Solve 31/2-[3/5-(0,5-2/5)]-(11/4)

$$3 \frac { 1 } { 2 } - [ \frac { 3 } { 5 } - ( 0,5 - \frac { 2 } { 5 } ) ] - ( 1 \frac { 1 } { 4 } )$$

Evaluate

$$1,75$$

Solution Steps

Multiply 3 and 2 to get 6.

$$\frac{6+1}{2}-\left(\frac{3}{5}-\left(0,5-\frac{2}{5}\right)\right)-\frac{1\times 4+1}{4}$$

Add 6 and 1 to get 7.

$$\frac{7}{2}-\left(\frac{3}{5}-\left(0,5-\frac{2}{5}\right)\right)-\frac{1\times 4+1}{4}$$

Convert decimal number 0,5 to fraction \frac{5}{10}. Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

$$\frac{7}{2}-\left(\frac{3}{5}-\left(\frac{1}{2}-\frac{2}{5}\right)\right)-\frac{1\times 4+1}{4}$$

Least common multiple of 2 and 5 is 10. Convert \frac{1}{2} and \frac{2}{5} to fractions with denominator 10.

$$\frac{7}{2}-\left(\frac{3}{5}-\left(\frac{5}{10}-\frac{4}{10}\right)\right)-\frac{1\times 4+1}{4}$$

Since \frac{5}{10} and \frac{4}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7}{2}-\left(\frac{3}{5}-\frac{5-4}{10}\right)-\frac{1\times 4+1}{4}$$

Subtract 4 from 5 to get 1.

$$\frac{7}{2}-\left(\frac{3}{5}-\frac{1}{10}\right)-\frac{1\times 4+1}{4}$$

Least common multiple of 5 and 10 is 10. Convert \frac{3}{5} and \frac{1}{10} to fractions with denominator 10.

$$\frac{7}{2}-\left(\frac{6}{10}-\frac{1}{10}\right)-\frac{1\times 4+1}{4}$$

Since \frac{6}{10} and \frac{1}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7}{2}-\frac{6-1}{10}-\frac{1\times 4+1}{4}$$

Subtract 1 from 6 to get 5.

$$\frac{7}{2}-\frac{5}{10}-\frac{1\times 4+1}{4}$$

Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

$$\frac{7}{2}-\frac{1}{2}-\frac{1\times 4+1}{4}$$

Since \frac{7}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7-1}{2}-\frac{1\times 4+1}{4}$$

Subtract 1 from 7 to get 6.

$$\frac{6}{2}-\frac{1\times 4+1}{4}$$

Divide 6 by 2 to get 3.

$$3-\frac{1\times 4+1}{4}$$

Multiply 1 and 4 to get 4.

$$3-\frac{4+1}{4}$$

Add 4 and 1 to get 5.

$$3-\frac{5}{4}$$

Convert 3 to fraction \frac{12}{4}.

$$\frac{12}{4}-\frac{5}{4}$$

Since \frac{12}{4} and \frac{5}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{12-5}{4}$$

Subtract 5 from 12 to get 7.

$$\frac{7}{4}$$

Factor

$$\frac{7}{2 ^ {2}} = 1\frac{3}{4} = 1.75$$