1.3.3.1: Exercises

Section 1.3.3.1 Exercises

1. Identify the property of real numbers illustrated by each equation.
   1. $(2 + 7) + 5 = 2 + (7 + 5)$
   2. $\sqrt{2}+(\sqrt{7}+\sqrt{5}) = \sqrt{2}+(\sqrt{5}+\sqrt{7})$
   3. $2(7+\sqrt{5}) = 14+2\sqrt{5}$
   4. $2\cdot \sqrt{7}=\sqrt{7}\cdot 2$
   5. $2(7+\sqrt{5}) = (7+\sqrt{5})2$
   6. $2 + 0 = 2$
   7. $\sqrt{5}\cdot 1=\sqrt{5}$
   8. $17 + (-17) = 0$
2. Evaluate $8 \left( \dfrac{3}{4}-\dfrac{1}{2}\right)$ in two ways using the distributive property.  Which way do you think is easier?
3. A deposit of P  dollars, invested at a simple interest rate, r, (in decimal form) will grow to amount A after t years.  $A=P(1+rt)$
4. Rewrite the right side of this formula so that it has no parentheses.
5. Simplify: $12(\dfrac{1}{3}n+\dfrac{3}{4})$.
6. Simplify: $100(0.3+0.25q)$.
7. Simplify: $100(0.7+0.15p)$.
8. Simplify: $100(0.04+0.35d)$.
9. Simplify: $−2(4y+1)$.
10. Simplify: $−3(6m+5)$.
11. Simplify: $−6(8n+11)$.
12. Simplify: $−11(4-3a)$.
13. Simplify: $−5(2-3a)$.
14. Simplify: $−7(8-15y)$.
15. Simplify: $−(y+5)$.
16. Simplify: $−(z-11)$.
17. Simplify: $−(x -4)$.
18. Simplify: $8−2(x + 3)$.
19. Simplify: $9−3(x + 2)$.
20. Simplify: $7x−5(x + 4)$.
21. Simplify: $4(x - 8)−(x + 3)$.
22. Simplify: $6(x - 9)−(x + 12)$.
23. Simplify: $8(x - 1)-(x + 5)$.