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2.9: Chapter 2 Review

Difficulty Level: At Grade Created by: CK-12
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Compare the real numbers.

  1. 7 and –11
  2. \begin{align*}\frac{4}{5}\end{align*}45 and \begin{align*}\frac{11}{16}\end{align*}1116
  3. \begin{align*}\frac{10}{15}\end{align*}1015 and \begin{align*}\frac{2}{3}\end{align*}23
  4. 0.985 and \begin{align*}\frac{31}{32}\end{align*}3132
  5. –16.12 and \begin{align*}\frac{-300}{9}\end{align*}3009

Order the real numbers from least to greatest.

  1. \begin{align*}\frac{8}{11}, \frac{7}{10}, \frac{5}{9}\end{align*}811,710,59
  2. \begin{align*}\frac{2}{7}, \frac{1}{11}, \frac{8}{13}, \frac{4}{7}, \frac{8}{9}\end{align*}27,111,813,47,89

Graph these values on the same number line.

  1. \begin{align*}3\frac{1}{3}\end{align*}313
  2. –1.875
  3. \begin{align*}\frac{7}{8}\end{align*}78
  4. \begin{align*}0.1\bar{6}\end{align*}0.16¯
  5. \begin{align*}\frac{-55}{5}\end{align*}555

Simplify by applying the Distributive Property.

  1. \begin{align*}6n(-2+5n)-n(-3n-8)\end{align*}6n(2+5n)n(3n8)
  2. \begin{align*}7x+2(-6x+2)\end{align*}7x+2(6x+2)
  3. \begin{align*}-7x(x+5)+3(4x-8)\end{align*}7x(x+5)+3(4x8)
  4. \begin{align*}-3(-6r-5)-2r(1+6r)\end{align*}3(6r5)2r(1+6r)
  5. \begin{align*}1+3(p+8)\end{align*}1+3(p+8)
  6. \begin{align*}3(1-5k)-1\end{align*}3(15k)1

Approximate the square root to the nearest hundredth.

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

Rewrite the square root without using a calculator.

  1. \begin{align*}\sqrt{50}\end{align*}50
  2. \begin{align*}\sqrt{8}\end{align*}8
  3. \begin{align*}\sqrt{80}\end{align*}80
  4. \begin{align*}\sqrt{32}\end{align*}32

Simplify by combining like terms.

  1. \begin{align*}8+b+1-7b\end{align*}8+b+17b
  2. \begin{align*}9n+9n+17\end{align*}9n+9n+17
  3. \begin{align*}7h-3+3\end{align*}7h3+3
  4. \begin{align*}9x+11-x-3+5x+2\end{align*}9x+11x3+5x+2

Evaluate.

  1. \begin{align*}\frac{8}{5}-\frac{4}{3}\end{align*}8543
  2. \begin{align*}\frac{4}{3}-\frac{1}{2}\end{align*}4312
  3. \begin{align*}\frac{1}{6}+ 1 \frac{5}{6}\end{align*}16+156
  4. \begin{align*}\frac{-5}{4}\times \frac{1}{3}\end{align*}54×13
  5. \begin{align*}\frac{4}{9} \times \frac{7}{4}\end{align*}49×74
  6. \begin{align*}-1\frac{5}{7} \times -2\frac{1}{2}\end{align*}157×212
  7. \begin{align*}\frac{1}{9} \div -1\frac{1}{3}\end{align*}19÷113
  8. \begin{align*}\frac{-3}{2} \div \frac{-10}{7}\end{align*}32÷107
  9. \begin{align*}-3\frac{7}{10} \div 2\frac{1}{4}\end{align*}3710÷214
  10. \begin{align*}1\frac{1}{5}-\left (-3\frac{3}{4}\right )\end{align*}
  11. \begin{align*}4 \frac{2}{3}+3\frac{2}{3}\end{align*}
  12. \begin{align*}5.4+(-9.7)\end{align*}
  13. \begin{align*}(-7.1)+(-0.4)\end{align*}
  14. \begin{align*}(-4.79)+(-3.63)\end{align*}
  15. \begin{align*}(-8.1)-(-8.9)\end{align*}
  16. \begin{align*}1.58-(-13.6)\end{align*}
  17. \begin{align*}(-13.6)+12-(-15.5)\end{align*}
  18. \begin{align*}(-5.6)-(-12.6)+(-6.6)\end{align*}
  19. \begin{align*}19.4+24.2\end{align*}
  20. \begin{align*}8.7+3.8+12.3\end{align*}
  21. \begin{align*}9.8-9.4\end{align*}
  22. \begin{align*}2.2-7.3\end{align*}

List all the categories that apply to the following numbers.

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

Which property has been applied?

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

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 \begin{align*}\frac{3}{8}\end{align*}-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 \begin{align*}\frac{3}{8} \ miles/hour\end{align*}. How long will it take to dig a trench 14 miles long?
  5. Georgia started with a given amount of money, \begin{align*}a\end{align*}. 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, \begin{align*}a\end{align*}, did Georgia have in the beginning?
  6. The formula for an area of a square is \begin{align*}A=s^2\end{align*}. A square garden has an area of 145 meters\begin{align*}^2\end{align*}. Find the length of the garden exactly.

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CK.MAT.ENG.SE.1.Algebra-Basic.2.9
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