Solve 5-[(0.9+1/4)*15]div17/8

$$5 - [ ( 0.9 + \frac { 1 } { 4 } ) \times 15 ] \div 1 \frac { 7 } { 8 }$$

Evaluate

$$-4.2$$

Solution Steps

Convert decimal number 0.9 to fraction \frac{9}{10}.

$$5-\frac{\left(\frac{9}{10}+\frac{1}{4}\right)\times 15}{\frac{1\times 8+7}{8}}$$

Least common multiple of 10 and 4 is 20. Convert \frac{9}{10} and \frac{1}{4} to fractions with denominator 20.

$$5-\frac{\left(\frac{18}{20}+\frac{5}{20}\right)\times 15}{\frac{1\times 8+7}{8}}$$

Since \frac{18}{20} and \frac{5}{20} have the same denominator, add them by adding their numerators.

$$5-\frac{\frac{18+5}{20}\times 15}{\frac{1\times 8+7}{8}}$$

Add 18 and 5 to get 23.

$$5-\frac{\frac{23}{20}\times 15}{\frac{1\times 8+7}{8}}$$

Express \frac{23}{20}\times 15 as a single fraction.

$$5-\frac{\frac{23\times 15}{20}}{\frac{1\times 8+7}{8}}$$

Multiply 23 and 15 to get 345.

$$5-\frac{\frac{345}{20}}{\frac{1\times 8+7}{8}}$$

Reduce the fraction \frac{345}{20} to lowest terms by extracting and canceling out 5.

$$5-\frac{\frac{69}{4}}{\frac{1\times 8+7}{8}}$$

Multiply 1 and 8 to get 8.

$$5-\frac{\frac{69}{4}}{\frac{8+7}{8}}$$

Add 8 and 7 to get 15.

$$5-\frac{\frac{69}{4}}{\frac{15}{8}}$$

Divide \frac{69}{4} by \frac{15}{8} by multiplying \frac{69}{4} by the reciprocal of \frac{15}{8}.

$$5-\frac{69}{4}\times \frac{8}{15}$$

Multiply \frac{69}{4} times \frac{8}{15} by multiplying numerator times numerator and denominator times denominator.

$$5-\frac{69\times 8}{4\times 15}$$

Do the multiplications in the fraction \frac{69\times 8}{4\times 15}.

$$5-\frac{552}{60}$$

Reduce the fraction \frac{552}{60} to lowest terms by extracting and canceling out 12.

$$5-\frac{46}{5}$$

Convert 5 to fraction \frac{25}{5}.

$$\frac{25}{5}-\frac{46}{5}$$

Since \frac{25}{5} and \frac{46}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{25-46}{5}$$

Subtract 46 from 25 to get -21.

$$-\frac{21}{5}$$

Factor

$$-4.2$$