Solve 41/7-21/14+31/2/6frac{2{3}+5frac{5}{9}-10frac{1}{19}}

$$\frac { 4 \frac { 1 } { 7 } - 2 \frac { 1 } { 14 } + 3 \frac { 1 } { 2 } } { 6 \frac { 2 } { 3 } + 5 \frac { 5 } { 9 } - 10 \frac { 1 } { 19 } }$$

Evaluate

$$\frac{6669}{2597}\approx 2.567963034$$

Solution Steps

Multiply 4 and 7 to get 28.

$$\frac{\frac{28+1}{7}-\frac{2\times 14+1}{14}+\frac{3\times 2+1}{2}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 19+1}{19}}$$

Add 28 and 1 to get 29.

$$\frac{\frac{29}{7}-\frac{2\times 14+1}{14}+\frac{3\times 2+1}{2}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 19+1}{19}}$$

Multiply 2 and 14 to get 28.

$$\frac{\frac{29}{7}-\frac{28+1}{14}+\frac{3\times 2+1}{2}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 19+1}{19}}$$

Add 28 and 1 to get 29.

$$\frac{\frac{29}{7}-\frac{29}{14}+\frac{3\times 2+1}{2}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 19+1}{19}}$$

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

$$\frac{\frac{58}{14}-\frac{29}{14}+\frac{3\times 2+1}{2}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 19+1}{19}}$$

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

$$\frac{\frac{58-29}{14}+\frac{3\times 2+1}{2}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 19+1}{19}}$$

Subtract 29 from 58 to get 29.

$$\frac{\frac{29}{14}+\frac{3\times 2+1}{2}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 19+1}{19}}$$

Multiply 3 and 2 to get 6.

$$\frac{\frac{29}{14}+\frac{6+1}{2}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 19+1}{19}}$$

Add 6 and 1 to get 7.

$$\frac{\frac{29}{14}+\frac{7}{2}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 19+1}{19}}$$

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

$$\frac{\frac{29}{14}+\frac{49}{14}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 19+1}{19}}$$

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

$$\frac{\frac{29+49}{14}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 19+1}{19}}$$

Add 29 and 49 to get 78.

$$\frac{\frac{78}{14}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 19+1}{19}}$$

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

$$\frac{\frac{39}{7}}{\frac{6\times 3+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 19+1}{19}}$$

Multiply 6 and 3 to get 18.

$$\frac{\frac{39}{7}}{\frac{18+2}{3}+\frac{5\times 9+5}{9}-\frac{10\times 19+1}{19}}$$

Add 18 and 2 to get 20.

$$\frac{\frac{39}{7}}{\frac{20}{3}+\frac{5\times 9+5}{9}-\frac{10\times 19+1}{19}}$$

Multiply 5 and 9 to get 45.

$$\frac{\frac{39}{7}}{\frac{20}{3}+\frac{45+5}{9}-\frac{10\times 19+1}{19}}$$

Add 45 and 5 to get 50.

$$\frac{\frac{39}{7}}{\frac{20}{3}+\frac{50}{9}-\frac{10\times 19+1}{19}}$$

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

$$\frac{\frac{39}{7}}{\frac{60}{9}+\frac{50}{9}-\frac{10\times 19+1}{19}}$$

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

$$\frac{\frac{39}{7}}{\frac{60+50}{9}-\frac{10\times 19+1}{19}}$$

Add 60 and 50 to get 110.

$$\frac{\frac{39}{7}}{\frac{110}{9}-\frac{10\times 19+1}{19}}$$

Multiply 10 and 19 to get 190.

$$\frac{\frac{39}{7}}{\frac{110}{9}-\frac{190+1}{19}}$$

Add 190 and 1 to get 191.

$$\frac{\frac{39}{7}}{\frac{110}{9}-\frac{191}{19}}$$

Least common multiple of 9 and 19 is 171. Convert \frac{110}{9} and \frac{191}{19} to fractions with denominator 171.

$$\frac{\frac{39}{7}}{\frac{2090}{171}-\frac{1719}{171}}$$

Since \frac{2090}{171} and \frac{1719}{171} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{39}{7}}{\frac{2090-1719}{171}}$$

Subtract 1719 from 2090 to get 371.

$$\frac{\frac{39}{7}}{\frac{371}{171}}$$

Divide \frac{39}{7} by \frac{371}{171} by multiplying \frac{39}{7} by the reciprocal of \frac{371}{171}.

$$\frac{39}{7}\times \frac{171}{371}$$

Multiply \frac{39}{7} times \frac{171}{371} by multiplying numerator times numerator and denominator times denominator.

$$\frac{39\times 171}{7\times 371}$$

Do the multiplications in the fraction \frac{39\times 171}{7\times 371}.

$$\frac{6669}{2597}$$

Factor

$$\frac{3 ^ {3} \cdot 13 \cdot 19}{7 ^ {2} \cdot 53} = 2\frac{1475}{2597} = 2.5679630342703117$$