Solve (3,75+21/2/2frac{1{2}-1,875}-23/4+1,5/2,75-1frac{1{2}})*frac{10}{11}

$$( \frac { 3,75 + 2 \frac { 1 } { 2 } } { 2 \frac { 1 } { 2 } - 1,875 } - \frac { 2 \frac { 3 } { 4 } + 1,5 } { 2,75 - 1 \frac { 1 } { 2 } } ) \cdot \frac { 10 } { 11 }$$

Evaluate

$$6$$

Solution Steps

Multiply 2 and 2 to get 4.

$$\left(\frac{3,75+\frac{4+1}{2}}{\frac{2\times 2+1}{2}-1,875}-\frac{\frac{2\times 4+3}{4}+1,5}{2,75-\frac{1\times 2+1}{2}}\right)\times \frac{10}{11}$$

Add 4 and 1 to get 5.

$$\left(\frac{3,75+\frac{5}{2}}{\frac{2\times 2+1}{2}-1,875}-\frac{\frac{2\times 4+3}{4}+1,5}{2,75-\frac{1\times 2+1}{2}}\right)\times \frac{10}{11}$$

Convert decimal number 3,75 to fraction \frac{375}{100}. Reduce the fraction \frac{375}{100} to lowest terms by extracting and canceling out 25.

$$\left(\frac{\frac{15}{4}+\frac{5}{2}}{\frac{2\times 2+1}{2}-1,875}-\frac{\frac{2\times 4+3}{4}+1,5}{2,75-\frac{1\times 2+1}{2}}\right)\times \frac{10}{11}$$

Least common multiple of 4 and 2 is 4. Convert \frac{15}{4} and \frac{5}{2} to fractions with denominator 4.

$$\left(\frac{\frac{15}{4}+\frac{10}{4}}{\frac{2\times 2+1}{2}-1,875}-\frac{\frac{2\times 4+3}{4}+1,5}{2,75-\frac{1\times 2+1}{2}}\right)\times \frac{10}{11}$$

Since \frac{15}{4} and \frac{10}{4} have the same denominator, add them by adding their numerators.

$$\left(\frac{\frac{15+10}{4}}{\frac{2\times 2+1}{2}-1,875}-\frac{\frac{2\times 4+3}{4}+1,5}{2,75-\frac{1\times 2+1}{2}}\right)\times \frac{10}{11}$$

Add 15 and 10 to get 25.

$$\left(\frac{\frac{25}{4}}{\frac{2\times 2+1}{2}-1,875}-\frac{\frac{2\times 4+3}{4}+1,5}{2,75-\frac{1\times 2+1}{2}}\right)\times \frac{10}{11}$$

Multiply 2 and 2 to get 4.

$$\left(\frac{\frac{25}{4}}{\frac{4+1}{2}-1,875}-\frac{\frac{2\times 4+3}{4}+1,5}{2,75-\frac{1\times 2+1}{2}}\right)\times \frac{10}{11}$$

Add 4 and 1 to get 5.

$$\left(\frac{\frac{25}{4}}{\frac{5}{2}-1,875}-\frac{\frac{2\times 4+3}{4}+1,5}{2,75-\frac{1\times 2+1}{2}}\right)\times \frac{10}{11}$$

Convert decimal number 1,875 to fraction \frac{1875}{1000}. Reduce the fraction \frac{1875}{1000} to lowest terms by extracting and canceling out 125.

$$\left(\frac{\frac{25}{4}}{\frac{5}{2}-\frac{15}{8}}-\frac{\frac{2\times 4+3}{4}+1,5}{2,75-\frac{1\times 2+1}{2}}\right)\times \frac{10}{11}$$

Least common multiple of 2 and 8 is 8. Convert \frac{5}{2} and \frac{15}{8} to fractions with denominator 8.

$$\left(\frac{\frac{25}{4}}{\frac{20}{8}-\frac{15}{8}}-\frac{\frac{2\times 4+3}{4}+1,5}{2,75-\frac{1\times 2+1}{2}}\right)\times \frac{10}{11}$$

Since \frac{20}{8} and \frac{15}{8} have the same denominator, subtract them by subtracting their numerators.

$$\left(\frac{\frac{25}{4}}{\frac{20-15}{8}}-\frac{\frac{2\times 4+3}{4}+1,5}{2,75-\frac{1\times 2+1}{2}}\right)\times \frac{10}{11}$$

Subtract 15 from 20 to get 5.

$$\left(\frac{\frac{25}{4}}{\frac{5}{8}}-\frac{\frac{2\times 4+3}{4}+1,5}{2,75-\frac{1\times 2+1}{2}}\right)\times \frac{10}{11}$$

Divide \frac{25}{4} by \frac{5}{8} by multiplying \frac{25}{4} by the reciprocal of \frac{5}{8}.

$$\left(\frac{25}{4}\times \frac{8}{5}-\frac{\frac{2\times 4+3}{4}+1,5}{2,75-\frac{1\times 2+1}{2}}\right)\times \frac{10}{11}$$

Multiply \frac{25}{4} times \frac{8}{5} by multiplying numerator times numerator and denominator times denominator.

$$\left(\frac{25\times 8}{4\times 5}-\frac{\frac{2\times 4+3}{4}+1,5}{2,75-\frac{1\times 2+1}{2}}\right)\times \frac{10}{11}$$

Do the multiplications in the fraction \frac{25\times 8}{4\times 5}.

$$\left(\frac{200}{20}-\frac{\frac{2\times 4+3}{4}+1,5}{2,75-\frac{1\times 2+1}{2}}\right)\times \frac{10}{11}$$

Divide 200 by 20 to get 10.

$$\left(10-\frac{\frac{2\times 4+3}{4}+1,5}{2,75-\frac{1\times 2+1}{2}}\right)\times \frac{10}{11}$$

Multiply 2 and 4 to get 8.

$$\left(10-\frac{\frac{8+3}{4}+1,5}{2,75-\frac{1\times 2+1}{2}}\right)\times \frac{10}{11}$$

Add 8 and 3 to get 11.

$$\left(10-\frac{\frac{11}{4}+1,5}{2,75-\frac{1\times 2+1}{2}}\right)\times \frac{10}{11}$$

Convert decimal number 1,5 to fraction \frac{15}{10}. Reduce the fraction \frac{15}{10} to lowest terms by extracting and canceling out 5.

$$\left(10-\frac{\frac{11}{4}+\frac{3}{2}}{2,75-\frac{1\times 2+1}{2}}\right)\times \frac{10}{11}$$

Least common multiple of 4 and 2 is 4. Convert \frac{11}{4} and \frac{3}{2} to fractions with denominator 4.

$$\left(10-\frac{\frac{11}{4}+\frac{6}{4}}{2,75-\frac{1\times 2+1}{2}}\right)\times \frac{10}{11}$$

Since \frac{11}{4} and \frac{6}{4} have the same denominator, add them by adding their numerators.

$$\left(10-\frac{\frac{11+6}{4}}{2,75-\frac{1\times 2+1}{2}}\right)\times \frac{10}{11}$$

Add 11 and 6 to get 17.

$$\left(10-\frac{\frac{17}{4}}{2,75-\frac{1\times 2+1}{2}}\right)\times \frac{10}{11}$$

Multiply 1 and 2 to get 2.

$$\left(10-\frac{\frac{17}{4}}{2,75-\frac{2+1}{2}}\right)\times \frac{10}{11}$$

Add 2 and 1 to get 3.

$$\left(10-\frac{\frac{17}{4}}{2,75-\frac{3}{2}}\right)\times \frac{10}{11}$$

Convert decimal number 2,75 to fraction \frac{275}{100}. Reduce the fraction \frac{275}{100} to lowest terms by extracting and canceling out 25.

$$\left(10-\frac{\frac{17}{4}}{\frac{11}{4}-\frac{3}{2}}\right)\times \frac{10}{11}$$

Least common multiple of 4 and 2 is 4. Convert \frac{11}{4} and \frac{3}{2} to fractions with denominator 4.

$$\left(10-\frac{\frac{17}{4}}{\frac{11}{4}-\frac{6}{4}}\right)\times \frac{10}{11}$$

Since \frac{11}{4} and \frac{6}{4} have the same denominator, subtract them by subtracting their numerators.

$$\left(10-\frac{\frac{17}{4}}{\frac{11-6}{4}}\right)\times \frac{10}{11}$$

Subtract 6 from 11 to get 5.

$$\left(10-\frac{\frac{17}{4}}{\frac{5}{4}}\right)\times \frac{10}{11}$$

Divide \frac{17}{4} by \frac{5}{4} by multiplying \frac{17}{4} by the reciprocal of \frac{5}{4}.

$$\left(10-\frac{17}{4}\times \frac{4}{5}\right)\times \frac{10}{11}$$

Multiply \frac{17}{4} times \frac{4}{5} by multiplying numerator times numerator and denominator times denominator.

$$\left(10-\frac{17\times 4}{4\times 5}\right)\times \frac{10}{11}$$

Cancel out 4 in both numerator and denominator.

$$\left(10-\frac{17}{5}\right)\times \frac{10}{11}$$

Convert 10 to fraction \frac{50}{5}.

$$\left(\frac{50}{5}-\frac{17}{5}\right)\times \frac{10}{11}$$

Since \frac{50}{5} and \frac{17}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{50-17}{5}\times \frac{10}{11}$$

Subtract 17 from 50 to get 33.

$$\frac{33}{5}\times \frac{10}{11}$$

Multiply \frac{33}{5} times \frac{10}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{33\times 10}{5\times 11}$$

Do the multiplications in the fraction \frac{33\times 10}{5\times 11}.

$$\frac{330}{55}$$

Divide 330 by 55 to get 6.

$$6$$

Factor

$$2\times 3$$