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1.3.3.1: Exercises

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    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: \(8(x - 1)-(x + 5)\).

    This page titled 1.3.3.1: Exercises is shared under a not declared license and was authored, remixed, and/or curated by Leah Griffith, Veronica Holbrook, Johnny Johnson & Nancy Garcia.