Solve 17/8*44/5-33/5:2,4/3frac{1{2}+2frac{1}{4}}-frac{3frac{1}{2}:2,8+5frac{2}{3}*frac{6}{17}}{12-8,75}

$$\frac { 1 \frac { 7 } { 8 } \cdot 4 \frac { 4 } { 5 } - 3 \frac { 3 } { 5 } : 2,4 } { 3 \frac { 1 } { 2 } + 2 \frac { 1 } { 4 } } - \frac { 3 \frac { 1 } { 2 } : 2,8 + 5 \frac { 2 } { 3 } \cdot \frac { 6 } { 17 } } { 12 - 8,75 }$$

Evaluate

$$\frac{7}{23}\approx 0,304347826$$

Solution Steps

Multiply 1 and 8 to get 8.

$$\frac{\frac{8+7}{8}\times \frac{4\times 5+4}{5}-\frac{\frac{3\times 5+3}{5}}{2,4}}{\frac{3\times 2+1}{2}+\frac{2\times 4+1}{4}}-\frac{\frac{\frac{3\times 2+1}{2}}{2,8}+\frac{5\times 3+2}{3}\times \frac{6}{17}}{12-8,75}$$

Add 8 and 7 to get 15.

$$\frac{\frac{15}{8}\times \frac{4\times 5+4}{5}-\frac{\frac{3\times 5+3}{5}}{2,4}}{\frac{3\times 2+1}{2}+\frac{2\times 4+1}{4}}-\frac{\frac{\frac{3\times 2+1}{2}}{2,8}+\frac{5\times 3+2}{3}\times \frac{6}{17}}{12-8,75}$$

Multiply 4 and 5 to get 20.

$$\frac{\frac{15}{8}\times \frac{20+4}{5}-\frac{\frac{3\times 5+3}{5}}{2,4}}{\frac{3\times 2+1}{2}+\frac{2\times 4+1}{4}}-\frac{\frac{\frac{3\times 2+1}{2}}{2,8}+\frac{5\times 3+2}{3}\times \frac{6}{17}}{12-8,75}$$

Add 20 and 4 to get 24.

$$\frac{\frac{15}{8}\times \frac{24}{5}-\frac{\frac{3\times 5+3}{5}}{2,4}}{\frac{3\times 2+1}{2}+\frac{2\times 4+1}{4}}-\frac{\frac{\frac{3\times 2+1}{2}}{2,8}+\frac{5\times 3+2}{3}\times \frac{6}{17}}{12-8,75}$$

Multiply \frac{15}{8} times \frac{24}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{15\times 24}{8\times 5}-\frac{\frac{3\times 5+3}{5}}{2,4}}{\frac{3\times 2+1}{2}+\frac{2\times 4+1}{4}}-\frac{\frac{\frac{3\times 2+1}{2}}{2,8}+\frac{5\times 3+2}{3}\times \frac{6}{17}}{12-8,75}$$

Do the multiplications in the fraction \frac{15\times 24}{8\times 5}.

$$\frac{\frac{360}{40}-\frac{\frac{3\times 5+3}{5}}{2,4}}{\frac{3\times 2+1}{2}+\frac{2\times 4+1}{4}}-\frac{\frac{\frac{3\times 2+1}{2}}{2,8}+\frac{5\times 3+2}{3}\times \frac{6}{17}}{12-8,75}$$

Divide 360 by 40 to get 9.

$$\frac{9-\frac{\frac{3\times 5+3}{5}}{2,4}}{\frac{3\times 2+1}{2}+\frac{2\times 4+1}{4}}-\frac{\frac{\frac{3\times 2+1}{2}}{2,8}+\frac{5\times 3+2}{3}\times \frac{6}{17}}{12-8,75}$$

Express \frac{\frac{3\times 5+3}{5}}{2,4} as a single fraction.

$$\frac{9-\frac{3\times 5+3}{5\times 2,4}}{\frac{3\times 2+1}{2}+\frac{2\times 4+1}{4}}-\frac{\frac{\frac{3\times 2+1}{2}}{2,8}+\frac{5\times 3+2}{3}\times \frac{6}{17}}{12-8,75}$$

Multiply 3 and 5 to get 15.

$$\frac{9-\frac{15+3}{5\times 2,4}}{\frac{3\times 2+1}{2}+\frac{2\times 4+1}{4}}-\frac{\frac{\frac{3\times 2+1}{2}}{2,8}+\frac{5\times 3+2}{3}\times \frac{6}{17}}{12-8,75}$$

Add 15 and 3 to get 18.

$$\frac{9-\frac{18}{5\times 2,4}}{\frac{3\times 2+1}{2}+\frac{2\times 4+1}{4}}-\frac{\frac{\frac{3\times 2+1}{2}}{2,8}+\frac{5\times 3+2}{3}\times \frac{6}{17}}{12-8,75}$$

Multiply 5 and 2,4 to get 12.

$$\frac{9-\frac{18}{12}}{\frac{3\times 2+1}{2}+\frac{2\times 4+1}{4}}-\frac{\frac{\frac{3\times 2+1}{2}}{2,8}+\frac{5\times 3+2}{3}\times \frac{6}{17}}{12-8,75}$$

Reduce the fraction \frac{18}{12} to lowest terms by extracting and canceling out 6.

$$\frac{9-\frac{3}{2}}{\frac{3\times 2+1}{2}+\frac{2\times 4+1}{4}}-\frac{\frac{\frac{3\times 2+1}{2}}{2,8}+\frac{5\times 3+2}{3}\times \frac{6}{17}}{12-8,75}$$

Convert 9 to fraction \frac{18}{2}.

$$\frac{\frac{18}{2}-\frac{3}{2}}{\frac{3\times 2+1}{2}+\frac{2\times 4+1}{4}}-\frac{\frac{\frac{3\times 2+1}{2}}{2,8}+\frac{5\times 3+2}{3}\times \frac{6}{17}}{12-8,75}$$

Since \frac{18}{2} and \frac{3}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{18-3}{2}}{\frac{3\times 2+1}{2}+\frac{2\times 4+1}{4}}-\frac{\frac{\frac{3\times 2+1}{2}}{2,8}+\frac{5\times 3+2}{3}\times \frac{6}{17}}{12-8,75}$$

Subtract 3 from 18 to get 15.

$$\frac{\frac{15}{2}}{\frac{3\times 2+1}{2}+\frac{2\times 4+1}{4}}-\frac{\frac{\frac{3\times 2+1}{2}}{2,8}+\frac{5\times 3+2}{3}\times \frac{6}{17}}{12-8,75}$$

Multiply 3 and 2 to get 6.

$$\frac{\frac{15}{2}}{\frac{6+1}{2}+\frac{2\times 4+1}{4}}-\frac{\frac{\frac{3\times 2+1}{2}}{2,8}+\frac{5\times 3+2}{3}\times \frac{6}{17}}{12-8,75}$$

Add 6 and 1 to get 7.

$$\frac{\frac{15}{2}}{\frac{7}{2}+\frac{2\times 4+1}{4}}-\frac{\frac{\frac{3\times 2+1}{2}}{2,8}+\frac{5\times 3+2}{3}\times \frac{6}{17}}{12-8,75}$$

Multiply 2 and 4 to get 8.

$$\frac{\frac{15}{2}}{\frac{7}{2}+\frac{8+1}{4}}-\frac{\frac{\frac{3\times 2+1}{2}}{2,8}+\frac{5\times 3+2}{3}\times \frac{6}{17}}{12-8,75}$$

Add 8 and 1 to get 9.

$$\frac{\frac{15}{2}}{\frac{7}{2}+\frac{9}{4}}-\frac{\frac{\frac{3\times 2+1}{2}}{2,8}+\frac{5\times 3+2}{3}\times \frac{6}{17}}{12-8,75}$$

Least common multiple of 2 and 4 is 4. Convert \frac{7}{2} and \frac{9}{4} to fractions with denominator 4.

$$\frac{\frac{15}{2}}{\frac{14}{4}+\frac{9}{4}}-\frac{\frac{\frac{3\times 2+1}{2}}{2,8}+\frac{5\times 3+2}{3}\times \frac{6}{17}}{12-8,75}$$

Since \frac{14}{4} and \frac{9}{4} have the same denominator, add them by adding their numerators.

$$\frac{\frac{15}{2}}{\frac{14+9}{4}}-\frac{\frac{\frac{3\times 2+1}{2}}{2,8}+\frac{5\times 3+2}{3}\times \frac{6}{17}}{12-8,75}$$

Add 14 and 9 to get 23.

$$\frac{\frac{15}{2}}{\frac{23}{4}}-\frac{\frac{\frac{3\times 2+1}{2}}{2,8}+\frac{5\times 3+2}{3}\times \frac{6}{17}}{12-8,75}$$

Divide \frac{15}{2} by \frac{23}{4} by multiplying \frac{15}{2} by the reciprocal of \frac{23}{4}.

$$\frac{15}{2}\times \frac{4}{23}-\frac{\frac{\frac{3\times 2+1}{2}}{2,8}+\frac{5\times 3+2}{3}\times \frac{6}{17}}{12-8,75}$$

Multiply \frac{15}{2} times \frac{4}{23} by multiplying numerator times numerator and denominator times denominator.

$$\frac{15\times 4}{2\times 23}-\frac{\frac{\frac{3\times 2+1}{2}}{2,8}+\frac{5\times 3+2}{3}\times \frac{6}{17}}{12-8,75}$$

Do the multiplications in the fraction \frac{15\times 4}{2\times 23}.

$$\frac{60}{46}-\frac{\frac{\frac{3\times 2+1}{2}}{2,8}+\frac{5\times 3+2}{3}\times \frac{6}{17}}{12-8,75}$$

Reduce the fraction \frac{60}{46} to lowest terms by extracting and canceling out 2.

$$\frac{30}{23}-\frac{\frac{\frac{3\times 2+1}{2}}{2,8}+\frac{5\times 3+2}{3}\times \frac{6}{17}}{12-8,75}$$

Express \frac{\frac{3\times 2+1}{2}}{2,8} as a single fraction.

$$\frac{30}{23}-\frac{\frac{3\times 2+1}{2\times 2,8}+\frac{5\times 3+2}{3}\times \frac{6}{17}}{12-8,75}$$

Multiply 3 and 2 to get 6.

$$\frac{30}{23}-\frac{\frac{6+1}{2\times 2,8}+\frac{5\times 3+2}{3}\times \frac{6}{17}}{12-8,75}$$

Add 6 and 1 to get 7.

$$\frac{30}{23}-\frac{\frac{7}{2\times 2,8}+\frac{5\times 3+2}{3}\times \frac{6}{17}}{12-8,75}$$

Multiply 2 and 2,8 to get 5,6.

$$\frac{30}{23}-\frac{\frac{7}{5,6}+\frac{5\times 3+2}{3}\times \frac{6}{17}}{12-8,75}$$

Expand \frac{7}{5,6} by multiplying both numerator and the denominator by 10.

$$\frac{30}{23}-\frac{\frac{70}{56}+\frac{5\times 3+2}{3}\times \frac{6}{17}}{12-8,75}$$

Reduce the fraction \frac{70}{56} to lowest terms by extracting and canceling out 14.

$$\frac{30}{23}-\frac{\frac{5}{4}+\frac{5\times 3+2}{3}\times \frac{6}{17}}{12-8,75}$$

Multiply 5 and 3 to get 15.

$$\frac{30}{23}-\frac{\frac{5}{4}+\frac{15+2}{3}\times \frac{6}{17}}{12-8,75}$$

Add 15 and 2 to get 17.

$$\frac{30}{23}-\frac{\frac{5}{4}+\frac{17}{3}\times \frac{6}{17}}{12-8,75}$$

Multiply \frac{17}{3} times \frac{6}{17} by multiplying numerator times numerator and denominator times denominator.

$$\frac{30}{23}-\frac{\frac{5}{4}+\frac{17\times 6}{3\times 17}}{12-8,75}$$

Cancel out 17 in both numerator and denominator.

$$\frac{30}{23}-\frac{\frac{5}{4}+\frac{6}{3}}{12-8,75}$$

Divide 6 by 3 to get 2.

$$\frac{30}{23}-\frac{\frac{5}{4}+2}{12-8,75}$$

Convert 2 to fraction \frac{8}{4}.

$$\frac{30}{23}-\frac{\frac{5}{4}+\frac{8}{4}}{12-8,75}$$

Since \frac{5}{4} and \frac{8}{4} have the same denominator, add them by adding their numerators.

$$\frac{30}{23}-\frac{\frac{5+8}{4}}{12-8,75}$$

Add 5 and 8 to get 13.

$$\frac{30}{23}-\frac{\frac{13}{4}}{12-8,75}$$

Subtract 8,75 from 12 to get 3,25.

$$\frac{30}{23}-\frac{\frac{13}{4}}{3,25}$$

Divide \frac{13}{4} by 3,25 to get 1.

$$\frac{30}{23}-1$$

Convert 1 to fraction \frac{23}{23}.

$$\frac{30}{23}-\frac{23}{23}$$

Since \frac{30}{23} and \frac{23}{23} have the same denominator, subtract them by subtracting their numerators.

$$\frac{30-23}{23}$$

Subtract 23 from 30 to get 7.

$$\frac{7}{23}$$

Factor

$$\frac{7}{23} = 0.30434782608695654$$