Solve (52/5-1.8)div[(1.15+13/30)*12/3]

$$( 5 \frac { 2 } { 5 } - 1.8 ) \div [ ( 1.15 + \frac { 13 } { 30 } ) \times 1 \frac { 2 } { 3 } ]$$

Evaluate

$$\frac{648}{475}\approx 1.364210526$$

Solution Steps

Multiply 5 and 5 to get 25.

$$\frac{\frac{25+2}{5}-1.8}{\left(1.15+\frac{13}{30}\right)\times \frac{1\times 3+2}{3}}$$

Add 25 and 2 to get 27.

$$\frac{\frac{27}{5}-1.8}{\left(1.15+\frac{13}{30}\right)\times \frac{1\times 3+2}{3}}$$

Convert decimal number 1.8 to fraction \frac{18}{10}. Reduce the fraction \frac{18}{10} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{27}{5}-\frac{9}{5}}{\left(1.15+\frac{13}{30}\right)\times \frac{1\times 3+2}{3}}$$

Since \frac{27}{5} and \frac{9}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{27-9}{5}}{\left(1.15+\frac{13}{30}\right)\times \frac{1\times 3+2}{3}}$$

Subtract 9 from 27 to get 18.

$$\frac{\frac{18}{5}}{\left(1.15+\frac{13}{30}\right)\times \frac{1\times 3+2}{3}}$$

Convert decimal number 1.15 to fraction \frac{115}{100}. Reduce the fraction \frac{115}{100} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{18}{5}}{\left(\frac{23}{20}+\frac{13}{30}\right)\times \frac{1\times 3+2}{3}}$$

Least common multiple of 20 and 30 is 60. Convert \frac{23}{20} and \frac{13}{30} to fractions with denominator 60.

$$\frac{\frac{18}{5}}{\left(\frac{69}{60}+\frac{26}{60}\right)\times \frac{1\times 3+2}{3}}$$

Since \frac{69}{60} and \frac{26}{60} have the same denominator, add them by adding their numerators.

$$\frac{\frac{18}{5}}{\frac{69+26}{60}\times \frac{1\times 3+2}{3}}$$

Add 69 and 26 to get 95.

$$\frac{\frac{18}{5}}{\frac{95}{60}\times \frac{1\times 3+2}{3}}$$

Reduce the fraction \frac{95}{60} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{18}{5}}{\frac{19}{12}\times \frac{1\times 3+2}{3}}$$

Multiply 1 and 3 to get 3.

$$\frac{\frac{18}{5}}{\frac{19}{12}\times \frac{3+2}{3}}$$

Add 3 and 2 to get 5.

$$\frac{\frac{18}{5}}{\frac{19}{12}\times \frac{5}{3}}$$

Multiply \frac{19}{12} times \frac{5}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{18}{5}}{\frac{19\times 5}{12\times 3}}$$

Do the multiplications in the fraction \frac{19\times 5}{12\times 3}.

$$\frac{\frac{18}{5}}{\frac{95}{36}}$$

Divide \frac{18}{5} by \frac{95}{36} by multiplying \frac{18}{5} by the reciprocal of \frac{95}{36}.

$$\frac{18}{5}\times \frac{36}{95}$$

Multiply \frac{18}{5} times \frac{36}{95} by multiplying numerator times numerator and denominator times denominator.

$$\frac{18\times 36}{5\times 95}$$

Do the multiplications in the fraction \frac{18\times 36}{5\times 95}.

$$\frac{648}{475}$$

Factor

$$\frac{2 ^ {3} \cdot 3 ^ {4}}{19 \cdot 5 ^ {2}} = 1\frac{173}{475} = 1.3642105263157895$$