Solve [17/13+{12/5-(15/11div71/2*1frac{1}{4}+1frac{1}{2})}]

$$[ 1 \frac { 7 } { 13 } + \{ 1 \frac { 2 } { 5 } - ( 1 \frac { 5 } { 11 } \div 7 \frac { 1 } { 2 } \times 1 \frac { 1 } { 4 } + 1 \frac { 1 } { 2 } ) \} ]$$

Evaluate

$$\frac{5131}{4290}\approx 1.196037296$$

Solution Steps

Multiply 1 and 13 to get 13.

$$\frac{13+7}{13}+\frac{1\times 5+2}{5}-\left(\frac{\frac{1\times 11+5}{11}}{\frac{7\times 2+1}{2}}\times \frac{1\times 4+1}{4}+\frac{1\times 2+1}{2}\right)$$

Add 13 and 7 to get 20.

$$\frac{20}{13}+\frac{1\times 5+2}{5}-\left(\frac{\frac{1\times 11+5}{11}}{\frac{7\times 2+1}{2}}\times \frac{1\times 4+1}{4}+\frac{1\times 2+1}{2}\right)$$

Multiply 1 and 5 to get 5.

$$\frac{20}{13}+\frac{5+2}{5}-\left(\frac{\frac{1\times 11+5}{11}}{\frac{7\times 2+1}{2}}\times \frac{1\times 4+1}{4}+\frac{1\times 2+1}{2}\right)$$

Add 5 and 2 to get 7.

$$\frac{20}{13}+\frac{7}{5}-\left(\frac{\frac{1\times 11+5}{11}}{\frac{7\times 2+1}{2}}\times \frac{1\times 4+1}{4}+\frac{1\times 2+1}{2}\right)$$

Divide \frac{1\times 11+5}{11} by \frac{7\times 2+1}{2} by multiplying \frac{1\times 11+5}{11} by the reciprocal of \frac{7\times 2+1}{2}.

$$\frac{20}{13}+\frac{7}{5}-\left(\frac{\left(1\times 11+5\right)\times 2}{11\left(7\times 2+1\right)}\times \frac{1\times 4+1}{4}+\frac{1\times 2+1}{2}\right)$$

Multiply 1 and 11 to get 11.

$$\frac{20}{13}+\frac{7}{5}-\left(\frac{\left(11+5\right)\times 2}{11\left(7\times 2+1\right)}\times \frac{1\times 4+1}{4}+\frac{1\times 2+1}{2}\right)$$

Add 11 and 5 to get 16.

$$\frac{20}{13}+\frac{7}{5}-\left(\frac{16\times 2}{11\left(7\times 2+1\right)}\times \frac{1\times 4+1}{4}+\frac{1\times 2+1}{2}\right)$$

Multiply 16 and 2 to get 32.

$$\frac{20}{13}+\frac{7}{5}-\left(\frac{32}{11\left(7\times 2+1\right)}\times \frac{1\times 4+1}{4}+\frac{1\times 2+1}{2}\right)$$

Multiply 7 and 2 to get 14.

$$\frac{20}{13}+\frac{7}{5}-\left(\frac{32}{11\left(14+1\right)}\times \frac{1\times 4+1}{4}+\frac{1\times 2+1}{2}\right)$$

Add 14 and 1 to get 15.

$$\frac{20}{13}+\frac{7}{5}-\left(\frac{32}{11\times 15}\times \frac{1\times 4+1}{4}+\frac{1\times 2+1}{2}\right)$$

Multiply 11 and 15 to get 165.

$$\frac{20}{13}+\frac{7}{5}-\left(\frac{32}{165}\times \frac{1\times 4+1}{4}+\frac{1\times 2+1}{2}\right)$$

Multiply 1 and 4 to get 4.

$$\frac{20}{13}+\frac{7}{5}-\left(\frac{32}{165}\times \frac{4+1}{4}+\frac{1\times 2+1}{2}\right)$$

Add 4 and 1 to get 5.

$$\frac{20}{13}+\frac{7}{5}-\left(\frac{32}{165}\times \frac{5}{4}+\frac{1\times 2+1}{2}\right)$$

Multiply \frac{32}{165} times \frac{5}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{20}{13}+\frac{7}{5}-\left(\frac{32\times 5}{165\times 4}+\frac{1\times 2+1}{2}\right)$$

Do the multiplications in the fraction \frac{32\times 5}{165\times 4}.

$$\frac{20}{13}+\frac{7}{5}-\left(\frac{160}{660}+\frac{1\times 2+1}{2}\right)$$

Reduce the fraction \frac{160}{660} to lowest terms by extracting and canceling out 20.

$$\frac{20}{13}+\frac{7}{5}-\left(\frac{8}{33}+\frac{1\times 2+1}{2}\right)$$

Multiply 1 and 2 to get 2.

$$\frac{20}{13}+\frac{7}{5}-\left(\frac{8}{33}+\frac{2+1}{2}\right)$$

Add 2 and 1 to get 3.

$$\frac{20}{13}+\frac{7}{5}-\left(\frac{8}{33}+\frac{3}{2}\right)$$

Least common multiple of 33 and 2 is 66. Convert \frac{8}{33} and \frac{3}{2} to fractions with denominator 66.

$$\frac{20}{13}+\frac{7}{5}-\left(\frac{16}{66}+\frac{99}{66}\right)$$

Since \frac{16}{66} and \frac{99}{66} have the same denominator, add them by adding their numerators.

$$\frac{20}{13}+\frac{7}{5}-\frac{16+99}{66}$$

Add 16 and 99 to get 115.

$$\frac{20}{13}+\frac{7}{5}-\frac{115}{66}$$

Least common multiple of 5 and 66 is 330. Convert \frac{7}{5} and \frac{115}{66} to fractions with denominator 330.

$$\frac{20}{13}+\frac{462}{330}-\frac{575}{330}$$

Since \frac{462}{330} and \frac{575}{330} have the same denominator, subtract them by subtracting their numerators.

$$\frac{20}{13}+\frac{462-575}{330}$$

Subtract 575 from 462 to get -113.

$$\frac{20}{13}-\frac{113}{330}$$

Least common multiple of 13 and 330 is 4290. Convert \frac{20}{13} and \frac{113}{330} to fractions with denominator 4290.

$$\frac{6600}{4290}-\frac{1469}{4290}$$

Since \frac{6600}{4290} and \frac{1469}{4290} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6600-1469}{4290}$$

Subtract 1469 from 6600 to get 5131.

$$\frac{5131}{4290}$$

Factor

$$\frac{7 \cdot 733}{2 \cdot 3 \cdot 5 \cdot 11 \cdot 13} = 1\frac{841}{4290} = 1.196037296037296$$