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Quiz 1
1. List all that apply: natural number, integer, rational number, irrational number.
(a) $18$
(b) $0.333\ldots$
(c) $-\sqrt{16}$
(d) $\dfrac{3}{9}$
(e) $\sqrt{5}$
Solution:
(a) natural number, integer, rational number
(b) rational number
(c) integer, rational number
(d) rational number
(e) irrational number

2. Simplify $|5-9|-|2+3|$.
Solution: Calculate $$|5-9|-|2+3| = |-4| - |5| = 4-5 = -1.$$

3. Compute $2 \cdot 3 + [1-(2 \cdot 2 + 1)]^2$.
Solution: Calculate $$\begin{array}{ll} 2\cdot 3 + [1-(2\cdot 2+1)]^2 &= 3+[1-(4+1)]^2 \\ &= 2\cdot 3 + [1-5]^2 \\ &= 6 + [-4]^2 \\ &= 6 + 16 \\ &= 22. \end{array}$$

4. Simplify $\left( \dfrac{x}{2y} \right)^2 \left( \dfrac{y}{x} \right)$.
Solution: Calculate $$\left( \dfrac{x}{2y} \right)^2 \left( \dfrac{y}{x} \right) = \left( \dfrac{x^2}{4y^2} \right) \left( \dfrac{y}{x} \right) = \dfrac{1}{4} x^{2-1}y^{1-2} = \dfrac{1}{4}xy^{-1} =\dfrac{x}{4y}$$

5. Compute $(20 - 5 \cdot 2)^2 \div (-1 + 3 \cdot 2 )$.
Solution: Calculate $$\begin{array}{ll} (20-5\cdot 2)^2 \div (-1 + 3 \cdot 2) &= (20 - 10)^2 \div (-1 + 6) \\ &= 10^2 \div 5 \\ &= 100 \div 5 \\ &= 20. \end{array}$$