without calculating determine whether each sum is

Question

rational or irrational.
2
1/7
+
3/5
𝜋 + 9

Answer 1

To determine whether each sum is rational or irrational without calculating, we can analyze the components of each expression.

1. The first sum is \( \frac{2}{1} + \frac{1}{7} + \frac{3}{5} \).

   • All of these numbers are rational since they can be expressed as fractions (where the numerator and the denominator are both integers).
   • The sum of rational numbers is always rational.

2. The second sum is \( \pi + 9 \).

   • Here, \( \pi \) is an irrational number and 9 is a rational number.
   • The sum of a rational number and an irrational number is always irrational.

In conclusion:

• The first sum \( \frac{2}{1} + \frac{1}{7} + \frac{3}{5} \) is rational.
• The second sum \( \pi + 9 \) is irrational.