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2.9: Chapter 2 Review

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Compare the real numbers.

  1. 7 and –11
  2. \frac{4}{5} and \frac{11}{16}
  3. \frac{10}{15} and \frac{2}{3}
  4. 0.985 and \frac{31}{32}
  5. –16.12 and \frac{-300}{9}

Order the real numbers from least to greatest.

  1. \frac{8}{11}, \frac{7}{10}, \frac{5}{9}
  2. \frac{2}{7}, \frac{1}{11}, \frac{8}{13}, \frac{4}{7}, \frac{8}{9}

Graph these values on the same number line.

  1. 3\frac{1}{3}
  2. –1.875
  3. \frac{7}{8}
  4. 0.1\bar{6}
  5. \frac{-55}{5}

Simplify by applying the Distributive Property.

  1. 6n(-2+5n)-n(-3n-8)
  2. 7x+2(-6x+2)
  3. -7x(x+5)+3(4x-8)
  4. -3(-6r-5)-2r(1+6r)
  5. 1+3(p+8)
  6. 3(1-5k)-1

Approximate the square root to the nearest hundredth.

  1. \sqrt{26}
  2. \sqrt{330}
  3. \sqrt{625}
  4. \sqrt{121}
  5. \sqrt{225}
  6. \sqrt{11}
  7. \sqrt{8}

Rewrite the square root without using a calculator.

  1. \sqrt{50}
  2. \sqrt{8}
  3. \sqrt{80}
  4. \sqrt{32}

Simplify by combining like terms.

  1. 8+b+1-7b
  2. 9n+9n+17
  3. 7h-3+3
  4. 9x+11-x-3+5x+2

Evaluate.

  1. \frac{8}{5}-\frac{4}{3}
  2. \frac{4}{3}-\frac{1}{2}
  3. \frac{1}{6}+ 1 \frac{5}{6}
  4. \frac{-5}{4}\times \frac{1}{3}
  5. \frac{4}{9} \times \frac{7}{4}
  6. -1\frac{5}{7} \times -2\frac{1}{2}
  7. \frac{1}{9} \div -1\frac{1}{3}
  8. \frac{-3}{2} \div \frac{-10}{7}
  9. -3\frac{7}{10} \div 2\frac{1}{4}
  10. 1\frac{1}{5}-\left (-3\frac{3}{4}\right )
  11. 4 \frac{2}{3}+3\frac{2}{3}
  12. 5.4+(-9.7)
  13. (-7.1)+(-0.4)
  14. (-4.79)+(-3.63)
  15. (-8.1)-(-8.9)
  16. 1.58-(-13.6)
  17. (-13.6)+12-(-15.5)
  18. (-5.6)-(-12.6)+(-6.6)
  19. 19.4+24.2
  20. 8.7+3.8+12.3
  21. 9.8-9.4
  22. 2.2-7.3

List all the categories that apply to the following numbers.

  1. 10.9
  2. \frac{-9}{10}
  3. 3\pi
  4. \frac{\pi}{2}-\frac{\pi}{2}
  5. –21
  6. 8

Which property has been applied?

  1. 6.78+(-6.78)=0
  2. 9.8+11.2+1.2=9.8+1.2+11.2
  3. 3a+(4a+8)=(3a+4a)+8
  4. \frac{4}{3}-\left (-\frac{5}{6}\right )=\frac{4}{3}+\frac{5}{6}
  5. (1)j=j
  6. 8(11)\left (\frac{1}{8}\right )=8\left (\frac{1}{8}\right )(11)

Solve the real-world situation.

  1. Carol has 18 feet of fencing and purchased an addition 132 inches. How much fencing does Carol have?
  2. Ulrich is making cookies for a fundraiser. Each cookie requires \frac{3}{8}-pound of dough. He has 12 pounds of cookie dough. How many cookies can Ulrich make?
  3. Herrick bought 11 DVDs at $19.99 each. Use the Distributive Property to show how Herrick can calculate mentally the amount of money he will need.
  4. Bagger 288 is a trench digger, which moves at \frac{3}{8} \ miles/hour. How long will it take to dig a trench 14 miles long?
  5. Georgia started with a given amount of money, a. She spent $4.80 on a large latte, $1.20 on an English muffin, $68.48 on a new shirt, and $32.45 for a present. She now has $0.16. How much money, a, did Georgia have in the beginning?
  6. The formula for an area of a square is A=s^2. A square garden has an area of 145 meters^2. Find the length of the garden exactly.

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