Solve 135%text{of}342-342%text{of}13.5=?

$$135 \% \text { of } 342 - 342 \% \text { of } 13.5 = ?$$

Evaluate

$$415.53$$

Solution Steps

Reduce the fraction \frac{135}{100} to lowest terms by extracting and canceling out 5.

$$\frac{27}{20}\times 342-\frac{342}{100}\times 13.5$$

Express \frac{27}{20}\times 342 as a single fraction.

$$\frac{27\times 342}{20}-\frac{342}{100}\times 13.5$$

Multiply 27 and 342 to get 9234.

$$\frac{9234}{20}-\frac{342}{100}\times 13.5$$

Reduce the fraction \frac{9234}{20} to lowest terms by extracting and canceling out 2.

$$\frac{4617}{10}-\frac{342}{100}\times 13.5$$

Reduce the fraction \frac{342}{100} to lowest terms by extracting and canceling out 2.

$$\frac{4617}{10}-\frac{171}{50}\times 13.5$$

Convert decimal number 13.5 to fraction \frac{135}{10}. Reduce the fraction \frac{135}{10} to lowest terms by extracting and canceling out 5.

$$\frac{4617}{10}-\frac{171}{50}\times \frac{27}{2}$$

Multiply \frac{171}{50} times \frac{27}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4617}{10}-\frac{171\times 27}{50\times 2}$$

Do the multiplications in the fraction \frac{171\times 27}{50\times 2}.

$$\frac{4617}{10}-\frac{4617}{100}$$

Least common multiple of 10 and 100 is 100. Convert \frac{4617}{10} and \frac{4617}{100} to fractions with denominator 100.

$$\frac{46170}{100}-\frac{4617}{100}$$

Since \frac{46170}{100} and \frac{4617}{100} have the same denominator, subtract them by subtracting their numerators.

$$\frac{46170-4617}{100}$$

Subtract 4617 from 46170 to get 41553.

$$\frac{41553}{100}$$

Factor

$$\frac{19 \cdot 3 ^ {7}}{2 ^ {2} \cdot 5 ^ {2}} = 415\frac{53}{100} = 415.53$$