Question

how to add fractions containing pi

Answer 1

"pi" is just another number. Fractions that contain the number pi can be dealt with like all other fractions.

Examples:

Example 1...

$\frac { 1 }{ \pi  } +\frac { 1 }{ \pi  } =\frac { 1+1 }{ \pi  } =\frac { 2 }{ \pi  }$

Example 2...

$\\ \\ \frac { \pi  }{ 3 } +\frac { 2\pi  }{ 3 } =\frac { \pi +2\pi  }{ 3 } =\frac { 3\pi  }{ 3 } =\pi $

Example 3...

$\\ \\ \frac { 2 }{ 3\pi  } +\frac { 5 }{ 4\pi  } \\ \\ =\frac { 2 }{ 3\pi  } \cdot \frac { 4 }{ 4 } +\frac { 5 }{ 4\pi  } \cdot \frac { 3 }{ 3 } \\ \\ =\frac { 8 }{ 12\pi  } +\frac { 15 }{ 12\pi  } \\ \\ =\frac { 8+15 }{ 12\pi  } \\ \\ =\frac { 23 }{ 12\pi  } $