Solve 44/5*41/6-42/3:frac{4/15+16frac{1}{2}}{9frac{3}{7}-frac{34}{63}*4frac{1}{2}}*frac{8frac{3}{5}-2frac{1}{5}}{19}:1frac{1}{7}

$$\frac { 4 \frac { 4 } { 5 } \cdot 4 \frac { 1 } { 6 } - 4 \frac { 2 } { 3 } : \frac { 4 } { 15 } + 16 \frac { 1 } { 2 } } { 9 \frac { 3 } { 7 } - \frac { 34 } { 63 } \cdot 4 \frac { 1 } { 2 } } \cdot \frac { 8 \frac { 3 } { 5 } - 2 \frac { 1 } { 5 } } { 19 } : 1 \frac { 1 } { 7 }$$

Evaluate

$$\frac{4}{5}=0.8$$

Solution Steps

Multiply 4 and 5 to get 20.

$$\frac{\frac{\frac{20+4}{5}\times \frac{4\times 6+1}{6}-\frac{\frac{4\times 3+2}{3}}{\frac{4}{15}}+\frac{16\times 2+1}{2}}{\frac{9\times 7+3}{7}-\frac{34}{63}\times \frac{4\times 2+1}{2}}\times \frac{\frac{8\times 5+3}{5}-\frac{2\times 5+1}{5}}{19}}{\frac{1\times 7+1}{7}}$$

Add 20 and 4 to get 24.

$$\frac{\frac{\frac{24}{5}\times \frac{4\times 6+1}{6}-\frac{\frac{4\times 3+2}{3}}{\frac{4}{15}}+\frac{16\times 2+1}{2}}{\frac{9\times 7+3}{7}-\frac{34}{63}\times \frac{4\times 2+1}{2}}\times \frac{\frac{8\times 5+3}{5}-\frac{2\times 5+1}{5}}{19}}{\frac{1\times 7+1}{7}}$$

Multiply 4 and 6 to get 24.

$$\frac{\frac{\frac{24}{5}\times \frac{24+1}{6}-\frac{\frac{4\times 3+2}{3}}{\frac{4}{15}}+\frac{16\times 2+1}{2}}{\frac{9\times 7+3}{7}-\frac{34}{63}\times \frac{4\times 2+1}{2}}\times \frac{\frac{8\times 5+3}{5}-\frac{2\times 5+1}{5}}{19}}{\frac{1\times 7+1}{7}}$$

Add 24 and 1 to get 25.

$$\frac{\frac{\frac{24}{5}\times \frac{25}{6}-\frac{\frac{4\times 3+2}{3}}{\frac{4}{15}}+\frac{16\times 2+1}{2}}{\frac{9\times 7+3}{7}-\frac{34}{63}\times \frac{4\times 2+1}{2}}\times \frac{\frac{8\times 5+3}{5}-\frac{2\times 5+1}{5}}{19}}{\frac{1\times 7+1}{7}}$$

Multiply \frac{24}{5} times \frac{25}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{\frac{24\times 25}{5\times 6}-\frac{\frac{4\times 3+2}{3}}{\frac{4}{15}}+\frac{16\times 2+1}{2}}{\frac{9\times 7+3}{7}-\frac{34}{63}\times \frac{4\times 2+1}{2}}\times \frac{\frac{8\times 5+3}{5}-\frac{2\times 5+1}{5}}{19}}{\frac{1\times 7+1}{7}}$$

Do the multiplications in the fraction \frac{24\times 25}{5\times 6}.

$$\frac{\frac{\frac{600}{30}-\frac{\frac{4\times 3+2}{3}}{\frac{4}{15}}+\frac{16\times 2+1}{2}}{\frac{9\times 7+3}{7}-\frac{34}{63}\times \frac{4\times 2+1}{2}}\times \frac{\frac{8\times 5+3}{5}-\frac{2\times 5+1}{5}}{19}}{\frac{1\times 7+1}{7}}$$

Divide 600 by 30 to get 20.

$$\frac{\frac{20-\frac{\frac{4\times 3+2}{3}}{\frac{4}{15}}+\frac{16\times 2+1}{2}}{\frac{9\times 7+3}{7}-\frac{34}{63}\times \frac{4\times 2+1}{2}}\times \frac{\frac{8\times 5+3}{5}-\frac{2\times 5+1}{5}}{19}}{\frac{1\times 7+1}{7}}$$

Divide \frac{4\times 3+2}{3} by \frac{4}{15} by multiplying \frac{4\times 3+2}{3} by the reciprocal of \frac{4}{15}.

$$\frac{\frac{20-\frac{\left(4\times 3+2\right)\times 15}{3\times 4}+\frac{16\times 2+1}{2}}{\frac{9\times 7+3}{7}-\frac{34}{63}\times \frac{4\times 2+1}{2}}\times \frac{\frac{8\times 5+3}{5}-\frac{2\times 5+1}{5}}{19}}{\frac{1\times 7+1}{7}}$$

Cancel out 3 in both numerator and denominator.

$$\frac{\frac{20-\frac{5\left(2+3\times 4\right)}{4}+\frac{16\times 2+1}{2}}{\frac{9\times 7+3}{7}-\frac{34}{63}\times \frac{4\times 2+1}{2}}\times \frac{\frac{8\times 5+3}{5}-\frac{2\times 5+1}{5}}{19}}{\frac{1\times 7+1}{7}}$$

Multiply 3 and 4 to get 12.

$$\frac{\frac{20-\frac{5\left(2+12\right)}{4}+\frac{16\times 2+1}{2}}{\frac{9\times 7+3}{7}-\frac{34}{63}\times \frac{4\times 2+1}{2}}\times \frac{\frac{8\times 5+3}{5}-\frac{2\times 5+1}{5}}{19}}{\frac{1\times 7+1}{7}}$$

Add 2 and 12 to get 14.

$$\frac{\frac{20-\frac{5\times 14}{4}+\frac{16\times 2+1}{2}}{\frac{9\times 7+3}{7}-\frac{34}{63}\times \frac{4\times 2+1}{2}}\times \frac{\frac{8\times 5+3}{5}-\frac{2\times 5+1}{5}}{19}}{\frac{1\times 7+1}{7}}$$

Multiply 5 and 14 to get 70.

$$\frac{\frac{20-\frac{70}{4}+\frac{16\times 2+1}{2}}{\frac{9\times 7+3}{7}-\frac{34}{63}\times \frac{4\times 2+1}{2}}\times \frac{\frac{8\times 5+3}{5}-\frac{2\times 5+1}{5}}{19}}{\frac{1\times 7+1}{7}}$$

Reduce the fraction \frac{70}{4} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{20-\frac{35}{2}+\frac{16\times 2+1}{2}}{\frac{9\times 7+3}{7}-\frac{34}{63}\times \frac{4\times 2+1}{2}}\times \frac{\frac{8\times 5+3}{5}-\frac{2\times 5+1}{5}}{19}}{\frac{1\times 7+1}{7}}$$

Convert 20 to fraction \frac{40}{2}.

$$\frac{\frac{\frac{40}{2}-\frac{35}{2}+\frac{16\times 2+1}{2}}{\frac{9\times 7+3}{7}-\frac{34}{63}\times \frac{4\times 2+1}{2}}\times \frac{\frac{8\times 5+3}{5}-\frac{2\times 5+1}{5}}{19}}{\frac{1\times 7+1}{7}}$$

Since \frac{40}{2} and \frac{35}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{\frac{40-35}{2}+\frac{16\times 2+1}{2}}{\frac{9\times 7+3}{7}-\frac{34}{63}\times \frac{4\times 2+1}{2}}\times \frac{\frac{8\times 5+3}{5}-\frac{2\times 5+1}{5}}{19}}{\frac{1\times 7+1}{7}}$$

Subtract 35 from 40 to get 5.

$$\frac{\frac{\frac{5}{2}+\frac{16\times 2+1}{2}}{\frac{9\times 7+3}{7}-\frac{34}{63}\times \frac{4\times 2+1}{2}}\times \frac{\frac{8\times 5+3}{5}-\frac{2\times 5+1}{5}}{19}}{\frac{1\times 7+1}{7}}$$

Multiply 16 and 2 to get 32.

$$\frac{\frac{\frac{5}{2}+\frac{32+1}{2}}{\frac{9\times 7+3}{7}-\frac{34}{63}\times \frac{4\times 2+1}{2}}\times \frac{\frac{8\times 5+3}{5}-\frac{2\times 5+1}{5}}{19}}{\frac{1\times 7+1}{7}}$$

Add 32 and 1 to get 33.

$$\frac{\frac{\frac{5}{2}+\frac{33}{2}}{\frac{9\times 7+3}{7}-\frac{34}{63}\times \frac{4\times 2+1}{2}}\times \frac{\frac{8\times 5+3}{5}-\frac{2\times 5+1}{5}}{19}}{\frac{1\times 7+1}{7}}$$

Since \frac{5}{2} and \frac{33}{2} have the same denominator, add them by adding their numerators.

$$\frac{\frac{\frac{5+33}{2}}{\frac{9\times 7+3}{7}-\frac{34}{63}\times \frac{4\times 2+1}{2}}\times \frac{\frac{8\times 5+3}{5}-\frac{2\times 5+1}{5}}{19}}{\frac{1\times 7+1}{7}}$$

Add 5 and 33 to get 38.

$$\frac{\frac{\frac{38}{2}}{\frac{9\times 7+3}{7}-\frac{34}{63}\times \frac{4\times 2+1}{2}}\times \frac{\frac{8\times 5+3}{5}-\frac{2\times 5+1}{5}}{19}}{\frac{1\times 7+1}{7}}$$

Divide 38 by 2 to get 19.

$$\frac{\frac{19}{\frac{9\times 7+3}{7}-\frac{34}{63}\times \frac{4\times 2+1}{2}}\times \frac{\frac{8\times 5+3}{5}-\frac{2\times 5+1}{5}}{19}}{\frac{1\times 7+1}{7}}$$

Multiply 9 and 7 to get 63.

$$\frac{\frac{19}{\frac{63+3}{7}-\frac{34}{63}\times \frac{4\times 2+1}{2}}\times \frac{\frac{8\times 5+3}{5}-\frac{2\times 5+1}{5}}{19}}{\frac{1\times 7+1}{7}}$$

Add 63 and 3 to get 66.

$$\frac{\frac{19}{\frac{66}{7}-\frac{34}{63}\times \frac{4\times 2+1}{2}}\times \frac{\frac{8\times 5+3}{5}-\frac{2\times 5+1}{5}}{19}}{\frac{1\times 7+1}{7}}$$

Multiply 4 and 2 to get 8.

$$\frac{\frac{19}{\frac{66}{7}-\frac{34}{63}\times \frac{8+1}{2}}\times \frac{\frac{8\times 5+3}{5}-\frac{2\times 5+1}{5}}{19}}{\frac{1\times 7+1}{7}}$$

Add 8 and 1 to get 9.

$$\frac{\frac{19}{\frac{66}{7}-\frac{34}{63}\times \frac{9}{2}}\times \frac{\frac{8\times 5+3}{5}-\frac{2\times 5+1}{5}}{19}}{\frac{1\times 7+1}{7}}$$

Multiply \frac{34}{63} times \frac{9}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{19}{\frac{66}{7}-\frac{34\times 9}{63\times 2}}\times \frac{\frac{8\times 5+3}{5}-\frac{2\times 5+1}{5}}{19}}{\frac{1\times 7+1}{7}}$$

Do the multiplications in the fraction \frac{34\times 9}{63\times 2}.

$$\frac{\frac{19}{\frac{66}{7}-\frac{306}{126}}\times \frac{\frac{8\times 5+3}{5}-\frac{2\times 5+1}{5}}{19}}{\frac{1\times 7+1}{7}}$$

Reduce the fraction \frac{306}{126} to lowest terms by extracting and canceling out 18.

$$\frac{\frac{19}{\frac{66}{7}-\frac{17}{7}}\times \frac{\frac{8\times 5+3}{5}-\frac{2\times 5+1}{5}}{19}}{\frac{1\times 7+1}{7}}$$

Since \frac{66}{7} and \frac{17}{7} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{19}{\frac{66-17}{7}}\times \frac{\frac{8\times 5+3}{5}-\frac{2\times 5+1}{5}}{19}}{\frac{1\times 7+1}{7}}$$

Subtract 17 from 66 to get 49.

$$\frac{\frac{19}{\frac{49}{7}}\times \frac{\frac{8\times 5+3}{5}-\frac{2\times 5+1}{5}}{19}}{\frac{1\times 7+1}{7}}$$

Divide 49 by 7 to get 7.

$$\frac{\frac{19}{7}\times \frac{\frac{8\times 5+3}{5}-\frac{2\times 5+1}{5}}{19}}{\frac{1\times 7+1}{7}}$$

Multiply 8 and 5 to get 40.

$$\frac{\frac{19}{7}\times \frac{\frac{40+3}{5}-\frac{2\times 5+1}{5}}{19}}{\frac{1\times 7+1}{7}}$$

Add 40 and 3 to get 43.

$$\frac{\frac{19}{7}\times \frac{\frac{43}{5}-\frac{2\times 5+1}{5}}{19}}{\frac{1\times 7+1}{7}}$$

Multiply 2 and 5 to get 10.

$$\frac{\frac{19}{7}\times \frac{\frac{43}{5}-\frac{10+1}{5}}{19}}{\frac{1\times 7+1}{7}}$$

Add 10 and 1 to get 11.

$$\frac{\frac{19}{7}\times \frac{\frac{43}{5}-\frac{11}{5}}{19}}{\frac{1\times 7+1}{7}}$$

Since \frac{43}{5} and \frac{11}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{19}{7}\times \frac{\frac{43-11}{5}}{19}}{\frac{1\times 7+1}{7}}$$

Subtract 11 from 43 to get 32.

$$\frac{\frac{19}{7}\times \frac{\frac{32}{5}}{19}}{\frac{1\times 7+1}{7}}$$

Express \frac{\frac{32}{5}}{19} as a single fraction.

$$\frac{\frac{19}{7}\times \frac{32}{5\times 19}}{\frac{1\times 7+1}{7}}$$

Multiply 5 and 19 to get 95.

$$\frac{\frac{19}{7}\times \frac{32}{95}}{\frac{1\times 7+1}{7}}$$

Multiply \frac{19}{7} times \frac{32}{95} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{19\times 32}{7\times 95}}{\frac{1\times 7+1}{7}}$$

Do the multiplications in the fraction \frac{19\times 32}{7\times 95}.

$$\frac{\frac{608}{665}}{\frac{1\times 7+1}{7}}$$

Reduce the fraction \frac{608}{665} to lowest terms by extracting and canceling out 19.

$$\frac{\frac{32}{35}}{\frac{1\times 7+1}{7}}$$

Multiply 1 and 7 to get 7.

$$\frac{\frac{32}{35}}{\frac{7+1}{7}}$$

Add 7 and 1 to get 8.

$$\frac{\frac{32}{35}}{\frac{8}{7}}$$

Divide \frac{32}{35} by \frac{8}{7} by multiplying \frac{32}{35} by the reciprocal of \frac{8}{7}.

$$\frac{32}{35}\times \frac{7}{8}$$

Multiply \frac{32}{35} times \frac{7}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{32\times 7}{35\times 8}$$

Do the multiplications in the fraction \frac{32\times 7}{35\times 8}.

$$\frac{224}{280}$$

Reduce the fraction \frac{224}{280} to lowest terms by extracting and canceling out 56.

$$\frac{4}{5}$$

Factor

$$\frac{2 ^ {2}}{5} = 0.8$$