Solve 23/5:(-119/20)+23/16

$$2 \frac { 3 } { 5 } : ( - 1 \frac { 19 } { 20 } ) + 2 \frac { 3 } { 16 }$$

Evaluate

$$\frac{41}{48}\approx 0.854166667$$

Solution Steps

Multiply 2 and 5 to get 10.

$$\frac{\frac{10+3}{5}}{-\frac{1\times 20+19}{20}}+\frac{2\times 16+3}{16}$$

Add 10 and 3 to get 13.

$$\frac{\frac{13}{5}}{-\frac{1\times 20+19}{20}}+\frac{2\times 16+3}{16}$$

Multiply 1 and 20 to get 20.

$$\frac{\frac{13}{5}}{-\frac{20+19}{20}}+\frac{2\times 16+3}{16}$$

Add 20 and 19 to get 39.

$$\frac{\frac{13}{5}}{-\frac{39}{20}}+\frac{2\times 16+3}{16}$$

Divide \frac{13}{5} by -\frac{39}{20} by multiplying \frac{13}{5} by the reciprocal of -\frac{39}{20}.

$$\frac{13}{5}\left(-\frac{20}{39}\right)+\frac{2\times 16+3}{16}$$

Multiply \frac{13}{5} times -\frac{20}{39} by multiplying numerator times numerator and denominator times denominator.

$$\frac{13\left(-20\right)}{5\times 39}+\frac{2\times 16+3}{16}$$

Do the multiplications in the fraction \frac{13\left(-20\right)}{5\times 39}.

$$\frac{-260}{195}+\frac{2\times 16+3}{16}$$

Reduce the fraction \frac{-260}{195} to lowest terms by extracting and canceling out 65.

$$-\frac{4}{3}+\frac{2\times 16+3}{16}$$

Multiply 2 and 16 to get 32.

$$-\frac{4}{3}+\frac{32+3}{16}$$

Add 32 and 3 to get 35.

$$-\frac{4}{3}+\frac{35}{16}$$

Least common multiple of 3 and 16 is 48. Convert -\frac{4}{3} and \frac{35}{16} to fractions with denominator 48.

$$-\frac{64}{48}+\frac{105}{48}$$

Since -\frac{64}{48} and \frac{105}{48} have the same denominator, add them by adding their numerators.

$$\frac{-64+105}{48}$$

Add -64 and 105 to get 41.

$$\frac{41}{48}$$

Factor

$$\frac{41}{2 ^ {4} \cdot 3} = 0.8541666666666666$$