Solve (42/3+0.75)*39/13/(5frac{4{45}-41/6)div5frac{8}{15}}div34frac{2}{7}

$$\frac { ( 4 \frac { 2 } { 3 } + 0.75 ) \times 3 \frac { 9 } { 13 } } { ( 5 \frac { 4 } { 45 } - 4 \frac { 1 } { 6 } ) \div 5 \frac { 8 } { 15 } } \div 34 \frac { 2 } { 7 }$$

Evaluate

$$3.5$$

Solution Steps

Divide \frac{\left(\frac{4\times 3+2}{3}+0.75\right)\times \frac{3\times 13+9}{13}}{\frac{\frac{5\times 45+4}{45}-\frac{4\times 6+1}{6}}{\frac{5\times 15+8}{15}}} by \frac{34\times 7+2}{7} by multiplying \frac{\left(\frac{4\times 3+2}{3}+0.75\right)\times \frac{3\times 13+9}{13}}{\frac{\frac{5\times 45+4}{45}-\frac{4\times 6+1}{6}}{\frac{5\times 15+8}{15}}} by the reciprocal of \frac{34\times 7+2}{7}.

$$\frac{\left(\frac{4\times 3+2}{3}+0.75\right)\times \frac{3\times 13+9}{13}\times 7}{\frac{\frac{5\times 45+4}{45}-\frac{4\times 6+1}{6}}{\frac{5\times 15+8}{15}}\left(34\times 7+2\right)}$$

Multiply 4 and 3 to get 12.

$$\frac{\left(\frac{12+2}{3}+0.75\right)\times \frac{3\times 13+9}{13}\times 7}{\frac{\frac{5\times 45+4}{45}-\frac{4\times 6+1}{6}}{\frac{5\times 15+8}{15}}\left(34\times 7+2\right)}$$

Add 12 and 2 to get 14.

$$\frac{\left(\frac{14}{3}+0.75\right)\times \frac{3\times 13+9}{13}\times 7}{\frac{\frac{5\times 45+4}{45}-\frac{4\times 6+1}{6}}{\frac{5\times 15+8}{15}}\left(34\times 7+2\right)}$$

Convert decimal number 0.75 to fraction \frac{75}{100}. Reduce the fraction \frac{75}{100} to lowest terms by extracting and canceling out 25.

$$\frac{\left(\frac{14}{3}+\frac{3}{4}\right)\times \frac{3\times 13+9}{13}\times 7}{\frac{\frac{5\times 45+4}{45}-\frac{4\times 6+1}{6}}{\frac{5\times 15+8}{15}}\left(34\times 7+2\right)}$$

Least common multiple of 3 and 4 is 12. Convert \frac{14}{3} and \frac{3}{4} to fractions with denominator 12.

$$\frac{\left(\frac{56}{12}+\frac{9}{12}\right)\times \frac{3\times 13+9}{13}\times 7}{\frac{\frac{5\times 45+4}{45}-\frac{4\times 6+1}{6}}{\frac{5\times 15+8}{15}}\left(34\times 7+2\right)}$$

Since \frac{56}{12} and \frac{9}{12} have the same denominator, add them by adding their numerators.

$$\frac{\frac{56+9}{12}\times \frac{3\times 13+9}{13}\times 7}{\frac{\frac{5\times 45+4}{45}-\frac{4\times 6+1}{6}}{\frac{5\times 15+8}{15}}\left(34\times 7+2\right)}$$

Add 56 and 9 to get 65.

$$\frac{\frac{65}{12}\times \frac{3\times 13+9}{13}\times 7}{\frac{\frac{5\times 45+4}{45}-\frac{4\times 6+1}{6}}{\frac{5\times 15+8}{15}}\left(34\times 7+2\right)}$$

Multiply 3 and 13 to get 39.

$$\frac{\frac{65}{12}\times \frac{39+9}{13}\times 7}{\frac{\frac{5\times 45+4}{45}-\frac{4\times 6+1}{6}}{\frac{5\times 15+8}{15}}\left(34\times 7+2\right)}$$

Add 39 and 9 to get 48.

$$\frac{\frac{65}{12}\times \frac{48}{13}\times 7}{\frac{\frac{5\times 45+4}{45}-\frac{4\times 6+1}{6}}{\frac{5\times 15+8}{15}}\left(34\times 7+2\right)}$$

Multiply \frac{65}{12} times \frac{48}{13} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{65\times 48}{12\times 13}\times 7}{\frac{\frac{5\times 45+4}{45}-\frac{4\times 6+1}{6}}{\frac{5\times 15+8}{15}}\left(34\times 7+2\right)}$$

Do the multiplications in the fraction \frac{65\times 48}{12\times 13}.

$$\frac{\frac{3120}{156}\times 7}{\frac{\frac{5\times 45+4}{45}-\frac{4\times 6+1}{6}}{\frac{5\times 15+8}{15}}\left(34\times 7+2\right)}$$

Divide 3120 by 156 to get 20.

$$\frac{20\times 7}{\frac{\frac{5\times 45+4}{45}-\frac{4\times 6+1}{6}}{\frac{5\times 15+8}{15}}\left(34\times 7+2\right)}$$

Multiply 20 and 7 to get 140.

$$\frac{140}{\frac{\frac{5\times 45+4}{45}-\frac{4\times 6+1}{6}}{\frac{5\times 15+8}{15}}\left(34\times 7+2\right)}$$

Multiply 5 and 45 to get 225.

$$\frac{140}{\frac{\frac{225+4}{45}-\frac{4\times 6+1}{6}}{\frac{5\times 15+8}{15}}\left(34\times 7+2\right)}$$

Add 225 and 4 to get 229.

$$\frac{140}{\frac{\frac{229}{45}-\frac{4\times 6+1}{6}}{\frac{5\times 15+8}{15}}\left(34\times 7+2\right)}$$

Multiply 4 and 6 to get 24.

$$\frac{140}{\frac{\frac{229}{45}-\frac{24+1}{6}}{\frac{5\times 15+8}{15}}\left(34\times 7+2\right)}$$

Add 24 and 1 to get 25.

$$\frac{140}{\frac{\frac{229}{45}-\frac{25}{6}}{\frac{5\times 15+8}{15}}\left(34\times 7+2\right)}$$

Least common multiple of 45 and 6 is 90. Convert \frac{229}{45} and \frac{25}{6} to fractions with denominator 90.

$$\frac{140}{\frac{\frac{458}{90}-\frac{375}{90}}{\frac{5\times 15+8}{15}}\left(34\times 7+2\right)}$$

Since \frac{458}{90} and \frac{375}{90} have the same denominator, subtract them by subtracting their numerators.

$$\frac{140}{\frac{\frac{458-375}{90}}{\frac{5\times 15+8}{15}}\left(34\times 7+2\right)}$$

Subtract 375 from 458 to get 83.

$$\frac{140}{\frac{\frac{83}{90}}{\frac{5\times 15+8}{15}}\left(34\times 7+2\right)}$$

Multiply 5 and 15 to get 75.

$$\frac{140}{\frac{\frac{83}{90}}{\frac{75+8}{15}}\left(34\times 7+2\right)}$$

Add 75 and 8 to get 83.

$$\frac{140}{\frac{\frac{83}{90}}{\frac{83}{15}}\left(34\times 7+2\right)}$$

Divide \frac{83}{90} by \frac{83}{15} by multiplying \frac{83}{90} by the reciprocal of \frac{83}{15}.

$$\frac{140}{\frac{83}{90}\times \frac{15}{83}\left(34\times 7+2\right)}$$

Multiply \frac{83}{90} times \frac{15}{83} by multiplying numerator times numerator and denominator times denominator.

$$\frac{140}{\frac{83\times 15}{90\times 83}\left(34\times 7+2\right)}$$

Cancel out 83 in both numerator and denominator.

$$\frac{140}{\frac{15}{90}\left(34\times 7+2\right)}$$

Reduce the fraction \frac{15}{90} to lowest terms by extracting and canceling out 15.

$$\frac{140}{\frac{1}{6}\left(34\times 7+2\right)}$$

Multiply 34 and 7 to get 238.

$$\frac{140}{\frac{1}{6}\left(238+2\right)}$$

Add 238 and 2 to get 240.

$$\frac{140}{\frac{1}{6}\times 240}$$

Multiply \frac{1}{6} and 240 to get \frac{240}{6}.

$$\frac{140}{\frac{240}{6}}$$

Divide 240 by 6 to get 40.

$$\frac{140}{40}$$

Reduce the fraction \frac{140}{40} to lowest terms by extracting and canceling out 20.

$$\frac{7}{2}$$

Factor

$$\frac{7}{2} = 3\frac{1}{2} = 3.5$$