Solve 29.5-[(0.4+1/4)*15]div17/8

$$29.5 - [ ( 0.4 + \frac { 1 } { 4 } ) \times 15 ] \div 1 \frac { 7 } { 8 }$$

Evaluate

$$24.3$$

Solution Steps

Convert decimal number 0.4 to fraction \frac{4}{10}. Reduce the fraction \frac{4}{10} to lowest terms by extracting and canceling out 2.

$$29.5-\frac{\left(\frac{2}{5}+\frac{1}{4}\right)\times 15}{\frac{1\times 8+7}{8}}$$

Least common multiple of 5 and 4 is 20. Convert \frac{2}{5} and \frac{1}{4} to fractions with denominator 20.

$$29.5-\frac{\left(\frac{8}{20}+\frac{5}{20}\right)\times 15}{\frac{1\times 8+7}{8}}$$

Since \frac{8}{20} and \frac{5}{20} have the same denominator, add them by adding their numerators.

$$29.5-\frac{\frac{8+5}{20}\times 15}{\frac{1\times 8+7}{8}}$$

Add 8 and 5 to get 13.

$$29.5-\frac{\frac{13}{20}\times 15}{\frac{1\times 8+7}{8}}$$

Express \frac{13}{20}\times 15 as a single fraction.

$$29.5-\frac{\frac{13\times 15}{20}}{\frac{1\times 8+7}{8}}$$

Multiply 13 and 15 to get 195.

$$29.5-\frac{\frac{195}{20}}{\frac{1\times 8+7}{8}}$$

Reduce the fraction \frac{195}{20} to lowest terms by extracting and canceling out 5.

$$29.5-\frac{\frac{39}{4}}{\frac{1\times 8+7}{8}}$$

Multiply 1 and 8 to get 8.

$$29.5-\frac{\frac{39}{4}}{\frac{8+7}{8}}$$

Add 8 and 7 to get 15.

$$29.5-\frac{\frac{39}{4}}{\frac{15}{8}}$$

Divide \frac{39}{4} by \frac{15}{8} by multiplying \frac{39}{4} by the reciprocal of \frac{15}{8}.

$$29.5-\frac{39}{4}\times \frac{8}{15}$$

Multiply \frac{39}{4} times \frac{8}{15} by multiplying numerator times numerator and denominator times denominator.

$$29.5-\frac{39\times 8}{4\times 15}$$

Do the multiplications in the fraction \frac{39\times 8}{4\times 15}.

$$29.5-\frac{312}{60}$$

Reduce the fraction \frac{312}{60} to lowest terms by extracting and canceling out 12.

$$29.5-\frac{26}{5}$$

Convert decimal number 29.5 to fraction \frac{295}{10}. Reduce the fraction \frac{295}{10} to lowest terms by extracting and canceling out 5.

$$\frac{59}{2}-\frac{26}{5}$$

Least common multiple of 2 and 5 is 10. Convert \frac{59}{2} and \frac{26}{5} to fractions with denominator 10.

$$\frac{295}{10}-\frac{52}{10}$$

Since \frac{295}{10} and \frac{52}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{295-52}{10}$$

Subtract 52 from 295 to get 243.

$$\frac{243}{10}$$

Factor

$$\frac{3 ^ {5}}{2 \cdot 5} = 24\frac{3}{10} = 24.3$$