Solve (11/5div(17/40+0.6-0.005))*1.7/frac{5{6}+11/3-1frac{23}{30}}+frac{4.75+7frac{1}{2}}{33div4frac{5}{7}}

$$\frac { ( 1 \frac { 1 } { 5 } \div ( \frac { 17 } { 40 } + 0.6 - 0.005 ) ) \cdot 1.7 } { \frac { 5 } { 6 } + 1 \frac { 1 } { 3 } - 1 \frac { 23 } { 30 } } + \frac { 4.75 + 7 \frac { 1 } { 2 } } { 33 \div 4 \frac { 5 } { 7 } }$$

Evaluate

$$6.75$$

Solution Steps

Multiply 1 and 5 to get 5.

$$\frac{\frac{\frac{5+1}{5}}{\frac{17}{40}+0.6-0.005}\times 1.7}{\frac{5}{6}+\frac{1\times 3+1}{3}-\frac{1\times 30+23}{30}}+\frac{4.75+\frac{7\times 2+1}{2}}{\frac{33}{\frac{4\times 7+5}{7}}}$$

Add 5 and 1 to get 6.

$$\frac{\frac{\frac{6}{5}}{\frac{17}{40}+0.6-0.005}\times 1.7}{\frac{5}{6}+\frac{1\times 3+1}{3}-\frac{1\times 30+23}{30}}+\frac{4.75+\frac{7\times 2+1}{2}}{\frac{33}{\frac{4\times 7+5}{7}}}$$

Convert decimal number 0.6 to fraction \frac{6}{10}. Reduce the fraction \frac{6}{10} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{\frac{6}{5}}{\frac{17}{40}+\frac{3}{5}-0.005}\times 1.7}{\frac{5}{6}+\frac{1\times 3+1}{3}-\frac{1\times 30+23}{30}}+\frac{4.75+\frac{7\times 2+1}{2}}{\frac{33}{\frac{4\times 7+5}{7}}}$$

Least common multiple of 40 and 5 is 40. Convert \frac{17}{40} and \frac{3}{5} to fractions with denominator 40.

$$\frac{\frac{\frac{6}{5}}{\frac{17}{40}+\frac{24}{40}-0.005}\times 1.7}{\frac{5}{6}+\frac{1\times 3+1}{3}-\frac{1\times 30+23}{30}}+\frac{4.75+\frac{7\times 2+1}{2}}{\frac{33}{\frac{4\times 7+5}{7}}}$$

Since \frac{17}{40} and \frac{24}{40} have the same denominator, add them by adding their numerators.

$$\frac{\frac{\frac{6}{5}}{\frac{17+24}{40}-0.005}\times 1.7}{\frac{5}{6}+\frac{1\times 3+1}{3}-\frac{1\times 30+23}{30}}+\frac{4.75+\frac{7\times 2+1}{2}}{\frac{33}{\frac{4\times 7+5}{7}}}$$

Add 17 and 24 to get 41.

$$\frac{\frac{\frac{6}{5}}{\frac{41}{40}-0.005}\times 1.7}{\frac{5}{6}+\frac{1\times 3+1}{3}-\frac{1\times 30+23}{30}}+\frac{4.75+\frac{7\times 2+1}{2}}{\frac{33}{\frac{4\times 7+5}{7}}}$$

Convert decimal number 0.005 to fraction \frac{5}{1000}. Reduce the fraction \frac{5}{1000} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{\frac{6}{5}}{\frac{41}{40}-\frac{1}{200}}\times 1.7}{\frac{5}{6}+\frac{1\times 3+1}{3}-\frac{1\times 30+23}{30}}+\frac{4.75+\frac{7\times 2+1}{2}}{\frac{33}{\frac{4\times 7+5}{7}}}$$

Least common multiple of 40 and 200 is 200. Convert \frac{41}{40} and \frac{1}{200} to fractions with denominator 200.

$$\frac{\frac{\frac{6}{5}}{\frac{205}{200}-\frac{1}{200}}\times 1.7}{\frac{5}{6}+\frac{1\times 3+1}{3}-\frac{1\times 30+23}{30}}+\frac{4.75+\frac{7\times 2+1}{2}}{\frac{33}{\frac{4\times 7+5}{7}}}$$

Since \frac{205}{200} and \frac{1}{200} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{\frac{6}{5}}{\frac{205-1}{200}}\times 1.7}{\frac{5}{6}+\frac{1\times 3+1}{3}-\frac{1\times 30+23}{30}}+\frac{4.75+\frac{7\times 2+1}{2}}{\frac{33}{\frac{4\times 7+5}{7}}}$$

Subtract 1 from 205 to get 204.

$$\frac{\frac{\frac{6}{5}}{\frac{204}{200}}\times 1.7}{\frac{5}{6}+\frac{1\times 3+1}{3}-\frac{1\times 30+23}{30}}+\frac{4.75+\frac{7\times 2+1}{2}}{\frac{33}{\frac{4\times 7+5}{7}}}$$

Reduce the fraction \frac{204}{200} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{\frac{6}{5}}{\frac{51}{50}}\times 1.7}{\frac{5}{6}+\frac{1\times 3+1}{3}-\frac{1\times 30+23}{30}}+\frac{4.75+\frac{7\times 2+1}{2}}{\frac{33}{\frac{4\times 7+5}{7}}}$$

Divide \frac{6}{5} by \frac{51}{50} by multiplying \frac{6}{5} by the reciprocal of \frac{51}{50}.

$$\frac{\frac{6}{5}\times \frac{50}{51}\times 1.7}{\frac{5}{6}+\frac{1\times 3+1}{3}-\frac{1\times 30+23}{30}}+\frac{4.75+\frac{7\times 2+1}{2}}{\frac{33}{\frac{4\times 7+5}{7}}}$$

Multiply \frac{6}{5} times \frac{50}{51} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{6\times 50}{5\times 51}\times 1.7}{\frac{5}{6}+\frac{1\times 3+1}{3}-\frac{1\times 30+23}{30}}+\frac{4.75+\frac{7\times 2+1}{2}}{\frac{33}{\frac{4\times 7+5}{7}}}$$

Do the multiplications in the fraction \frac{6\times 50}{5\times 51}.

$$\frac{\frac{300}{255}\times 1.7}{\frac{5}{6}+\frac{1\times 3+1}{3}-\frac{1\times 30+23}{30}}+\frac{4.75+\frac{7\times 2+1}{2}}{\frac{33}{\frac{4\times 7+5}{7}}}$$

Reduce the fraction \frac{300}{255} to lowest terms by extracting and canceling out 15.

$$\frac{\frac{20}{17}\times 1.7}{\frac{5}{6}+\frac{1\times 3+1}{3}-\frac{1\times 30+23}{30}}+\frac{4.75+\frac{7\times 2+1}{2}}{\frac{33}{\frac{4\times 7+5}{7}}}$$

Convert decimal number 1.7 to fraction \frac{17}{10}.

$$\frac{\frac{20}{17}\times \frac{17}{10}}{\frac{5}{6}+\frac{1\times 3+1}{3}-\frac{1\times 30+23}{30}}+\frac{4.75+\frac{7\times 2+1}{2}}{\frac{33}{\frac{4\times 7+5}{7}}}$$

Multiply \frac{20}{17} times \frac{17}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{20\times 17}{17\times 10}}{\frac{5}{6}+\frac{1\times 3+1}{3}-\frac{1\times 30+23}{30}}+\frac{4.75+\frac{7\times 2+1}{2}}{\frac{33}{\frac{4\times 7+5}{7}}}$$

Cancel out 17 in both numerator and denominator.

$$\frac{\frac{20}{10}}{\frac{5}{6}+\frac{1\times 3+1}{3}-\frac{1\times 30+23}{30}}+\frac{4.75+\frac{7\times 2+1}{2}}{\frac{33}{\frac{4\times 7+5}{7}}}$$

Divide 20 by 10 to get 2.

$$\frac{2}{\frac{5}{6}+\frac{1\times 3+1}{3}-\frac{1\times 30+23}{30}}+\frac{4.75+\frac{7\times 2+1}{2}}{\frac{33}{\frac{4\times 7+5}{7}}}$$

Multiply 1 and 3 to get 3.

$$\frac{2}{\frac{5}{6}+\frac{3+1}{3}-\frac{1\times 30+23}{30}}+\frac{4.75+\frac{7\times 2+1}{2}}{\frac{33}{\frac{4\times 7+5}{7}}}$$

Add 3 and 1 to get 4.

$$\frac{2}{\frac{5}{6}+\frac{4}{3}-\frac{1\times 30+23}{30}}+\frac{4.75+\frac{7\times 2+1}{2}}{\frac{33}{\frac{4\times 7+5}{7}}}$$

Least common multiple of 6 and 3 is 6. Convert \frac{5}{6} and \frac{4}{3} to fractions with denominator 6.

$$\frac{2}{\frac{5}{6}+\frac{8}{6}-\frac{1\times 30+23}{30}}+\frac{4.75+\frac{7\times 2+1}{2}}{\frac{33}{\frac{4\times 7+5}{7}}}$$

Since \frac{5}{6} and \frac{8}{6} have the same denominator, add them by adding their numerators.

$$\frac{2}{\frac{5+8}{6}-\frac{1\times 30+23}{30}}+\frac{4.75+\frac{7\times 2+1}{2}}{\frac{33}{\frac{4\times 7+5}{7}}}$$

Add 5 and 8 to get 13.

$$\frac{2}{\frac{13}{6}-\frac{1\times 30+23}{30}}+\frac{4.75+\frac{7\times 2+1}{2}}{\frac{33}{\frac{4\times 7+5}{7}}}$$

Multiply 1 and 30 to get 30.

$$\frac{2}{\frac{13}{6}-\frac{30+23}{30}}+\frac{4.75+\frac{7\times 2+1}{2}}{\frac{33}{\frac{4\times 7+5}{7}}}$$

Add 30 and 23 to get 53.

$$\frac{2}{\frac{13}{6}-\frac{53}{30}}+\frac{4.75+\frac{7\times 2+1}{2}}{\frac{33}{\frac{4\times 7+5}{7}}}$$

Least common multiple of 6 and 30 is 30. Convert \frac{13}{6} and \frac{53}{30} to fractions with denominator 30.

$$\frac{2}{\frac{65}{30}-\frac{53}{30}}+\frac{4.75+\frac{7\times 2+1}{2}}{\frac{33}{\frac{4\times 7+5}{7}}}$$

Since \frac{65}{30} and \frac{53}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2}{\frac{65-53}{30}}+\frac{4.75+\frac{7\times 2+1}{2}}{\frac{33}{\frac{4\times 7+5}{7}}}$$

Subtract 53 from 65 to get 12.

$$\frac{2}{\frac{12}{30}}+\frac{4.75+\frac{7\times 2+1}{2}}{\frac{33}{\frac{4\times 7+5}{7}}}$$

Reduce the fraction \frac{12}{30} to lowest terms by extracting and canceling out 6.

$$\frac{2}{\frac{2}{5}}+\frac{4.75+\frac{7\times 2+1}{2}}{\frac{33}{\frac{4\times 7+5}{7}}}$$

Divide 2 by \frac{2}{5} by multiplying 2 by the reciprocal of \frac{2}{5}.

$$2\times \frac{5}{2}+\frac{4.75+\frac{7\times 2+1}{2}}{\frac{33}{\frac{4\times 7+5}{7}}}$$

Cancel out 2 and 2.

$$5+\frac{4.75+\frac{7\times 2+1}{2}}{\frac{33}{\frac{4\times 7+5}{7}}}$$

Multiply 7 and 2 to get 14.

$$5+\frac{4.75+\frac{14+1}{2}}{\frac{33}{\frac{4\times 7+5}{7}}}$$

Add 14 and 1 to get 15.

$$5+\frac{4.75+\frac{15}{2}}{\frac{33}{\frac{4\times 7+5}{7}}}$$

Convert decimal number 4.75 to fraction \frac{475}{100}. Reduce the fraction \frac{475}{100} to lowest terms by extracting and canceling out 25.

$$5+\frac{\frac{19}{4}+\frac{15}{2}}{\frac{33}{\frac{4\times 7+5}{7}}}$$

Least common multiple of 4 and 2 is 4. Convert \frac{19}{4} and \frac{15}{2} to fractions with denominator 4.

$$5+\frac{\frac{19}{4}+\frac{30}{4}}{\frac{33}{\frac{4\times 7+5}{7}}}$$

Since \frac{19}{4} and \frac{30}{4} have the same denominator, add them by adding their numerators.

$$5+\frac{\frac{19+30}{4}}{\frac{33}{\frac{4\times 7+5}{7}}}$$

Add 19 and 30 to get 49.

$$5+\frac{\frac{49}{4}}{\frac{33}{\frac{4\times 7+5}{7}}}$$

Divide 33 by \frac{4\times 7+5}{7} by multiplying 33 by the reciprocal of \frac{4\times 7+5}{7}.

$$5+\frac{\frac{49}{4}}{\frac{33\times 7}{4\times 7+5}}$$

Multiply 33 and 7 to get 231.

$$5+\frac{\frac{49}{4}}{\frac{231}{4\times 7+5}}$$

Multiply 4 and 7 to get 28.

$$5+\frac{\frac{49}{4}}{\frac{231}{28+5}}$$

Add 28 and 5 to get 33.

$$5+\frac{\frac{49}{4}}{\frac{231}{33}}$$

Divide 231 by 33 to get 7.

$$5+\frac{\frac{49}{4}}{7}$$

Express \frac{\frac{49}{4}}{7} as a single fraction.

$$5+\frac{49}{4\times 7}$$

Multiply 4 and 7 to get 28.

$$5+\frac{49}{28}$$

Reduce the fraction \frac{49}{28} to lowest terms by extracting and canceling out 7.

$$5+\frac{7}{4}$$

Convert 5 to fraction \frac{20}{4}.

$$\frac{20}{4}+\frac{7}{4}$$

Since \frac{20}{4} and \frac{7}{4} have the same denominator, add them by adding their numerators.

$$\frac{20+7}{4}$$

Add 20 and 7 to get 27.

$$\frac{27}{4}$$

Factor

$$\frac{3 ^ {3}}{2 ^ {2}} = 6\frac{3}{4} = 6.75$$