Solve 0,32*3/40+3/5/0,2:2frac{1{2}-11/5}=

$$\frac { 0,32 \cdot \frac { 3 } { 40 } + \frac { 3 } { 5 } } { 0,2 : 2 \frac { 1 } { 2 } - 1 \frac { 1 } { 5 } } =$$

Evaluate

$$-\frac{39}{70}\approx -0,557142857$$

Solution Steps

Convert decimal number 0,32 to fraction \frac{32}{100}. Reduce the fraction \frac{32}{100} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{8}{25}\times \frac{3}{40}+\frac{3}{5}}{\frac{0,2}{\frac{2\times 2+1}{2}}-\frac{1\times 5+1}{5}}$$

Multiply \frac{8}{25} times \frac{3}{40} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{8\times 3}{25\times 40}+\frac{3}{5}}{\frac{0,2}{\frac{2\times 2+1}{2}}-\frac{1\times 5+1}{5}}$$

Do the multiplications in the fraction \frac{8\times 3}{25\times 40}.

$$\frac{\frac{24}{1000}+\frac{3}{5}}{\frac{0,2}{\frac{2\times 2+1}{2}}-\frac{1\times 5+1}{5}}$$

Reduce the fraction \frac{24}{1000} to lowest terms by extracting and canceling out 8.

$$\frac{\frac{3}{125}+\frac{3}{5}}{\frac{0,2}{\frac{2\times 2+1}{2}}-\frac{1\times 5+1}{5}}$$

Least common multiple of 125 and 5 is 125. Convert \frac{3}{125} and \frac{3}{5} to fractions with denominator 125.

$$\frac{\frac{3}{125}+\frac{75}{125}}{\frac{0,2}{\frac{2\times 2+1}{2}}-\frac{1\times 5+1}{5}}$$

Since \frac{3}{125} and \frac{75}{125} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3+75}{125}}{\frac{0,2}{\frac{2\times 2+1}{2}}-\frac{1\times 5+1}{5}}$$

Add 3 and 75 to get 78.

$$\frac{\frac{78}{125}}{\frac{0,2}{\frac{2\times 2+1}{2}}-\frac{1\times 5+1}{5}}$$

Divide 0,2 by \frac{2\times 2+1}{2} by multiplying 0,2 by the reciprocal of \frac{2\times 2+1}{2}.

$$\frac{\frac{78}{125}}{\frac{0,2\times 2}{2\times 2+1}-\frac{1\times 5+1}{5}}$$

Multiply 0,2 and 2 to get 0,4.

$$\frac{\frac{78}{125}}{\frac{0,4}{2\times 2+1}-\frac{1\times 5+1}{5}}$$

Multiply 2 and 2 to get 4.

$$\frac{\frac{78}{125}}{\frac{0,4}{4+1}-\frac{1\times 5+1}{5}}$$

Add 4 and 1 to get 5.

$$\frac{\frac{78}{125}}{\frac{0,4}{5}-\frac{1\times 5+1}{5}}$$

Expand \frac{0,4}{5} by multiplying both numerator and the denominator by 10.

$$\frac{\frac{78}{125}}{\frac{4}{50}-\frac{1\times 5+1}{5}}$$

Reduce the fraction \frac{4}{50} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{78}{125}}{\frac{2}{25}-\frac{1\times 5+1}{5}}$$

Multiply 1 and 5 to get 5.

$$\frac{\frac{78}{125}}{\frac{2}{25}-\frac{5+1}{5}}$$

Add 5 and 1 to get 6.

$$\frac{\frac{78}{125}}{\frac{2}{25}-\frac{6}{5}}$$

Least common multiple of 25 and 5 is 25. Convert \frac{2}{25} and \frac{6}{5} to fractions with denominator 25.

$$\frac{\frac{78}{125}}{\frac{2}{25}-\frac{30}{25}}$$

Since \frac{2}{25} and \frac{30}{25} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{78}{125}}{\frac{2-30}{25}}$$

Subtract 30 from 2 to get -28.

$$\frac{\frac{78}{125}}{-\frac{28}{25}}$$

Divide \frac{78}{125} by -\frac{28}{25} by multiplying \frac{78}{125} by the reciprocal of -\frac{28}{25}.

$$\frac{78}{125}\left(-\frac{25}{28}\right)$$

Multiply \frac{78}{125} times -\frac{25}{28} by multiplying numerator times numerator and denominator times denominator.

$$\frac{78\left(-25\right)}{125\times 28}$$

Do the multiplications in the fraction \frac{78\left(-25\right)}{125\times 28}.

$$\frac{-1950}{3500}$$

Reduce the fraction \frac{-1950}{3500} to lowest terms by extracting and canceling out 50.

$$-\frac{39}{70}$$

Factor

$$-\frac{39}{70} = -0.5571428571428572$$