Question: 5. Simplify each expression. L21, L22
a. $\frac{2}{3} - \frac{1}{3} + \frac{(16 - 7)}{3}$
b. $\frac{\sqrt{64} - 11 \cdot 3}{-44 \div 4 + 6^2}$
1. **State the problem:** Simplify each given expression.
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### Part a
2. Expression: $$\frac{2}{3} - \frac{1}{3} + \frac{16 - 7}{3}$$
3. Simplify inside the parentheses: $$16 - 7 = 9$$
4. Substitute back: $$\frac{2}{3} - \frac{1}{3} + \frac{9}{3}$$
5. Combine the fractions with common denominator 3:
$$\frac{2}{3} - \frac{1}{3} + \frac{9}{3} = \frac{2 - 1 + 9}{3} = \frac{10}{3}$$
6. **Final answer for part a:** $$\frac{10}{3}$$
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### Part b
7. Expression: $$\frac{\sqrt{64} - 11 \cdot 3}{-44 \div 4 + 6^2}$$
8. Calculate numerator components:
$$\sqrt{64} = 8$$
$$11 \cdot 3 = 33$$
So numerator: $$8 - 33 = -25$$
9. Calculate denominator components:
$$-44 \div 4 = -11$$
$$6^2 = 36$$
So denominator: $$-11 + 36 = 25$$
10. Substitute numerator and denominator:
$$\frac{-25}{25}$$
11. Simplify fraction by canceling 25:
$$\frac{\cancel{25} \cdot (-1)}{\cancel{25}} = -1$$
12. **Final answer for part b:** $$-1$$