Solve (1999*1/24+16821/3)*13/5-35/11*3frac{2}{3}

$$(1999 \times \frac{ 1 }{ 24 } +1682 \frac{ 1 }{ 3 } ) \times 1 \frac{ 3 }{ 5 } -3 \frac{ 5 }{ 11 } \times 3 \frac{ 2 }{ 3 }$$

Evaluate

$$\frac{8437}{3}\approx 2812.333333333$$

Solution Steps

Multiply 1999 and \frac{1}{24} to get \frac{1999}{24}.

$$\left(\frac{1999}{24}+\frac{1682\times 3+1}{3}\right)\times \frac{1\times 5+3}{5}-\frac{3\times 11+5}{11}\times \frac{3\times 3+2}{3}$$

Multiply 1682 and 3 to get 5046.

$$\left(\frac{1999}{24}+\frac{5046+1}{3}\right)\times \frac{1\times 5+3}{5}-\frac{3\times 11+5}{11}\times \frac{3\times 3+2}{3}$$

Add 5046 and 1 to get 5047.

$$\left(\frac{1999}{24}+\frac{5047}{3}\right)\times \frac{1\times 5+3}{5}-\frac{3\times 11+5}{11}\times \frac{3\times 3+2}{3}$$

Least common multiple of 24 and 3 is 24. Convert \frac{1999}{24} and \frac{5047}{3} to fractions with denominator 24.

$$\left(\frac{1999}{24}+\frac{40376}{24}\right)\times \frac{1\times 5+3}{5}-\frac{3\times 11+5}{11}\times \frac{3\times 3+2}{3}$$

Since \frac{1999}{24} and \frac{40376}{24} have the same denominator, add them by adding their numerators.

$$\frac{1999+40376}{24}\times \frac{1\times 5+3}{5}-\frac{3\times 11+5}{11}\times \frac{3\times 3+2}{3}$$

Add 1999 and 40376 to get 42375.

$$\frac{42375}{24}\times \frac{1\times 5+3}{5}-\frac{3\times 11+5}{11}\times \frac{3\times 3+2}{3}$$

Reduce the fraction \frac{42375}{24} to lowest terms by extracting and canceling out 3.

$$\frac{14125}{8}\times \frac{1\times 5+3}{5}-\frac{3\times 11+5}{11}\times \frac{3\times 3+2}{3}$$

Multiply 1 and 5 to get 5.

$$\frac{14125}{8}\times \frac{5+3}{5}-\frac{3\times 11+5}{11}\times \frac{3\times 3+2}{3}$$

Add 5 and 3 to get 8.

$$\frac{14125}{8}\times \frac{8}{5}-\frac{3\times 11+5}{11}\times \frac{3\times 3+2}{3}$$

Multiply \frac{14125}{8} times \frac{8}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{14125\times 8}{8\times 5}-\frac{3\times 11+5}{11}\times \frac{3\times 3+2}{3}$$

Cancel out 8 in both numerator and denominator.

$$\frac{14125}{5}-\frac{3\times 11+5}{11}\times \frac{3\times 3+2}{3}$$

Divide 14125 by 5 to get 2825.

$$2825-\frac{3\times 11+5}{11}\times \frac{3\times 3+2}{3}$$

Multiply 3 and 11 to get 33.

$$2825-\frac{33+5}{11}\times \frac{3\times 3+2}{3}$$

Add 33 and 5 to get 38.

$$2825-\frac{38}{11}\times \frac{3\times 3+2}{3}$$

Multiply 3 and 3 to get 9.

$$2825-\frac{38}{11}\times \frac{9+2}{3}$$

Add 9 and 2 to get 11.

$$2825-\frac{38}{11}\times \frac{11}{3}$$

Multiply \frac{38}{11} times \frac{11}{3} by multiplying numerator times numerator and denominator times denominator.

$$2825-\frac{38\times 11}{11\times 3}$$

Cancel out 11 in both numerator and denominator.

$$2825-\frac{38}{3}$$

Convert 2825 to fraction \frac{8475}{3}.

$$\frac{8475}{3}-\frac{38}{3}$$

Since \frac{8475}{3} and \frac{38}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8475-38}{3}$$

Subtract 38 from 8475 to get 8437.

$$\frac{8437}{3}$$

Factor

$$\frac{11 \cdot 13 \cdot 59}{3} = 2812\frac{1}{3} = 2812.3333333333335$$