Solve 61/4-(32/5-23/20)-43/10*(1frac{3}{4}+2frac{3}{20}-3frac{9}{10})=

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

Evaluate

$$5$$

Solution Steps

Multiply 6 and 4 to get 24.

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

Add 24 and 1 to get 25.

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

Multiply 3 and 5 to get 15.

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

Add 15 and 2 to get 17.

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

Multiply 2 and 20 to get 40.

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

Add 40 and 3 to get 43.

$$\frac{25}{4}-\left(\frac{17}{5}-\frac{43}{20}\right)-\frac{4\times 10+3}{10}\left(\frac{1\times 4+3}{4}+\frac{2\times 20+3}{20}-\frac{3\times 10+9}{10}\right)$$

Least common multiple of 5 and 20 is 20. Convert \frac{17}{5} and \frac{43}{20} to fractions with denominator 20.

$$\frac{25}{4}-\left(\frac{68}{20}-\frac{43}{20}\right)-\frac{4\times 10+3}{10}\left(\frac{1\times 4+3}{4}+\frac{2\times 20+3}{20}-\frac{3\times 10+9}{10}\right)$$

Since \frac{68}{20} and \frac{43}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{25}{4}-\frac{68-43}{20}-\frac{4\times 10+3}{10}\left(\frac{1\times 4+3}{4}+\frac{2\times 20+3}{20}-\frac{3\times 10+9}{10}\right)$$

Subtract 43 from 68 to get 25.

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

Reduce the fraction \frac{25}{20} to lowest terms by extracting and canceling out 5.

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

Since \frac{25}{4} and \frac{5}{4} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 5 from 25 to get 20.

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

Divide 20 by 4 to get 5.

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

Multiply 4 and 10 to get 40.

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

Add 40 and 3 to get 43.

$$5-\frac{43}{10}\left(\frac{1\times 4+3}{4}+\frac{2\times 20+3}{20}-\frac{3\times 10+9}{10}\right)$$

Multiply 1 and 4 to get 4.

$$5-\frac{43}{10}\left(\frac{4+3}{4}+\frac{2\times 20+3}{20}-\frac{3\times 10+9}{10}\right)$$

Add 4 and 3 to get 7.

$$5-\frac{43}{10}\left(\frac{7}{4}+\frac{2\times 20+3}{20}-\frac{3\times 10+9}{10}\right)$$

Multiply 2 and 20 to get 40.

$$5-\frac{43}{10}\left(\frac{7}{4}+\frac{40+3}{20}-\frac{3\times 10+9}{10}\right)$$

Add 40 and 3 to get 43.

$$5-\frac{43}{10}\left(\frac{7}{4}+\frac{43}{20}-\frac{3\times 10+9}{10}\right)$$

Least common multiple of 4 and 20 is 20. Convert \frac{7}{4} and \frac{43}{20} to fractions with denominator 20.

$$5-\frac{43}{10}\left(\frac{35}{20}+\frac{43}{20}-\frac{3\times 10+9}{10}\right)$$

Since \frac{35}{20} and \frac{43}{20} have the same denominator, add them by adding their numerators.

$$5-\frac{43}{10}\left(\frac{35+43}{20}-\frac{3\times 10+9}{10}\right)$$

Add 35 and 43 to get 78.

$$5-\frac{43}{10}\left(\frac{78}{20}-\frac{3\times 10+9}{10}\right)$$

Reduce the fraction \frac{78}{20} to lowest terms by extracting and canceling out 2.

$$5-\frac{43}{10}\left(\frac{39}{10}-\frac{3\times 10+9}{10}\right)$$

Multiply 3 and 10 to get 30.

$$5-\frac{43}{10}\left(\frac{39}{10}-\frac{30+9}{10}\right)$$

Add 30 and 9 to get 39.

$$5-\frac{43}{10}\left(\frac{39}{10}-\frac{39}{10}\right)$$

Subtract \frac{39}{10} from \frac{39}{10} to get 0.

$$5-\frac{43}{10}\times 0$$

Multiply \frac{43}{10} and 0 to get 0.

$$5-0$$

Subtract 0 from 5 to get 5.

$$5$$

Factor

$$5$$