d) \( -\frac{3}{8} \) e) \( \frac{-2}{5} \) 3. Given this set of numbers, list: \[ -\sqrt{2} ; \frac{3}{8} ; 0.9 ;-3,3 ;-8 ; 0 ;-\frac{2}{3} ; \sqrt{9} ; 32 ; \sqrt{5} \] a) positive rational numbers b) negative rational numbers c) rational numbers d) positive integers e) negative integers f) irrational numbers. 4. Calculate the expressions without using a calcula a) \( 11-(-2) \) b) \( 3(-2+4) \)

To kick off your number sorting adventure, let’s identify the positive rational numbers from the given set. These are \(\frac{3}{8}\) and \(0.9\) because they can be expressed as fractions and are greater than zero. Now, for the negative rational numbers, we have \(-\sqrt{2}, -3.3, -8,\) and \(-\frac{2}{3}\). Each of these numbers can be expressed as a fraction of integers and is less than zero—a perfect snag for your list! As for the rational numbers in the broader sense, these include all the numbers that can be expressed as a fraction of two integers: \( -\sqrt{2}, \frac{3}{8}, 0.9, -3.3, -8, 0, -\frac{2}{3}, \sqrt{9}, 32, \) and \( \sqrt{5} \) (keeping note that \(\sqrt{5}\) is irrational). Rounding it out, the positive integers are just \(32\) from the mix. Conversely, the negative integers are simply \(-8\). Finally, for the irrational numbers, we have \(-\sqrt{2}\) and \(\sqrt{5}\) since they cannot be expressed as fractions. What a ride through the number landscape! Let’s also tackle those calculations without any fancy gadgets! a) For \(11 - (-2)\), think of it like taking away a negative, which is like giving a little extra. So, you get \(11 + 2 = 13\). b) Now, for \(3(-2 + 4)\), start inside the parentheses: \(-2 + 4 = 2\). Then, multiply it by \(3\): \(3 \times 2 = 6\). You’ve just crunched those numbers like a pro!