Solve 61/4-(32/5-25/20)-45/10*(1frac{5}{4}+2frac{3}{20}-3frac{9}{10})=

$$6 \frac { 1 } { 4 } - ( 3 \frac { 2 } { 5 } - 2 \frac { 5 } { 20 } ) - 4 \frac { 5 } { 10 } \cdot ( 1 \frac { 5 } { 4 } + 2 \frac { 3 } { 20 } - 3 \frac { 9 } { 10 } ) =$$

Evaluate

$$\frac{57}{20}=2.85$$

Solution Steps

Multiply 6 and 4 to get 24.

$$\frac{24+1}{4}-\left(\frac{3\times 5+2}{5}-\frac{2\times 20+5}{20}\right)-\frac{4\times 10+5}{10}\left(\frac{1\times 4+5}{4}+\frac{2\times 20+3}{20}-\frac{3\times 10+9}{10}\right)$$

Add 24 and 1 to get 25.

$$\frac{25}{4}-\left(\frac{3\times 5+2}{5}-\frac{2\times 20+5}{20}\right)-\frac{4\times 10+5}{10}\left(\frac{1\times 4+5}{4}+\frac{2\times 20+3}{20}-\frac{3\times 10+9}{10}\right)$$

Multiply 3 and 5 to get 15.

$$\frac{25}{4}-\left(\frac{15+2}{5}-\frac{2\times 20+5}{20}\right)-\frac{4\times 10+5}{10}\left(\frac{1\times 4+5}{4}+\frac{2\times 20+3}{20}-\frac{3\times 10+9}{10}\right)$$

Add 15 and 2 to get 17.

$$\frac{25}{4}-\left(\frac{17}{5}-\frac{2\times 20+5}{20}\right)-\frac{4\times 10+5}{10}\left(\frac{1\times 4+5}{4}+\frac{2\times 20+3}{20}-\frac{3\times 10+9}{10}\right)$$

Multiply 2 and 20 to get 40.

$$\frac{25}{4}-\left(\frac{17}{5}-\frac{40+5}{20}\right)-\frac{4\times 10+5}{10}\left(\frac{1\times 4+5}{4}+\frac{2\times 20+3}{20}-\frac{3\times 10+9}{10}\right)$$

Add 40 and 5 to get 45.

$$\frac{25}{4}-\left(\frac{17}{5}-\frac{45}{20}\right)-\frac{4\times 10+5}{10}\left(\frac{1\times 4+5}{4}+\frac{2\times 20+3}{20}-\frac{3\times 10+9}{10}\right)$$

Reduce the fraction \frac{45}{20} to lowest terms by extracting and canceling out 5.

$$\frac{25}{4}-\left(\frac{17}{5}-\frac{9}{4}\right)-\frac{4\times 10+5}{10}\left(\frac{1\times 4+5}{4}+\frac{2\times 20+3}{20}-\frac{3\times 10+9}{10}\right)$$

Least common multiple of 5 and 4 is 20. Convert \frac{17}{5} and \frac{9}{4} to fractions with denominator 20.

$$\frac{25}{4}-\left(\frac{68}{20}-\frac{45}{20}\right)-\frac{4\times 10+5}{10}\left(\frac{1\times 4+5}{4}+\frac{2\times 20+3}{20}-\frac{3\times 10+9}{10}\right)$$

Since \frac{68}{20} and \frac{45}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{25}{4}-\frac{68-45}{20}-\frac{4\times 10+5}{10}\left(\frac{1\times 4+5}{4}+\frac{2\times 20+3}{20}-\frac{3\times 10+9}{10}\right)$$

Subtract 45 from 68 to get 23.

$$\frac{25}{4}-\frac{23}{20}-\frac{4\times 10+5}{10}\left(\frac{1\times 4+5}{4}+\frac{2\times 20+3}{20}-\frac{3\times 10+9}{10}\right)$$

Least common multiple of 4 and 20 is 20. Convert \frac{25}{4} and \frac{23}{20} to fractions with denominator 20.

$$\frac{125}{20}-\frac{23}{20}-\frac{4\times 10+5}{10}\left(\frac{1\times 4+5}{4}+\frac{2\times 20+3}{20}-\frac{3\times 10+9}{10}\right)$$

Since \frac{125}{20} and \frac{23}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{125-23}{20}-\frac{4\times 10+5}{10}\left(\frac{1\times 4+5}{4}+\frac{2\times 20+3}{20}-\frac{3\times 10+9}{10}\right)$$

Subtract 23 from 125 to get 102.

$$\frac{102}{20}-\frac{4\times 10+5}{10}\left(\frac{1\times 4+5}{4}+\frac{2\times 20+3}{20}-\frac{3\times 10+9}{10}\right)$$

Reduce the fraction \frac{102}{20} to lowest terms by extracting and canceling out 2.

$$\frac{51}{10}-\frac{4\times 10+5}{10}\left(\frac{1\times 4+5}{4}+\frac{2\times 20+3}{20}-\frac{3\times 10+9}{10}\right)$$

Multiply 4 and 10 to get 40.

$$\frac{51}{10}-\frac{40+5}{10}\left(\frac{1\times 4+5}{4}+\frac{2\times 20+3}{20}-\frac{3\times 10+9}{10}\right)$$

Add 40 and 5 to get 45.

$$\frac{51}{10}-\frac{45}{10}\left(\frac{1\times 4+5}{4}+\frac{2\times 20+3}{20}-\frac{3\times 10+9}{10}\right)$$

Reduce the fraction \frac{45}{10} to lowest terms by extracting and canceling out 5.

$$\frac{51}{10}-\frac{9}{2}\left(\frac{1\times 4+5}{4}+\frac{2\times 20+3}{20}-\frac{3\times 10+9}{10}\right)$$

Multiply 1 and 4 to get 4.

$$\frac{51}{10}-\frac{9}{2}\left(\frac{4+5}{4}+\frac{2\times 20+3}{20}-\frac{3\times 10+9}{10}\right)$$

Add 4 and 5 to get 9.

$$\frac{51}{10}-\frac{9}{2}\left(\frac{9}{4}+\frac{2\times 20+3}{20}-\frac{3\times 10+9}{10}\right)$$

Multiply 2 and 20 to get 40.

$$\frac{51}{10}-\frac{9}{2}\left(\frac{9}{4}+\frac{40+3}{20}-\frac{3\times 10+9}{10}\right)$$

Add 40 and 3 to get 43.

$$\frac{51}{10}-\frac{9}{2}\left(\frac{9}{4}+\frac{43}{20}-\frac{3\times 10+9}{10}\right)$$

Least common multiple of 4 and 20 is 20. Convert \frac{9}{4} and \frac{43}{20} to fractions with denominator 20.

$$\frac{51}{10}-\frac{9}{2}\left(\frac{45}{20}+\frac{43}{20}-\frac{3\times 10+9}{10}\right)$$

Since \frac{45}{20} and \frac{43}{20} have the same denominator, add them by adding their numerators.

$$\frac{51}{10}-\frac{9}{2}\left(\frac{45+43}{20}-\frac{3\times 10+9}{10}\right)$$

Add 45 and 43 to get 88.

$$\frac{51}{10}-\frac{9}{2}\left(\frac{88}{20}-\frac{3\times 10+9}{10}\right)$$

Reduce the fraction \frac{88}{20} to lowest terms by extracting and canceling out 4.

$$\frac{51}{10}-\frac{9}{2}\left(\frac{22}{5}-\frac{3\times 10+9}{10}\right)$$

Multiply 3 and 10 to get 30.

$$\frac{51}{10}-\frac{9}{2}\left(\frac{22}{5}-\frac{30+9}{10}\right)$$

Add 30 and 9 to get 39.

$$\frac{51}{10}-\frac{9}{2}\left(\frac{22}{5}-\frac{39}{10}\right)$$

Least common multiple of 5 and 10 is 10. Convert \frac{22}{5} and \frac{39}{10} to fractions with denominator 10.

$$\frac{51}{10}-\frac{9}{2}\left(\frac{44}{10}-\frac{39}{10}\right)$$

Since \frac{44}{10} and \frac{39}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{51}{10}-\frac{9}{2}\times \frac{44-39}{10}$$

Subtract 39 from 44 to get 5.

$$\frac{51}{10}-\frac{9}{2}\times \frac{5}{10}$$

Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

$$\frac{51}{10}-\frac{9}{2}\times \frac{1}{2}$$

Multiply \frac{9}{2} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{51}{10}-\frac{9\times 1}{2\times 2}$$

Do the multiplications in the fraction \frac{9\times 1}{2\times 2}.

$$\frac{51}{10}-\frac{9}{4}$$

Least common multiple of 10 and 4 is 20. Convert \frac{51}{10} and \frac{9}{4} to fractions with denominator 20.

$$\frac{102}{20}-\frac{45}{20}$$

Since \frac{102}{20} and \frac{45}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{102-45}{20}$$

Subtract 45 from 102 to get 57.

$$\frac{57}{20}$$

Factor

$$\frac{3 \cdot 19}{2 ^ {2} \cdot 5} = 2\frac{17}{20} = 2.85$$