Solve -61/2/5frac{1{5}}+21/4/-1frac{1{5}}

$$- \frac{ 6 \frac{ 1 }{ 2 } }{ 5 \frac{ 1 }{ 5 } } + \frac{ 2 \frac{ 1 }{ 4 } }{ -1 \frac{ 1 }{ 5 } }$$

Evaluate

$$-\frac{25}{8}=-3.125$$

Solution Steps

Divide \frac{6\times 2+1}{2} by \frac{5\times 5+1}{5} by multiplying \frac{6\times 2+1}{2} by the reciprocal of \frac{5\times 5+1}{5}.

$$-\frac{\left(6\times 2+1\right)\times 5}{2\left(5\times 5+1\right)}+\frac{\frac{2\times 4+1}{4}}{-\frac{1\times 5+1}{5}}$$

Multiply 6 and 2 to get 12.

$$-\frac{\left(12+1\right)\times 5}{2\left(5\times 5+1\right)}+\frac{\frac{2\times 4+1}{4}}{-\frac{1\times 5+1}{5}}$$

Add 12 and 1 to get 13.

$$-\frac{13\times 5}{2\left(5\times 5+1\right)}+\frac{\frac{2\times 4+1}{4}}{-\frac{1\times 5+1}{5}}$$

Multiply 13 and 5 to get 65.

$$-\frac{65}{2\left(5\times 5+1\right)}+\frac{\frac{2\times 4+1}{4}}{-\frac{1\times 5+1}{5}}$$

Multiply 5 and 5 to get 25.

$$-\frac{65}{2\left(25+1\right)}+\frac{\frac{2\times 4+1}{4}}{-\frac{1\times 5+1}{5}}$$

Add 25 and 1 to get 26.

$$-\frac{65}{2\times 26}+\frac{\frac{2\times 4+1}{4}}{-\frac{1\times 5+1}{5}}$$

Multiply 2 and 26 to get 52.

$$-\frac{65}{52}+\frac{\frac{2\times 4+1}{4}}{-\frac{1\times 5+1}{5}}$$

Reduce the fraction \frac{65}{52} to lowest terms by extracting and canceling out 13.

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

Multiply 2 and 4 to get 8.

$$-\frac{5}{4}+\frac{\frac{8+1}{4}}{-\frac{1\times 5+1}{5}}$$

Add 8 and 1 to get 9.

$$-\frac{5}{4}+\frac{\frac{9}{4}}{-\frac{1\times 5+1}{5}}$$

Multiply 1 and 5 to get 5.

$$-\frac{5}{4}+\frac{\frac{9}{4}}{-\frac{5+1}{5}}$$

Add 5 and 1 to get 6.

$$-\frac{5}{4}+\frac{\frac{9}{4}}{-\frac{6}{5}}$$

Divide \frac{9}{4} by -\frac{6}{5} by multiplying \frac{9}{4} by the reciprocal of -\frac{6}{5}.

$$-\frac{5}{4}+\frac{9}{4}\left(-\frac{5}{6}\right)$$

Multiply \frac{9}{4} times -\frac{5}{6} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{5}{4}+\frac{9\left(-5\right)}{4\times 6}$$

Do the multiplications in the fraction \frac{9\left(-5\right)}{4\times 6}.

$$-\frac{5}{4}+\frac{-45}{24}$$

Reduce the fraction \frac{-45}{24} to lowest terms by extracting and canceling out 3.

$$-\frac{5}{4}-\frac{15}{8}$$

Least common multiple of 4 and 8 is 8. Convert -\frac{5}{4} and \frac{15}{8} to fractions with denominator 8.

$$-\frac{10}{8}-\frac{15}{8}$$

Since -\frac{10}{8} and \frac{15}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-10-15}{8}$$

Subtract 15 from -10 to get -25.

$$-\frac{25}{8}$$

Factor

$$-\frac{25}{8} = -3\frac{1}{8} = -3.125$$