Solve (-52/5)-(-2.25)-(-23/5)-(+3/4)

$$( - 5 \frac { 2 } { 5 } ) - ( - 2.25 ) - ( - 2 \frac { 3 } { 5 } ) - ( + \frac { 3 } { 4 } )$$

Evaluate

$$-1.3$$

Solution Steps

Multiply 5 and 5 to get 25.

$$-\frac{25+2}{5}-\left(-2.25\right)-\left(-\frac{2\times 5+3}{5}\right)-\frac{3}{4}$$

Add 25 and 2 to get 27.

$$-\frac{27}{5}-\left(-2.25\right)-\left(-\frac{2\times 5+3}{5}\right)-\frac{3}{4}$$

The opposite of -2.25 is 2.25.

$$-\frac{27}{5}+2.25-\left(-\frac{2\times 5+3}{5}\right)-\frac{3}{4}$$

Convert decimal number 2.25 to fraction \frac{225}{100}. Reduce the fraction \frac{225}{100} to lowest terms by extracting and canceling out 25.

$$-\frac{27}{5}+\frac{9}{4}-\left(-\frac{2\times 5+3}{5}\right)-\frac{3}{4}$$

Least common multiple of 5 and 4 is 20. Convert -\frac{27}{5} and \frac{9}{4} to fractions with denominator 20.

$$-\frac{108}{20}+\frac{45}{20}-\left(-\frac{2\times 5+3}{5}\right)-\frac{3}{4}$$

Since -\frac{108}{20} and \frac{45}{20} have the same denominator, add them by adding their numerators.

$$\frac{-108+45}{20}-\left(-\frac{2\times 5+3}{5}\right)-\frac{3}{4}$$

Add -108 and 45 to get -63.

$$-\frac{63}{20}-\left(-\frac{2\times 5+3}{5}\right)-\frac{3}{4}$$

Multiply 2 and 5 to get 10.

$$-\frac{63}{20}-\left(-\frac{10+3}{5}\right)-\frac{3}{4}$$

Add 10 and 3 to get 13.

$$-\frac{63}{20}-\left(-\frac{13}{5}\right)-\frac{3}{4}$$

The opposite of -\frac{13}{5} is \frac{13}{5}.

$$-\frac{63}{20}+\frac{13}{5}-\frac{3}{4}$$

Least common multiple of 20 and 5 is 20. Convert -\frac{63}{20} and \frac{13}{5} to fractions with denominator 20.

$$-\frac{63}{20}+\frac{52}{20}-\frac{3}{4}$$

Since -\frac{63}{20} and \frac{52}{20} have the same denominator, add them by adding their numerators.

$$\frac{-63+52}{20}-\frac{3}{4}$$

Add -63 and 52 to get -11.

$$-\frac{11}{20}-\frac{3}{4}$$

Least common multiple of 20 and 4 is 20. Convert -\frac{11}{20} and \frac{3}{4} to fractions with denominator 20.

$$-\frac{11}{20}-\frac{15}{20}$$

Since -\frac{11}{20} and \frac{15}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-11-15}{20}$$

Subtract 15 from -11 to get -26.

$$\frac{-26}{20}$$

Reduce the fraction \frac{-26}{20} to lowest terms by extracting and canceling out 2.

$$-\frac{13}{10}$$

Factor

$$-1.3$$