Solve 3/42/3+1/3/frac{3{5}-frac{2}{7}}+frac{1}{9}

$$\frac{ 3 }{ 4 } \frac{ \frac{ 2 }{ 3 } + \frac{ 1 }{ 3 } }{ \frac{ 3 }{ 5 } - \frac{ 2 }{ 7 } } + \frac{ 1 }{ 9 }$$

Evaluate

$$\frac{989}{396}\approx 2.497474747$$

Solution Steps

Since \frac{2}{3} and \frac{1}{3} have the same denominator, add them by adding their numerators.

$$\frac{3}{4}\times \frac{\frac{2+1}{3}}{\frac{3}{5}-\frac{2}{7}}+\frac{1}{9}$$

Add 2 and 1 to get 3.

$$\frac{3}{4}\times \frac{\frac{3}{3}}{\frac{3}{5}-\frac{2}{7}}+\frac{1}{9}$$

Divide 3 by 3 to get 1.

$$\frac{3}{4}\times \frac{1}{\frac{3}{5}-\frac{2}{7}}+\frac{1}{9}$$

Least common multiple of 5 and 7 is 35. Convert \frac{3}{5} and \frac{2}{7} to fractions with denominator 35.

$$\frac{3}{4}\times \frac{1}{\frac{21}{35}-\frac{10}{35}}+\frac{1}{9}$$

Since \frac{21}{35} and \frac{10}{35} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3}{4}\times \frac{1}{\frac{21-10}{35}}+\frac{1}{9}$$

Subtract 10 from 21 to get 11.

$$\frac{3}{4}\times \frac{1}{\frac{11}{35}}+\frac{1}{9}$$

Divide 1 by \frac{11}{35} by multiplying 1 by the reciprocal of \frac{11}{35}.

$$\frac{3}{4}\times 1\times \frac{35}{11}+\frac{1}{9}$$

Multiply 1 and \frac{35}{11} to get \frac{35}{11}.

$$\frac{3}{4}\times \frac{35}{11}+\frac{1}{9}$$

Multiply \frac{3}{4} times \frac{35}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 35}{4\times 11}+\frac{1}{9}$$

Do the multiplications in the fraction \frac{3\times 35}{4\times 11}.

$$\frac{105}{44}+\frac{1}{9}$$

Least common multiple of 44 and 9 is 396. Convert \frac{105}{44} and \frac{1}{9} to fractions with denominator 396.

$$\frac{945}{396}+\frac{44}{396}$$

Since \frac{945}{396} and \frac{44}{396} have the same denominator, add them by adding their numerators.

$$\frac{945+44}{396}$$

Add 945 and 44 to get 989.

$$\frac{989}{396}$$

Factor

$$\frac{23 \cdot 43}{2 ^ {2} \cdot 3 ^ {2} \cdot 11} = 2\frac{197}{396} = 2.4974747474747474$$