Solve 41/7-21/14+31/2/6frac{2{3}+5frac{5}{9}-10frac{1}{18}}

$$\frac{ 4 \frac{ 1 }{ 7 } -2 \frac{ 1 }{ 14 } +3 \frac{ 1 }{ 2 } }{ 6 \frac{ 2 }{ 3 } +5 \frac{ 5 }{ 9 } -10 \frac{ 1 }{ 18 } }$$

Evaluate

$$\frac{18}{7}\approx 2.571428571$$

Solution Steps

Multiply 4 and 7 to get 28.

$$\frac{\frac{28+1}{7}-\frac{2\times 14+1}{14}+\frac{3\times 2+1}{2}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 18+1}{18}}$$

Add 28 and 1 to get 29.

$$\frac{\frac{29}{7}-\frac{2\times 14+1}{14}+\frac{3\times 2+1}{2}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 18+1}{18}}$$

Multiply 2 and 14 to get 28.

$$\frac{\frac{29}{7}-\frac{28+1}{14}+\frac{3\times 2+1}{2}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 18+1}{18}}$$

Add 28 and 1 to get 29.

$$\frac{\frac{29}{7}-\frac{29}{14}+\frac{3\times 2+1}{2}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 18+1}{18}}$$

Least common multiple of 7 and 14 is 14. Convert \frac{29}{7} and \frac{29}{14} to fractions with denominator 14.

$$\frac{\frac{58}{14}-\frac{29}{14}+\frac{3\times 2+1}{2}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 18+1}{18}}$$

Since \frac{58}{14} and \frac{29}{14} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{58-29}{14}+\frac{3\times 2+1}{2}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 18+1}{18}}$$

Subtract 29 from 58 to get 29.

$$\frac{\frac{29}{14}+\frac{3\times 2+1}{2}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 18+1}{18}}$$

Multiply 3 and 2 to get 6.

$$\frac{\frac{29}{14}+\frac{6+1}{2}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 18+1}{18}}$$

Add 6 and 1 to get 7.

$$\frac{\frac{29}{14}+\frac{7}{2}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 18+1}{18}}$$

Least common multiple of 14 and 2 is 14. Convert \frac{29}{14} and \frac{7}{2} to fractions with denominator 14.

$$\frac{\frac{29}{14}+\frac{49}{14}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 18+1}{18}}$$

Since \frac{29}{14} and \frac{49}{14} have the same denominator, add them by adding their numerators.

$$\frac{\frac{29+49}{14}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 18+1}{18}}$$

Add 29 and 49 to get 78.

$$\frac{\frac{78}{14}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 18+1}{18}}$$

Reduce the fraction \frac{78}{14} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{39}{7}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 18+1}{18}}$$

Multiply 6 and 3 to get 18.

$$\frac{\frac{39}{7}}{\frac{18+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 18+1}{18}}$$

Add 18 and 2 to get 20.

$$\frac{\frac{39}{7}}{\frac{20}{3}+\frac{5\times 9+5}{9}-\frac{10\times 18+1}{18}}$$

Multiply 5 and 9 to get 45.

$$\frac{\frac{39}{7}}{\frac{20}{3}+\frac{45+5}{9}-\frac{10\times 18+1}{18}}$$

Add 45 and 5 to get 50.

$$\frac{\frac{39}{7}}{\frac{20}{3}+\frac{50}{9}-\frac{10\times 18+1}{18}}$$

Least common multiple of 3 and 9 is 9. Convert \frac{20}{3} and \frac{50}{9} to fractions with denominator 9.

$$\frac{\frac{39}{7}}{\frac{60}{9}+\frac{50}{9}-\frac{10\times 18+1}{18}}$$

Since \frac{60}{9} and \frac{50}{9} have the same denominator, add them by adding their numerators.

$$\frac{\frac{39}{7}}{\frac{60+50}{9}-\frac{10\times 18+1}{18}}$$

Add 60 and 50 to get 110.

$$\frac{\frac{39}{7}}{\frac{110}{9}-\frac{10\times 18+1}{18}}$$

Multiply 10 and 18 to get 180.

$$\frac{\frac{39}{7}}{\frac{110}{9}-\frac{180+1}{18}}$$

Add 180 and 1 to get 181.

$$\frac{\frac{39}{7}}{\frac{110}{9}-\frac{181}{18}}$$

Least common multiple of 9 and 18 is 18. Convert \frac{110}{9} and \frac{181}{18} to fractions with denominator 18.

$$\frac{\frac{39}{7}}{\frac{220}{18}-\frac{181}{18}}$$

Since \frac{220}{18} and \frac{181}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{39}{7}}{\frac{220-181}{18}}$$

Subtract 181 from 220 to get 39.

$$\frac{\frac{39}{7}}{\frac{39}{18}}$$

Reduce the fraction \frac{39}{18} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{39}{7}}{\frac{13}{6}}$$

Divide \frac{39}{7} by \frac{13}{6} by multiplying \frac{39}{7} by the reciprocal of \frac{13}{6}.

$$\frac{39}{7}\times \frac{6}{13}$$

Multiply \frac{39}{7} times \frac{6}{13} by multiplying numerator times numerator and denominator times denominator.

$$\frac{39\times 6}{7\times 13}$$

Do the multiplications in the fraction \frac{39\times 6}{7\times 13}.

$$\frac{234}{91}$$

Reduce the fraction \frac{234}{91} to lowest terms by extracting and canceling out 13.

$$\frac{18}{7}$$

Factor

$$\frac{2 \cdot 3 ^ {2}}{7} = 2\frac{4}{7} = 2.5714285714285716$$