Solve 101/2-[13/16-(3.875-23/4)]quad105/9-3frac{7}{12}-2frac{5}{18}+3frac{1}{2}-1.75

$$10 \frac { 1 } { 2 } - [ 1 \frac { 3 } { 16 } - ( 3.875 - 2 \frac { 3 } { 4 } ) ] \quad 10 \frac { 5 } { 9 } - 3 \frac { 7 } { 12 } - 2 \frac { 5 } { 18 } + 3 \frac { 1 } { 2 } - 1.75$$

Evaluate

$$\frac{275}{48}\approx 5.729166667$$

Solution Steps

Multiply 10 and 2 to get 20.

$$\frac{20+1}{2}-\left(\frac{1\times 16+3}{16}-\left(3.875-\frac{2\times 4+3}{4}\right)\right)\times \frac{10\times 9+5}{9}-\frac{3\times 12+7}{12}-\frac{2\times 18+5}{18}+\frac{3\times 2+1}{2}-1.75$$

Add 20 and 1 to get 21.

$$\frac{21}{2}-\left(\frac{1\times 16+3}{16}-\left(3.875-\frac{2\times 4+3}{4}\right)\right)\times \frac{10\times 9+5}{9}-\frac{3\times 12+7}{12}-\frac{2\times 18+5}{18}+\frac{3\times 2+1}{2}-1.75$$

Multiply 1 and 16 to get 16.

$$\frac{21}{2}-\left(\frac{16+3}{16}-\left(3.875-\frac{2\times 4+3}{4}\right)\right)\times \frac{10\times 9+5}{9}-\frac{3\times 12+7}{12}-\frac{2\times 18+5}{18}+\frac{3\times 2+1}{2}-1.75$$

Add 16 and 3 to get 19.

$$\frac{21}{2}-\left(\frac{19}{16}-\left(3.875-\frac{2\times 4+3}{4}\right)\right)\times \frac{10\times 9+5}{9}-\frac{3\times 12+7}{12}-\frac{2\times 18+5}{18}+\frac{3\times 2+1}{2}-1.75$$

Multiply 2 and 4 to get 8.

$$\frac{21}{2}-\left(\frac{19}{16}-\left(3.875-\frac{8+3}{4}\right)\right)\times \frac{10\times 9+5}{9}-\frac{3\times 12+7}{12}-\frac{2\times 18+5}{18}+\frac{3\times 2+1}{2}-1.75$$

Add 8 and 3 to get 11.

$$\frac{21}{2}-\left(\frac{19}{16}-\left(3.875-\frac{11}{4}\right)\right)\times \frac{10\times 9+5}{9}-\frac{3\times 12+7}{12}-\frac{2\times 18+5}{18}+\frac{3\times 2+1}{2}-1.75$$

Convert decimal number 3.875 to fraction \frac{3875}{1000}. Reduce the fraction \frac{3875}{1000} to lowest terms by extracting and canceling out 125.

$$\frac{21}{2}-\left(\frac{19}{16}-\left(\frac{31}{8}-\frac{11}{4}\right)\right)\times \frac{10\times 9+5}{9}-\frac{3\times 12+7}{12}-\frac{2\times 18+5}{18}+\frac{3\times 2+1}{2}-1.75$$

Least common multiple of 8 and 4 is 8. Convert \frac{31}{8} and \frac{11}{4} to fractions with denominator 8.

$$\frac{21}{2}-\left(\frac{19}{16}-\left(\frac{31}{8}-\frac{22}{8}\right)\right)\times \frac{10\times 9+5}{9}-\frac{3\times 12+7}{12}-\frac{2\times 18+5}{18}+\frac{3\times 2+1}{2}-1.75$$

Since \frac{31}{8} and \frac{22}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{21}{2}-\left(\frac{19}{16}-\frac{31-22}{8}\right)\times \frac{10\times 9+5}{9}-\frac{3\times 12+7}{12}-\frac{2\times 18+5}{18}+\frac{3\times 2+1}{2}-1.75$$

Subtract 22 from 31 to get 9.

$$\frac{21}{2}-\left(\frac{19}{16}-\frac{9}{8}\right)\times \frac{10\times 9+5}{9}-\frac{3\times 12+7}{12}-\frac{2\times 18+5}{18}+\frac{3\times 2+1}{2}-1.75$$

Least common multiple of 16 and 8 is 16. Convert \frac{19}{16} and \frac{9}{8} to fractions with denominator 16.

$$\frac{21}{2}-\left(\frac{19}{16}-\frac{18}{16}\right)\times \frac{10\times 9+5}{9}-\frac{3\times 12+7}{12}-\frac{2\times 18+5}{18}+\frac{3\times 2+1}{2}-1.75$$

Since \frac{19}{16} and \frac{18}{16} have the same denominator, subtract them by subtracting their numerators.

$$\frac{21}{2}-\frac{19-18}{16}\times \frac{10\times 9+5}{9}-\frac{3\times 12+7}{12}-\frac{2\times 18+5}{18}+\frac{3\times 2+1}{2}-1.75$$

Subtract 18 from 19 to get 1.

$$\frac{21}{2}-\frac{1}{16}\times \frac{10\times 9+5}{9}-\frac{3\times 12+7}{12}-\frac{2\times 18+5}{18}+\frac{3\times 2+1}{2}-1.75$$

Multiply 10 and 9 to get 90.

$$\frac{21}{2}-\frac{1}{16}\times \frac{90+5}{9}-\frac{3\times 12+7}{12}-\frac{2\times 18+5}{18}+\frac{3\times 2+1}{2}-1.75$$

Add 90 and 5 to get 95.

$$\frac{21}{2}-\frac{1}{16}\times \frac{95}{9}-\frac{3\times 12+7}{12}-\frac{2\times 18+5}{18}+\frac{3\times 2+1}{2}-1.75$$

Multiply \frac{1}{16} times \frac{95}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{21}{2}-\frac{1\times 95}{16\times 9}-\frac{3\times 12+7}{12}-\frac{2\times 18+5}{18}+\frac{3\times 2+1}{2}-1.75$$

Do the multiplications in the fraction \frac{1\times 95}{16\times 9}.

$$\frac{21}{2}-\frac{95}{144}-\frac{3\times 12+7}{12}-\frac{2\times 18+5}{18}+\frac{3\times 2+1}{2}-1.75$$

Least common multiple of 2 and 144 is 144. Convert \frac{21}{2} and \frac{95}{144} to fractions with denominator 144.

$$\frac{1512}{144}-\frac{95}{144}-\frac{3\times 12+7}{12}-\frac{2\times 18+5}{18}+\frac{3\times 2+1}{2}-1.75$$

Since \frac{1512}{144} and \frac{95}{144} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1512-95}{144}-\frac{3\times 12+7}{12}-\frac{2\times 18+5}{18}+\frac{3\times 2+1}{2}-1.75$$

Subtract 95 from 1512 to get 1417.

$$\frac{1417}{144}-\frac{3\times 12+7}{12}-\frac{2\times 18+5}{18}+\frac{3\times 2+1}{2}-1.75$$

Multiply 3 and 12 to get 36.

$$\frac{1417}{144}-\frac{36+7}{12}-\frac{2\times 18+5}{18}+\frac{3\times 2+1}{2}-1.75$$

Add 36 and 7 to get 43.

$$\frac{1417}{144}-\frac{43}{12}-\frac{2\times 18+5}{18}+\frac{3\times 2+1}{2}-1.75$$

Least common multiple of 144 and 12 is 144. Convert \frac{1417}{144} and \frac{43}{12} to fractions with denominator 144.

$$\frac{1417}{144}-\frac{516}{144}-\frac{2\times 18+5}{18}+\frac{3\times 2+1}{2}-1.75$$

Since \frac{1417}{144} and \frac{516}{144} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1417-516}{144}-\frac{2\times 18+5}{18}+\frac{3\times 2+1}{2}-1.75$$

Subtract 516 from 1417 to get 901.

$$\frac{901}{144}-\frac{2\times 18+5}{18}+\frac{3\times 2+1}{2}-1.75$$

Multiply 2 and 18 to get 36.

$$\frac{901}{144}-\frac{36+5}{18}+\frac{3\times 2+1}{2}-1.75$$

Add 36 and 5 to get 41.

$$\frac{901}{144}-\frac{41}{18}+\frac{3\times 2+1}{2}-1.75$$

Least common multiple of 144 and 18 is 144. Convert \frac{901}{144} and \frac{41}{18} to fractions with denominator 144.

$$\frac{901}{144}-\frac{328}{144}+\frac{3\times 2+1}{2}-1.75$$

Since \frac{901}{144} and \frac{328}{144} have the same denominator, subtract them by subtracting their numerators.

$$\frac{901-328}{144}+\frac{3\times 2+1}{2}-1.75$$

Subtract 328 from 901 to get 573.

$$\frac{573}{144}+\frac{3\times 2+1}{2}-1.75$$

Reduce the fraction \frac{573}{144} to lowest terms by extracting and canceling out 3.

$$\frac{191}{48}+\frac{3\times 2+1}{2}-1.75$$

Multiply 3 and 2 to get 6.

$$\frac{191}{48}+\frac{6+1}{2}-1.75$$

Add 6 and 1 to get 7.

$$\frac{191}{48}+\frac{7}{2}-1.75$$

Least common multiple of 48 and 2 is 48. Convert \frac{191}{48} and \frac{7}{2} to fractions with denominator 48.

$$\frac{191}{48}+\frac{168}{48}-1.75$$

Since \frac{191}{48} and \frac{168}{48} have the same denominator, add them by adding their numerators.

$$\frac{191+168}{48}-1.75$$

Add 191 and 168 to get 359.

$$\frac{359}{48}-1.75$$

Convert decimal number 1.75 to fraction \frac{175}{100}. Reduce the fraction \frac{175}{100} to lowest terms by extracting and canceling out 25.

$$\frac{359}{48}-\frac{7}{4}$$

Least common multiple of 48 and 4 is 48. Convert \frac{359}{48} and \frac{7}{4} to fractions with denominator 48.

$$\frac{359}{48}-\frac{84}{48}$$

Since \frac{359}{48} and \frac{84}{48} have the same denominator, subtract them by subtracting their numerators.

$$\frac{359-84}{48}$$

Subtract 84 from 359 to get 275.

$$\frac{275}{48}$$

Factor

$$\frac{11 \cdot 5 ^ {2}}{3 \cdot 2 ^ {4}} = 5\frac{35}{48} = 5.729166666666667$$