Solve 13/4151/2/frac{31{32}}-51/21frac{2}{11}+frac{6frac{1}{4}}{2frac{1}{2}}frac{3}{5}frac{45}{2.3^29}

$$\frac{ 1 \frac{ 3 }{ 4 } 15 \frac{ 1 }{ 2 } }{ \frac{ 31 }{ 32 } } -5 \frac{ 1 }{ 2 } 1 \frac{ 2 }{ 11 } + \frac{ 6 \frac{ 1 }{ 4 } }{ 2 \frac{ 1 }{ 2 } } \frac{ 3 }{ 5 } \frac{ 45 }{ { 2.3 }^{ 2 } 9 }$$

Evaluate

$$\frac{24247}{1058}\approx 22.917769376$$

Solution Steps

Multiply 1 and 4 to get 4.

$$\frac{\frac{4+3}{4}\times \frac{15\times 2+1}{2}}{\frac{31}{32}}-\frac{5\times 2+1}{2}\times \frac{1\times 11+2}{11}+\frac{\frac{6\times 4+1}{4}}{\frac{2\times 2+1}{2}}\times \frac{3}{5}\times \frac{45}{2.3^{2}\times 9}$$

Add 4 and 3 to get 7.

$$\frac{\frac{7}{4}\times \frac{15\times 2+1}{2}}{\frac{31}{32}}-\frac{5\times 2+1}{2}\times \frac{1\times 11+2}{11}+\frac{\frac{6\times 4+1}{4}}{\frac{2\times 2+1}{2}}\times \frac{3}{5}\times \frac{45}{2.3^{2}\times 9}$$

Multiply 15 and 2 to get 30.

$$\frac{\frac{7}{4}\times \frac{30+1}{2}}{\frac{31}{32}}-\frac{5\times 2+1}{2}\times \frac{1\times 11+2}{11}+\frac{\frac{6\times 4+1}{4}}{\frac{2\times 2+1}{2}}\times \frac{3}{5}\times \frac{45}{2.3^{2}\times 9}$$

Add 30 and 1 to get 31.

$$\frac{\frac{7}{4}\times \frac{31}{2}}{\frac{31}{32}}-\frac{5\times 2+1}{2}\times \frac{1\times 11+2}{11}+\frac{\frac{6\times 4+1}{4}}{\frac{2\times 2+1}{2}}\times \frac{3}{5}\times \frac{45}{2.3^{2}\times 9}$$

Multiply \frac{7}{4} times \frac{31}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{7\times 31}{4\times 2}}{\frac{31}{32}}-\frac{5\times 2+1}{2}\times \frac{1\times 11+2}{11}+\frac{\frac{6\times 4+1}{4}}{\frac{2\times 2+1}{2}}\times \frac{3}{5}\times \frac{45}{2.3^{2}\times 9}$$

Do the multiplications in the fraction \frac{7\times 31}{4\times 2}.

$$\frac{\frac{217}{8}}{\frac{31}{32}}-\frac{5\times 2+1}{2}\times \frac{1\times 11+2}{11}+\frac{\frac{6\times 4+1}{4}}{\frac{2\times 2+1}{2}}\times \frac{3}{5}\times \frac{45}{2.3^{2}\times 9}$$

Divide \frac{217}{8} by \frac{31}{32} by multiplying \frac{217}{8} by the reciprocal of \frac{31}{32}.

$$\frac{217}{8}\times \frac{32}{31}-\frac{5\times 2+1}{2}\times \frac{1\times 11+2}{11}+\frac{\frac{6\times 4+1}{4}}{\frac{2\times 2+1}{2}}\times \frac{3}{5}\times \frac{45}{2.3^{2}\times 9}$$

Multiply \frac{217}{8} times \frac{32}{31} by multiplying numerator times numerator and denominator times denominator.

$$\frac{217\times 32}{8\times 31}-\frac{5\times 2+1}{2}\times \frac{1\times 11+2}{11}+\frac{\frac{6\times 4+1}{4}}{\frac{2\times 2+1}{2}}\times \frac{3}{5}\times \frac{45}{2.3^{2}\times 9}$$

Do the multiplications in the fraction \frac{217\times 32}{8\times 31}.

$$\frac{6944}{248}-\frac{5\times 2+1}{2}\times \frac{1\times 11+2}{11}+\frac{\frac{6\times 4+1}{4}}{\frac{2\times 2+1}{2}}\times \frac{3}{5}\times \frac{45}{2.3^{2}\times 9}$$

Divide 6944 by 248 to get 28.

$$28-\frac{5\times 2+1}{2}\times \frac{1\times 11+2}{11}+\frac{\frac{6\times 4+1}{4}}{\frac{2\times 2+1}{2}}\times \frac{3}{5}\times \frac{45}{2.3^{2}\times 9}$$

Multiply 5 and 2 to get 10.

$$28-\frac{10+1}{2}\times \frac{1\times 11+2}{11}+\frac{\frac{6\times 4+1}{4}}{\frac{2\times 2+1}{2}}\times \frac{3}{5}\times \frac{45}{2.3^{2}\times 9}$$

Add 10 and 1 to get 11.

$$28-\frac{11}{2}\times \frac{1\times 11+2}{11}+\frac{\frac{6\times 4+1}{4}}{\frac{2\times 2+1}{2}}\times \frac{3}{5}\times \frac{45}{2.3^{2}\times 9}$$

Multiply 1 and 11 to get 11.

$$28-\frac{11}{2}\times \frac{11+2}{11}+\frac{\frac{6\times 4+1}{4}}{\frac{2\times 2+1}{2}}\times \frac{3}{5}\times \frac{45}{2.3^{2}\times 9}$$

Add 11 and 2 to get 13.

$$28-\frac{11}{2}\times \frac{13}{11}+\frac{\frac{6\times 4+1}{4}}{\frac{2\times 2+1}{2}}\times \frac{3}{5}\times \frac{45}{2.3^{2}\times 9}$$

Multiply \frac{11}{2} times \frac{13}{11} by multiplying numerator times numerator and denominator times denominator.

$$28-\frac{11\times 13}{2\times 11}+\frac{\frac{6\times 4+1}{4}}{\frac{2\times 2+1}{2}}\times \frac{3}{5}\times \frac{45}{2.3^{2}\times 9}$$

Cancel out 11 in both numerator and denominator.

$$28-\frac{13}{2}+\frac{\frac{6\times 4+1}{4}}{\frac{2\times 2+1}{2}}\times \frac{3}{5}\times \frac{45}{2.3^{2}\times 9}$$

Convert 28 to fraction \frac{56}{2}.

$$\frac{56}{2}-\frac{13}{2}+\frac{\frac{6\times 4+1}{4}}{\frac{2\times 2+1}{2}}\times \frac{3}{5}\times \frac{45}{2.3^{2}\times 9}$$

Since \frac{56}{2} and \frac{13}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{56-13}{2}+\frac{\frac{6\times 4+1}{4}}{\frac{2\times 2+1}{2}}\times \frac{3}{5}\times \frac{45}{2.3^{2}\times 9}$$

Subtract 13 from 56 to get 43.

$$\frac{43}{2}+\frac{\frac{6\times 4+1}{4}}{\frac{2\times 2+1}{2}}\times \frac{3}{5}\times \frac{45}{2.3^{2}\times 9}$$

Divide \frac{6\times 4+1}{4} by \frac{2\times 2+1}{2} by multiplying \frac{6\times 4+1}{4} by the reciprocal of \frac{2\times 2+1}{2}.

$$\frac{43}{2}+\frac{\left(6\times 4+1\right)\times 2}{4\left(2\times 2+1\right)}\times \frac{3}{5}\times \frac{45}{2.3^{2}\times 9}$$

Cancel out 2 in both numerator and denominator.

$$\frac{43}{2}+\frac{1+4\times 6}{2\left(1+2\times 2\right)}\times \frac{3}{5}\times \frac{45}{2.3^{2}\times 9}$$

Multiply 4 and 6 to get 24.

$$\frac{43}{2}+\frac{1+24}{2\left(1+2\times 2\right)}\times \frac{3}{5}\times \frac{45}{2.3^{2}\times 9}$$

Add 1 and 24 to get 25.

$$\frac{43}{2}+\frac{25}{2\left(1+2\times 2\right)}\times \frac{3}{5}\times \frac{45}{2.3^{2}\times 9}$$

Multiply 2 and 2 to get 4.

$$\frac{43}{2}+\frac{25}{2\left(1+4\right)}\times \frac{3}{5}\times \frac{45}{2.3^{2}\times 9}$$

Add 1 and 4 to get 5.

$$\frac{43}{2}+\frac{25}{2\times 5}\times \frac{3}{5}\times \frac{45}{2.3^{2}\times 9}$$

Multiply 2 and 5 to get 10.

$$\frac{43}{2}+\frac{25}{10}\times \frac{3}{5}\times \frac{45}{2.3^{2}\times 9}$$

Reduce the fraction \frac{25}{10} to lowest terms by extracting and canceling out 5.

$$\frac{43}{2}+\frac{5}{2}\times \frac{3}{5}\times \frac{45}{2.3^{2}\times 9}$$

Multiply \frac{5}{2} times \frac{3}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{43}{2}+\frac{5\times 3}{2\times 5}\times \frac{45}{2.3^{2}\times 9}$$

Cancel out 5 in both numerator and denominator.

$$\frac{43}{2}+\frac{3}{2}\times \frac{45}{2.3^{2}\times 9}$$

Calculate 2.3 to the power of 2 and get 5.29.

$$\frac{43}{2}+\frac{3}{2}\times \frac{45}{5.29\times 9}$$

Multiply 5.29 and 9 to get 47.61.

$$\frac{43}{2}+\frac{3}{2}\times \frac{45}{47.61}$$

Expand \frac{45}{47.61} by multiplying both numerator and the denominator by 100.

$$\frac{43}{2}+\frac{3}{2}\times \frac{4500}{4761}$$

Reduce the fraction \frac{4500}{4761} to lowest terms by extracting and canceling out 9.

$$\frac{43}{2}+\frac{3}{2}\times \frac{500}{529}$$

Multiply \frac{3}{2} times \frac{500}{529} by multiplying numerator times numerator and denominator times denominator.

$$\frac{43}{2}+\frac{3\times 500}{2\times 529}$$

Do the multiplications in the fraction \frac{3\times 500}{2\times 529}.

$$\frac{43}{2}+\frac{1500}{1058}$$

Reduce the fraction \frac{1500}{1058} to lowest terms by extracting and canceling out 2.

$$\frac{43}{2}+\frac{750}{529}$$

Least common multiple of 2 and 529 is 1058. Convert \frac{43}{2} and \frac{750}{529} to fractions with denominator 1058.

$$\frac{22747}{1058}+\frac{1500}{1058}$$

Since \frac{22747}{1058} and \frac{1500}{1058} have the same denominator, add them by adding their numerators.

$$\frac{22747+1500}{1058}$$

Add 22747 and 1500 to get 24247.

$$\frac{24247}{1058}$$

Factor

$$\frac{24247}{2 \cdot 23 ^ {2}} = 22\frac{971}{1058} = 22.917769376181475$$