Visual Encyclopedia

# Algebra

Algebra (from Arabic "al-jabr", literally meaning "reunion of broken parts") is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics. As such, it includes everything from elementary equation solving to the study of abstractions such as groups, rings, and fields. The more basic parts of algebra are called elementary algebra; the more abstract parts are called abstract algebra or modern algebra. Elementary algebra is generally considered to be essential for any study of mathematics, science, or engineering, as well as such applications as medicine and economics. Abstract algebra is a major area in advanced mathematics, studied primarily by professional mathematicians.

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### Pre - Algebra / Algebra Test

This is a test of pre-algebra and algebra skills that I wrote for a student that I tutor. Can you pass it? 1. 5 + 6 = 2. 10 – 7= 3. 3 x 5 = 4. 20 ÷ 4 = 5. 3 x 4 = 6. 2 x 6 = 7. 2 x 4 = 8. 3 x 5 = 9. 2^4 = 10. 10^4 = 11. 2 + 3 = 12. 6 – 4 = 13. 3 + 1 – 2 + 4 – 3 – 2 = 14. 3 – 3 = 15. 4 – 7 = 16. 5 x 2 = 17. -3 x 2 = 18. 6 ÷ 2 = 19. 3 ÷ 4 = 20. Round the following to the nearest tens place: a. 39 = b. 734 = c. 899 = 21. 53 x 7 = 22. 53 x 47 = 23. 860 ÷ 5 = 24. 3 inches x 3 inches = 25. 10 miles x 5 miles = 26. 140 miles ÷ 2 hours = 27. True or False: 3 x 4 ≠ 34 28. 2 + 2 ? 5 (, or =) 29. 110 ? 58 + 5 (, or =) 30. True or False: 49 ≈ 50 31. True or False: 1,024 ≈ 1,000,000 32. │- 50 + 10 │ = 33. 5 + 3 x 2 + 8 ÷ 4 = 34. 3 + 52 – 6 = 35. (1 + 15 ÷ 5) + (3 – 6) x 5 = 36. Bobo is spinning five fewer plates than Nunu. If Nunu is spinning 17 plates, then how many plates are Bobo and Nunu spinning? 37. The height of a house is half as long as its width. The width of the house is 80 feet. How tall is the house? 38. The express train is moving three times faster than the local train. If the local train is going 25 miles per hour, then what is the difference in speed between the express train and the local train? 39. Aunt Effie has \$732.84 hidden in her pillowcase. Aunt Jezebel has \$234.19 less than Aunt Effie has. How much money do the two women have all together? 40. Four women collected money to save the endangered Salt Creek Tiger Beetle. Keisha collected \$160, Brie collected \$50 more than Keisha did, Amy collected twice as much as Brie, and together Amy and Sophia collected \$700. All together, how much money did the women collect? 41. On a recent payday, Travis took a shopping trip. He bought six shirts for \$19.95 each and two pairs of pants for \$34.60 each. He then bought a jacket that cost \$37.08 less than he paid for both pairs of pants. If he paid the cashier with three \$100 bills, then how much change did he receive? 42. A bat and a baseball cost a dollar and ten cents. The bat costs a dollar more than the ball. How much does the ball cost? 43. In a lake, there is a patch of lily pads. Every day, the patch doubles in size. If it takes 48 days for the patch to cover the lake, then how long would it take the patch to cover half of the lake? 44. 431 ÷ 1 = 45. 28 ÷ 28 = 46. 538 ÷ 2 = 47. 625 ÷ 5 = 48. 170 ÷ 10 = 49. 51 ÷ 3 = 50. 243 ÷ 9 = 51. List the factors of 18. 52. List the first five multiples of 8. 53. List the prime factors of 84. 54. True or false: 71 is a prime number. 55. Find the greatest common factor of 28, 42, and 70. 56. Find the least common multiple of 2, 3, and 5. 57. 78/78 ? 1 58. 63/73 ? 1 59. 99/97 ? 1 60. Reduce 32/100. 61. Reduce 24/60. 62. Convert 31/3 to a mixed number. 63. Convert 5 and 2/3 to an improper fraction. 64. Simplify the following algebraic expressions. a. -2x + 5 + 10x - 9 b. 3(x + 7) + 2(-x + 4) + 5x 65. Simplify the expressions. a. (2x - 6) / 2 b. (-x - 2) / (x + 2) c. (5x - 5)/10 66. Solve for x in the following equations. a. -x = 6 b. 2x - 8 = -x + 4 c. 2x + 1/2 = 2/3 d. x/3 + 2 = 5 e. -5/x = 2 67. Evaluate for the given values of x and y. a. x^2 - y^2 , for x = 4 and y = 5 b. |4x - 2y| , for x = -2 and y = 3 c. 3x^3 - 4y^4 , for x = -1 and y = -2 68. Solve the following inequalities. a. x + 6 < 0 b. x + 1 > 5 c. 2(x - 2) < 12 69. What is the reciprocal of each of the following numbers? a. -1 b. 0 c. 3/4 d. 2 5/7 e. 0.02 70. Evaluate the following expressions involving mixed numbers. a. 3 3/4 + 6 1/7 b. (1 3/5) * (3 1/3) - 2 1/2 c. (5 2/3) / (4 1/5) d. (3 4/7 - 1 1/2) / (2 3/8 + 2 1/4) 71. Evaluate the following exponential expressions. a. -4^2 b. (-2)^3 c. (-2)^4 d. 10000 (write as an exponent) e. 5661 (write as an exponent) 72. Convert to fractions and write in simplest form. a. 0.02 b. 12% c. 0.5% d. 1.12 73. Convert to decimals. a. 1/5 b. 120% c. 0.2% d. 4 8/5 74. Convert to percents. a. 3/10 b. 1.4 c. 123.45 d. 2 4/5 75. Which of these numbers is divisible by 3? a. 156,312 b. 176,314 76. Which of these numbers is divisible by 4? a. 3,432 b. 1,257 77. Which of these numbers is divisible by 6? a. 1,233 b. 3,432 78. Which of these numbers is divisible by 9? a. 2,538 b. 1,451 79. Evaluate 8x + 7 given that x - 3 = 10. I will post the answers later this week (so no one is tempted to cheat). Do your best!

Contributed by Christine Ruff

### Algebra Humor

x and y

Contributed by Lindsay Favero

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