Solve (22.9div4/5+27.1*11/4)*8/25

$$( 22.9 \div \frac { 4 } { 5 } + 27.1 \times 1 \frac { 1 } { 4 } ) \times \frac { 8 } { 25 }$$

Evaluate

$$20$$

Solution Steps

Divide 22.9 by \frac{4}{5} by multiplying 22.9 by the reciprocal of \frac{4}{5}.

$$\left(22.9\times \frac{5}{4}+27.1\times \frac{1\times 4+1}{4}\right)\times \frac{8}{25}$$

Convert decimal number 22.9 to fraction \frac{229}{10}.

$$\left(\frac{229}{10}\times \frac{5}{4}+27.1\times \frac{1\times 4+1}{4}\right)\times \frac{8}{25}$$

Multiply \frac{229}{10} times \frac{5}{4} by multiplying numerator times numerator and denominator times denominator.

$$\left(\frac{229\times 5}{10\times 4}+27.1\times \frac{1\times 4+1}{4}\right)\times \frac{8}{25}$$

Do the multiplications in the fraction \frac{229\times 5}{10\times 4}.

$$\left(\frac{1145}{40}+27.1\times \frac{1\times 4+1}{4}\right)\times \frac{8}{25}$$

Reduce the fraction \frac{1145}{40} to lowest terms by extracting and canceling out 5.

$$\left(\frac{229}{8}+27.1\times \frac{1\times 4+1}{4}\right)\times \frac{8}{25}$$

Multiply 1 and 4 to get 4.

$$\left(\frac{229}{8}+27.1\times \frac{4+1}{4}\right)\times \frac{8}{25}$$

Add 4 and 1 to get 5.

$$\left(\frac{229}{8}+27.1\times \frac{5}{4}\right)\times \frac{8}{25}$$

Convert decimal number 27.1 to fraction \frac{271}{10}.

$$\left(\frac{229}{8}+\frac{271}{10}\times \frac{5}{4}\right)\times \frac{8}{25}$$

Multiply \frac{271}{10} times \frac{5}{4} by multiplying numerator times numerator and denominator times denominator.

$$\left(\frac{229}{8}+\frac{271\times 5}{10\times 4}\right)\times \frac{8}{25}$$

Do the multiplications in the fraction \frac{271\times 5}{10\times 4}.

$$\left(\frac{229}{8}+\frac{1355}{40}\right)\times \frac{8}{25}$$

Reduce the fraction \frac{1355}{40} to lowest terms by extracting and canceling out 5.

$$\left(\frac{229}{8}+\frac{271}{8}\right)\times \frac{8}{25}$$

Since \frac{229}{8} and \frac{271}{8} have the same denominator, add them by adding their numerators.

$$\frac{229+271}{8}\times \frac{8}{25}$$

Add 229 and 271 to get 500.

$$\frac{500}{8}\times \frac{8}{25}$$

Reduce the fraction \frac{500}{8} to lowest terms by extracting and canceling out 4.

$$\frac{125}{2}\times \frac{8}{25}$$

Multiply \frac{125}{2} times \frac{8}{25} by multiplying numerator times numerator and denominator times denominator.

$$\frac{125\times 8}{2\times 25}$$

Do the multiplications in the fraction \frac{125\times 8}{2\times 25}.

$$\frac{1000}{50}$$

Divide 1000 by 50 to get 20.

$$20$$

Factor

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