Solve (121/2-35/6)-(28/9+14/5)-(5frac{5}{8}-4frac{3}{4})-(6frac{9}{40}-5frac{11}{90})

$$( 12 \frac { 1 } { 2 } - 3 \frac { 5 } { 6 } ) - ( 2 \frac { 8 } { 9 } + 1 \frac { 4 } { 5 } ) - ( 5 \frac { 5 } { 8 } - 4 \frac { 3 } { 4 } ) - ( 6 \frac { 9 } { 40 } - 5 \frac { 11 } { 90 } )$$

Evaluate

$$2$$

Solution Steps

Multiply 12 and 2 to get 24.

$$\frac{24+1}{2}-\frac{3\times 6+5}{6}-\left(\frac{2\times 9+8}{9}+\frac{1\times 5+4}{5}\right)-\left(\frac{5\times 8+5}{8}-\frac{4\times 4+3}{4}\right)-\left(\frac{6\times 40+9}{40}-\frac{5\times 90+11}{90}\right)$$

Add 24 and 1 to get 25.

$$\frac{25}{2}-\frac{3\times 6+5}{6}-\left(\frac{2\times 9+8}{9}+\frac{1\times 5+4}{5}\right)-\left(\frac{5\times 8+5}{8}-\frac{4\times 4+3}{4}\right)-\left(\frac{6\times 40+9}{40}-\frac{5\times 90+11}{90}\right)$$

Multiply 3 and 6 to get 18.

$$\frac{25}{2}-\frac{18+5}{6}-\left(\frac{2\times 9+8}{9}+\frac{1\times 5+4}{5}\right)-\left(\frac{5\times 8+5}{8}-\frac{4\times 4+3}{4}\right)-\left(\frac{6\times 40+9}{40}-\frac{5\times 90+11}{90}\right)$$

Add 18 and 5 to get 23.

$$\frac{25}{2}-\frac{23}{6}-\left(\frac{2\times 9+8}{9}+\frac{1\times 5+4}{5}\right)-\left(\frac{5\times 8+5}{8}-\frac{4\times 4+3}{4}\right)-\left(\frac{6\times 40+9}{40}-\frac{5\times 90+11}{90}\right)$$

Least common multiple of 2 and 6 is 6. Convert \frac{25}{2} and \frac{23}{6} to fractions with denominator 6.

$$\frac{75}{6}-\frac{23}{6}-\left(\frac{2\times 9+8}{9}+\frac{1\times 5+4}{5}\right)-\left(\frac{5\times 8+5}{8}-\frac{4\times 4+3}{4}\right)-\left(\frac{6\times 40+9}{40}-\frac{5\times 90+11}{90}\right)$$

Since \frac{75}{6} and \frac{23}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{75-23}{6}-\left(\frac{2\times 9+8}{9}+\frac{1\times 5+4}{5}\right)-\left(\frac{5\times 8+5}{8}-\frac{4\times 4+3}{4}\right)-\left(\frac{6\times 40+9}{40}-\frac{5\times 90+11}{90}\right)$$

Subtract 23 from 75 to get 52.

$$\frac{52}{6}-\left(\frac{2\times 9+8}{9}+\frac{1\times 5+4}{5}\right)-\left(\frac{5\times 8+5}{8}-\frac{4\times 4+3}{4}\right)-\left(\frac{6\times 40+9}{40}-\frac{5\times 90+11}{90}\right)$$

Reduce the fraction \frac{52}{6} to lowest terms by extracting and canceling out 2.

$$\frac{26}{3}-\left(\frac{2\times 9+8}{9}+\frac{1\times 5+4}{5}\right)-\left(\frac{5\times 8+5}{8}-\frac{4\times 4+3}{4}\right)-\left(\frac{6\times 40+9}{40}-\frac{5\times 90+11}{90}\right)$$

Multiply 2 and 9 to get 18.

$$\frac{26}{3}-\left(\frac{18+8}{9}+\frac{1\times 5+4}{5}\right)-\left(\frac{5\times 8+5}{8}-\frac{4\times 4+3}{4}\right)-\left(\frac{6\times 40+9}{40}-\frac{5\times 90+11}{90}\right)$$

Add 18 and 8 to get 26.

$$\frac{26}{3}-\left(\frac{26}{9}+\frac{1\times 5+4}{5}\right)-\left(\frac{5\times 8+5}{8}-\frac{4\times 4+3}{4}\right)-\left(\frac{6\times 40+9}{40}-\frac{5\times 90+11}{90}\right)$$

Multiply 1 and 5 to get 5.

$$\frac{26}{3}-\left(\frac{26}{9}+\frac{5+4}{5}\right)-\left(\frac{5\times 8+5}{8}-\frac{4\times 4+3}{4}\right)-\left(\frac{6\times 40+9}{40}-\frac{5\times 90+11}{90}\right)$$

Add 5 and 4 to get 9.

$$\frac{26}{3}-\left(\frac{26}{9}+\frac{9}{5}\right)-\left(\frac{5\times 8+5}{8}-\frac{4\times 4+3}{4}\right)-\left(\frac{6\times 40+9}{40}-\frac{5\times 90+11}{90}\right)$$

Least common multiple of 9 and 5 is 45. Convert \frac{26}{9} and \frac{9}{5} to fractions with denominator 45.

$$\frac{26}{3}-\left(\frac{130}{45}+\frac{81}{45}\right)-\left(\frac{5\times 8+5}{8}-\frac{4\times 4+3}{4}\right)-\left(\frac{6\times 40+9}{40}-\frac{5\times 90+11}{90}\right)$$

Since \frac{130}{45} and \frac{81}{45} have the same denominator, add them by adding their numerators.

$$\frac{26}{3}-\frac{130+81}{45}-\left(\frac{5\times 8+5}{8}-\frac{4\times 4+3}{4}\right)-\left(\frac{6\times 40+9}{40}-\frac{5\times 90+11}{90}\right)$$

Add 130 and 81 to get 211.

$$\frac{26}{3}-\frac{211}{45}-\left(\frac{5\times 8+5}{8}-\frac{4\times 4+3}{4}\right)-\left(\frac{6\times 40+9}{40}-\frac{5\times 90+11}{90}\right)$$

Least common multiple of 3 and 45 is 45. Convert \frac{26}{3} and \frac{211}{45} to fractions with denominator 45.

$$\frac{390}{45}-\frac{211}{45}-\left(\frac{5\times 8+5}{8}-\frac{4\times 4+3}{4}\right)-\left(\frac{6\times 40+9}{40}-\frac{5\times 90+11}{90}\right)$$

Since \frac{390}{45} and \frac{211}{45} have the same denominator, subtract them by subtracting their numerators.

$$\frac{390-211}{45}-\left(\frac{5\times 8+5}{8}-\frac{4\times 4+3}{4}\right)-\left(\frac{6\times 40+9}{40}-\frac{5\times 90+11}{90}\right)$$

Subtract 211 from 390 to get 179.

$$\frac{179}{45}-\left(\frac{5\times 8+5}{8}-\frac{4\times 4+3}{4}\right)-\left(\frac{6\times 40+9}{40}-\frac{5\times 90+11}{90}\right)$$

Multiply 5 and 8 to get 40.

$$\frac{179}{45}-\left(\frac{40+5}{8}-\frac{4\times 4+3}{4}\right)-\left(\frac{6\times 40+9}{40}-\frac{5\times 90+11}{90}\right)$$

Add 40 and 5 to get 45.

$$\frac{179}{45}-\left(\frac{45}{8}-\frac{4\times 4+3}{4}\right)-\left(\frac{6\times 40+9}{40}-\frac{5\times 90+11}{90}\right)$$

Multiply 4 and 4 to get 16.

$$\frac{179}{45}-\left(\frac{45}{8}-\frac{16+3}{4}\right)-\left(\frac{6\times 40+9}{40}-\frac{5\times 90+11}{90}\right)$$

Add 16 and 3 to get 19.

$$\frac{179}{45}-\left(\frac{45}{8}-\frac{19}{4}\right)-\left(\frac{6\times 40+9}{40}-\frac{5\times 90+11}{90}\right)$$

Least common multiple of 8 and 4 is 8. Convert \frac{45}{8} and \frac{19}{4} to fractions with denominator 8.

$$\frac{179}{45}-\left(\frac{45}{8}-\frac{38}{8}\right)-\left(\frac{6\times 40+9}{40}-\frac{5\times 90+11}{90}\right)$$

Since \frac{45}{8} and \frac{38}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{179}{45}-\frac{45-38}{8}-\left(\frac{6\times 40+9}{40}-\frac{5\times 90+11}{90}\right)$$

Subtract 38 from 45 to get 7.

$$\frac{179}{45}-\frac{7}{8}-\left(\frac{6\times 40+9}{40}-\frac{5\times 90+11}{90}\right)$$

Least common multiple of 45 and 8 is 360. Convert \frac{179}{45} and \frac{7}{8} to fractions with denominator 360.

$$\frac{1432}{360}-\frac{315}{360}-\left(\frac{6\times 40+9}{40}-\frac{5\times 90+11}{90}\right)$$

Since \frac{1432}{360} and \frac{315}{360} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1432-315}{360}-\left(\frac{6\times 40+9}{40}-\frac{5\times 90+11}{90}\right)$$

Subtract 315 from 1432 to get 1117.

$$\frac{1117}{360}-\left(\frac{6\times 40+9}{40}-\frac{5\times 90+11}{90}\right)$$

Multiply 6 and 40 to get 240.

$$\frac{1117}{360}-\left(\frac{240+9}{40}-\frac{5\times 90+11}{90}\right)$$

Add 240 and 9 to get 249.

$$\frac{1117}{360}-\left(\frac{249}{40}-\frac{5\times 90+11}{90}\right)$$

Multiply 5 and 90 to get 450.

$$\frac{1117}{360}-\left(\frac{249}{40}-\frac{450+11}{90}\right)$$

Add 450 and 11 to get 461.

$$\frac{1117}{360}-\left(\frac{249}{40}-\frac{461}{90}\right)$$

Least common multiple of 40 and 90 is 360. Convert \frac{249}{40} and \frac{461}{90} to fractions with denominator 360.

$$\frac{1117}{360}-\left(\frac{2241}{360}-\frac{1844}{360}\right)$$

Since \frac{2241}{360} and \frac{1844}{360} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1117}{360}-\frac{2241-1844}{360}$$

Subtract 1844 from 2241 to get 397.

$$\frac{1117}{360}-\frac{397}{360}$$

Since \frac{1117}{360} and \frac{397}{360} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1117-397}{360}$$

Subtract 397 from 1117 to get 720.

$$\frac{720}{360}$$

Divide 720 by 360 to get 2.

$$2$$

Factor

$$2$$