Solve 0,25*(4,75-3/20)*3,2/0,23:frac{5{8}*0,5}

$$\frac { 0,25 \cdot ( 4,75 - \frac { 3 } { 20 } ) \cdot 3,2 } { 0,23 : \frac { 5 } { 8 } \cdot 0,5 }$$

Evaluate

$$20$$

Solution Steps

Convert decimal number 4,75 to fraction \frac{475}{100}. Reduce the fraction \frac{475}{100} to lowest terms by extracting and canceling out 25.

$$\frac{0,25\left(\frac{19}{4}-\frac{3}{20}\right)\times 3,2}{\frac{0,23}{\frac{5}{8}}\times 0,5}$$

Least common multiple of 4 and 20 is 20. Convert \frac{19}{4} and \frac{3}{20} to fractions with denominator 20.

$$\frac{0,25\left(\frac{95}{20}-\frac{3}{20}\right)\times 3,2}{\frac{0,23}{\frac{5}{8}}\times 0,5}$$

Since \frac{95}{20} and \frac{3}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{0,25\times \frac{95-3}{20}\times 3,2}{\frac{0,23}{\frac{5}{8}}\times 0,5}$$

Subtract 3 from 95 to get 92.

$$\frac{0,25\times \frac{92}{20}\times 3,2}{\frac{0,23}{\frac{5}{8}}\times 0,5}$$

Reduce the fraction \frac{92}{20} to lowest terms by extracting and canceling out 4.

$$\frac{0,25\times \frac{23}{5}\times 3,2}{\frac{0,23}{\frac{5}{8}}\times 0,5}$$

Convert decimal number 0,25 to fraction \frac{25}{100}. Reduce the fraction \frac{25}{100} to lowest terms by extracting and canceling out 25.

$$\frac{\frac{1}{4}\times \frac{23}{5}\times 3,2}{\frac{0,23}{\frac{5}{8}}\times 0,5}$$

Multiply \frac{1}{4} times \frac{23}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{1\times 23}{4\times 5}\times 3,2}{\frac{0,23}{\frac{5}{8}}\times 0,5}$$

Do the multiplications in the fraction \frac{1\times 23}{4\times 5}.

$$\frac{\frac{23}{20}\times 3,2}{\frac{0,23}{\frac{5}{8}}\times 0,5}$$

Convert decimal number 3,2 to fraction \frac{32}{10}. Reduce the fraction \frac{32}{10} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{23}{20}\times \frac{16}{5}}{\frac{0,23}{\frac{5}{8}}\times 0,5}$$

Multiply \frac{23}{20} times \frac{16}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{23\times 16}{20\times 5}}{\frac{0,23}{\frac{5}{8}}\times 0,5}$$

Do the multiplications in the fraction \frac{23\times 16}{20\times 5}.

$$\frac{\frac{368}{100}}{\frac{0,23}{\frac{5}{8}}\times 0,5}$$

Reduce the fraction \frac{368}{100} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{92}{25}}{\frac{0,23}{\frac{5}{8}}\times 0,5}$$

Divide 0,23 by \frac{5}{8} by multiplying 0,23 by the reciprocal of \frac{5}{8}.

$$\frac{\frac{92}{25}}{0,23\times \frac{8}{5}\times 0,5}$$

Convert decimal number 0,23 to fraction \frac{23}{100}.

$$\frac{\frac{92}{25}}{\frac{23}{100}\times \frac{8}{5}\times 0,5}$$

Multiply \frac{23}{100} times \frac{8}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{92}{25}}{\frac{23\times 8}{100\times 5}\times 0,5}$$

Do the multiplications in the fraction \frac{23\times 8}{100\times 5}.

$$\frac{\frac{92}{25}}{\frac{184}{500}\times 0,5}$$

Reduce the fraction \frac{184}{500} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{92}{25}}{\frac{46}{125}\times 0,5}$$

Convert decimal number 0,5 to fraction \frac{5}{10}. Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{92}{25}}{\frac{46}{125}\times \frac{1}{2}}$$

Multiply \frac{46}{125} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{92}{25}}{\frac{46\times 1}{125\times 2}}$$

Do the multiplications in the fraction \frac{46\times 1}{125\times 2}.

$$\frac{\frac{92}{25}}{\frac{46}{250}}$$

Reduce the fraction \frac{46}{250} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{92}{25}}{\frac{23}{125}}$$

Divide \frac{92}{25} by \frac{23}{125} by multiplying \frac{92}{25} by the reciprocal of \frac{23}{125}.

$$\frac{92}{25}\times \frac{125}{23}$$

Multiply \frac{92}{25} times \frac{125}{23} by multiplying numerator times numerator and denominator times denominator.

$$\frac{92\times 125}{25\times 23}$$

Do the multiplications in the fraction \frac{92\times 125}{25\times 23}.

$$\frac{11500}{575}$$

Divide 11500 by 575 to get 20.

$$20$$

Factor

$$5\times 2^{2}$$