}{\frac{2\times 3+2}{3}-\left(-\frac{1\times 5+3}{5}\right)}$$

Least common multiple of 9 and 15 is 45. Convert -\frac{64}{9} and \frac{44}{15} to fractions with denominator 45.

$$\frac{-\frac{320}{45}+\frac{132}{45}}{\frac{2\times 3+2}{3}-\left(-\frac{1\times 5+3}{5}\right)}$$

Since -\frac{320}{45} and \frac{132}{45} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-320+132}{45}}{\frac{2\times 3+2}{3}-\left(-\frac{1\times 5+3}{5}\right)}$$

Add -320 and 132 to get -188.

$$\frac{-\frac{188}{45}}{\frac{2\times 3+2}{3}-\left(-\frac{1\times 5+3}{5}\right)}$$

Multiply 2 and 3 to get 6.

$$\frac{-\frac{188}{45}}{\frac{6+2}{3}-\left(-\frac{1\times 5+3}{5}\right)}$$

Add 6 and 2 to get 8.

$$\frac{-\frac{188}{45}}{\frac{8}{3}-\left(-\frac{1\times 5+3}{5}\right)}$$

Multiply 1 and 5 to get 5.

$$\frac{-\frac{188}{45}}{\frac{8}{3}-\left(-\frac{5+3}{5}\right)}$$

Add 5 and 3 to get 8.

$$\frac{-\frac{188}{45}}{\frac{8}{3}-\left(-\frac{8}{5}\right)}$$

The opposite of -\frac{8}{5} is \frac{8}{5}.

$$\frac{-\frac{188}{45}}{\frac{8}{3}+\frac{8}{5}}$$

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

$$\frac{-\frac{188}{45}}{\frac{40}{15}+\frac{24}{15}}$$

Since \frac{40}{15} and \frac{24}{15} have the same denominator, add them by adding their numerators.

$$\frac{-\frac{188}{45}}{\frac{40+24}{15}}$$

Add 40 and 24 to get 64.

$$\frac{-\frac{188}{45}}{\frac{64}{15}}$$

Divide -\frac{188}{45} by \frac{64}{15} by multiplying -\frac{188}{45} by the reciprocal of \frac{64}{15}.

$$-\frac{188}{45}\times \frac{15}{64}$$

Multiply -\frac{188}{45} times \frac{15}{64} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-188\times 15}{45\times 64}$$

Do the multiplications in the fraction \frac{-188\times 15}{45\times 64}.

$$\frac{-2820}{2880}$$

Reduce the fraction \frac{-2820}{2880} to lowest terms by extracting and canceling out 60.

$$-\frac{47}{48}$$

Factor

$$-\frac{47}{48} = -0.9791666666666666$$