Question

. Without calculating determine whether each sum is
rational or irrational.
2
1/7
+
3/5
𝜋 + 9

Answer 1

To determine whether each sum is rational or irrational, we can analyze the components of each sum.

1. **\( \frac{1}{7} + \frac{3}{5} \)**:
- Both \( \frac{1}{7} \) and \( \frac{3}{5} \) are rational numbers (since both can be expressed as fractions of integers).
- The sum of two rational numbers is also a rational number.
- Therefore, \( \frac{1}{7} + \frac{3}{5} \) is **rational**.

2. **\( \pi + 9 \)**:
- \( \pi \) is an irrational number (it cannot be expressed as a fraction of integers).
- The number 9 is a rational number.
- The sum of a rational number and an irrational number is always irrational.
- Therefore, \( \pi + 9 \) is **irrational**.

In summary:
- \( \frac{1}{7} + \frac{3}{5} \) is rational.
- \( \pi + 9 \) is irrational.