Solve (51/4-61/6)*(31/4-0,55)

$$( 5 \frac { 1 } { 4 } - 6 \frac { 1 } { 6 } ) \cdot ( 3 \frac { 1 } { 4 } - 0,55 )$$

Evaluate

$$-2,475$$

Solution Steps

Multiply 5 and 4 to get 20.

$$\left(\frac{20+1}{4}-\frac{6\times 6+1}{6}\right)\left(\frac{3\times 4+1}{4}-0,55\right)$$

Add 20 and 1 to get 21.

$$\left(\frac{21}{4}-\frac{6\times 6+1}{6}\right)\left(\frac{3\times 4+1}{4}-0,55\right)$$

Multiply 6 and 6 to get 36.

$$\left(\frac{21}{4}-\frac{36+1}{6}\right)\left(\frac{3\times 4+1}{4}-0,55\right)$$

Add 36 and 1 to get 37.

$$\left(\frac{21}{4}-\frac{37}{6}\right)\left(\frac{3\times 4+1}{4}-0,55\right)$$

Least common multiple of 4 and 6 is 12. Convert \frac{21}{4} and \frac{37}{6} to fractions with denominator 12.

$$\left(\frac{63}{12}-\frac{74}{12}\right)\left(\frac{3\times 4+1}{4}-0,55\right)$$

Since \frac{63}{12} and \frac{74}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{63-74}{12}\left(\frac{3\times 4+1}{4}-0,55\right)$$

Subtract 74 from 63 to get -11.

$$-\frac{11}{12}\left(\frac{3\times 4+1}{4}-0,55\right)$$

Multiply 3 and 4 to get 12.

$$-\frac{11}{12}\left(\frac{12+1}{4}-0,55\right)$$

Add 12 and 1 to get 13.

$$-\frac{11}{12}\left(\frac{13}{4}-0,55\right)$$

Convert decimal number 0,55 to fraction \frac{55}{100}. Reduce the fraction \frac{55}{100} to lowest terms by extracting and canceling out 5.

$$-\frac{11}{12}\left(\frac{13}{4}-\frac{11}{20}\right)$$

Least common multiple of 4 and 20 is 20. Convert \frac{13}{4} and \frac{11}{20} to fractions with denominator 20.

$$-\frac{11}{12}\left(\frac{65}{20}-\frac{11}{20}\right)$$

Since \frac{65}{20} and \frac{11}{20} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{11}{12}\times \frac{65-11}{20}$$

Subtract 11 from 65 to get 54.

$$-\frac{11}{12}\times \frac{54}{20}$$

Reduce the fraction \frac{54}{20} to lowest terms by extracting and canceling out 2.

$$-\frac{11}{12}\times \frac{27}{10}$$

Multiply -\frac{11}{12} times \frac{27}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-11\times 27}{12\times 10}$$

Do the multiplications in the fraction \frac{-11\times 27}{12\times 10}.

$$\frac{-297}{120}$$

Reduce the fraction \frac{-297}{120} to lowest terms by extracting and canceling out 3.

$$-\frac{99}{40}$$

Factor

$$-2,475$$