Solve (1/3+1/4+1/5+1/6+frac{1}{7}+frac{1}{8}+frac{1}{9})*7div9

$$( \frac{ 1 }{ 3 } + \frac{ 1 }{ 4 } + \frac{ 1 }{ 5 } + \frac{ 1 }{ 6 } + \frac{ 1 }{ 7 } + \frac{ 1 }{ 8 } + \frac{ 1 }{ 9 } ) \times 7 \div 9$$

Evaluate

$$\frac{3349}{3240}\approx 1.033641975$$

Solution Steps

Least common multiple of 3 and 4 is 12. Convert \frac{1}{3} and \frac{1}{4} to fractions with denominator 12.

$$\frac{\left(\frac{4}{12}+\frac{3}{12}+\frac{1}{5}+\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}\right)\times 7}{9}$$

Since \frac{4}{12} and \frac{3}{12} have the same denominator, add them by adding their numerators.

$$\frac{\left(\frac{4+3}{12}+\frac{1}{5}+\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}\right)\times 7}{9}$$

Add 4 and 3 to get 7.

$$\frac{\left(\frac{7}{12}+\frac{1}{5}+\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}\right)\times 7}{9}$$

Least common multiple of 12 and 5 is 60. Convert \frac{7}{12} and \frac{1}{5} to fractions with denominator 60.

$$\frac{\left(\frac{35}{60}+\frac{12}{60}+\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}\right)\times 7}{9}$$

Since \frac{35}{60} and \frac{12}{60} have the same denominator, add them by adding their numerators.

$$\frac{\left(\frac{35+12}{60}+\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}\right)\times 7}{9}$$

Add 35 and 12 to get 47.

$$\frac{\left(\frac{47}{60}+\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}\right)\times 7}{9}$$

Least common multiple of 60 and 6 is 60. Convert \frac{47}{60} and \frac{1}{6} to fractions with denominator 60.

$$\frac{\left(\frac{47}{60}+\frac{10}{60}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}\right)\times 7}{9}$$

Since \frac{47}{60} and \frac{10}{60} have the same denominator, add them by adding their numerators.

$$\frac{\left(\frac{47+10}{60}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}\right)\times 7}{9}$$

Add 47 and 10 to get 57.

$$\frac{\left(\frac{57}{60}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}\right)\times 7}{9}$$

Reduce the fraction \frac{57}{60} to lowest terms by extracting and canceling out 3.

$$\frac{\left(\frac{19}{20}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}\right)\times 7}{9}$$

Least common multiple of 20 and 7 is 140. Convert \frac{19}{20} and \frac{1}{7} to fractions with denominator 140.

$$\frac{\left(\frac{133}{140}+\frac{20}{140}+\frac{1}{8}+\frac{1}{9}\right)\times 7}{9}$$

Since \frac{133}{140} and \frac{20}{140} have the same denominator, add them by adding their numerators.

$$\frac{\left(\frac{133+20}{140}+\frac{1}{8}+\frac{1}{9}\right)\times 7}{9}$$

Add 133 and 20 to get 153.

$$\frac{\left(\frac{153}{140}+\frac{1}{8}+\frac{1}{9}\right)\times 7}{9}$$

Least common multiple of 140 and 8 is 280. Convert \frac{153}{140} and \frac{1}{8} to fractions with denominator 280.

$$\frac{\left(\frac{306}{280}+\frac{35}{280}+\frac{1}{9}\right)\times 7}{9}$$

Since \frac{306}{280} and \frac{35}{280} have the same denominator, add them by adding their numerators.

$$\frac{\left(\frac{306+35}{280}+\frac{1}{9}\right)\times 7}{9}$$

Add 306 and 35 to get 341.

$$\frac{\left(\frac{341}{280}+\frac{1}{9}\right)\times 7}{9}$$

Least common multiple of 280 and 9 is 2520. Convert \frac{341}{280} and \frac{1}{9} to fractions with denominator 2520.

$$\frac{\left(\frac{3069}{2520}+\frac{280}{2520}\right)\times 7}{9}$$

Since \frac{3069}{2520} and \frac{280}{2520} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3069+280}{2520}\times 7}{9}$$

Add 3069 and 280 to get 3349.

$$\frac{\frac{3349}{2520}\times 7}{9}$$

Express \frac{3349}{2520}\times 7 as a single fraction.

$$\frac{\frac{3349\times 7}{2520}}{9}$$

Multiply 3349 and 7 to get 23443.

$$\frac{\frac{23443}{2520}}{9}$$

Reduce the fraction \frac{23443}{2520} to lowest terms by extracting and canceling out 7.

$$\frac{\frac{3349}{360}}{9}$$

Express \frac{\frac{3349}{360}}{9} as a single fraction.

$$\frac{3349}{360\times 9}$$

Multiply 360 and 9 to get 3240.

$$\frac{3349}{3240}$$

Factor

$$\frac{17 \cdot 197}{2 ^ {3} \cdot 3 ^ {4} \cdot 5} = 1\frac{109}{3240} = 1.0336419753086419$$