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Praxis Middle School Mathematics: Numbers and Operations

Integers, fractions, decimals, percents, and ratios for middle school, including what to do when a student's arithmetic goes wrong.

Teacher certification exams are administered by testing organizations. FreeExam is not affiliated with those organizations, and these questions are original practice, not an official test.

Praxis is a trademark of Educational Testing Service. FreeExam is not affiliated with Educational Testing Service, and these questions are original practice, not an official test.

  1. 1.The morning temperature is −8°. By noon it has risen 13°. What is the noon temperature?

  2. 2.A diver is at −12 feet and goes 7 feet deeper. What is the new position?

  3. 3.What is |−6| + |3|?

  4. 4.What is (−4) × (−5)?

  5. 5.What is −18 ÷ 6?

  6. 6.A student computes −3 − (−8) as −11. What is the value, and what was combined?

  7. 7.What is 3/4 + 1/8?

  8. 8.What is 2/3 − 1/6?

  9. 9.What is (2/5) × (3/4)?

  10. 10.What is (3/4) ÷ (1/2)?

  11. 11.A student divides 3/5 by 2/3 by flipping 3/5 and multiplying. What is (3/5) ÷ (2/3)?

  12. 12.What is 0.6 × 0.4?

  13. 13.What is 15% of 80?

  14. 14.9 is what percent of 36?

  15. 15.A $40 jacket is discounted 20%. What is the sale price?

  16. 16.A student finds 20% of 50 by dividing 50 by 20 and gets 2.5. What is 20% of 50?

  17. 17.A paint mix is 3 parts blue and 5 parts white. A batch uses 40 cups in all. How many cups are blue?

  18. 18.A bus travels 120 miles in 3 hours at a steady speed. What is the unit rate in miles per hour?

  19. 19.Solve 2/5 = x/20.

  20. 20.What is the greatest common factor of 12 and 18?

  21. 21.What is the least common multiple of 4 and 6?

  22. 22.A student says 21 is prime because it is odd. Which statement is right?

  23. 23.What is 2^5?

  24. 24.What is √49?

  25. 25.What is √(16/25)?

  26. 26.What is 4.2 × 10^3 in ordinary form?

  27. 27.A student evaluates 2 + 3 × 4 as 20 by adding first. What is the value?

  28. 28.A student says −2^2 and (−2)^2 are both 4. Which comparison is right?

  29. 29.Which symbol makes −1/2 □ −0.6 true?

  30. 30.What is 3/8 written as a decimal?

  31. 31.Which fraction equals the repeating decimal 0.333...?

  32. 32.Which whole number lies between √10 and √20?

  33. 33.A recipe uses 2 cups of rice for 8 servings. How many cups are needed for 12 servings?

  34. 34.A student adds 1/2 + 1/3 by adding the numerators and the denominators, getting 2/5. What is the sum?

  35. 35.In 3.047, which place is the digit 4 in?

  36. 36.What is 6.48 rounded to the nearest tenth?

  37. 37.The product of a negative number and a positive number is which kind of number?

  38. 38.What is 5 − (−2) + (−7)?

  39. 39.What is 1.5 × 10^(−2) in ordinary form?

  40. 40.Which number is irrational?

  41. 41.A student multiplies 0.2 × 0.3 and gets 0.6 by multiplying 2 × 3 and keeping one decimal place. What is the product?

  42. 42.A price rises from $20 to $25. What is the percent increase?

  43. 43.A student says 4/4 is undefined because the numerator and denominator match. What is 4/4?

  44. 44.A student lists the factors of 18 as 1, 2, 3, 6, and 18. Which factor is missing?

  45. 45.A rectangle is 8 units by 7 units. What is its area?

  46. 46.What is 144 ÷ 12?

  47. 47.What is 2 1/4 written as an improper fraction?

  48. 48.What is 11/3 written as a mixed number?

  49. 49.A student multiplies 2 1/2 × 4 by multiplying 2 × 4 and leaving the 1/2, getting 8 1/2. What is the product?

  50. 50.The ratio of boys to girls in a club is 2 to 3. There are 10 boys. How many girls are there?

  51. 51.On a map, 1 inch represents 4 miles. A road measures 3.5 inches. How long is the road?

  52. 52.Which fraction is greater, 5/8 or 3/5?

  53. 53.What is −7 + 4 × (−2)?

  54. 54.A tank is 3/5 full. The class uses 2/3 of the water that is in the tank. What fraction of the whole tank is used?

  55. 55.What is 0.125 as a fraction in lowest terms?

  56. 56.What is 40% as a fraction in lowest terms?

  57. 57.A student converts 1/4 to a percent and writes 4%. What is the percent?

  58. 58.Which number is greatest: −2, −8, 0, or −1?

  59. 59.Which value is least: 1/2, 0.4, 3/8, or 0.45?

  60. 60.What is 10^4?

  61. 61.A student says 5^0 is 0 because the exponent says to use no factors. What is 5^0?

  62. 62.What is 3^(−1) written as a fraction?

  63. 63.What is √(81/100)?

  64. 64.A student says the cube of 4 is 12 because 4 × 3 = 12. What is 4^3?

  65. 65.A class has 24 students, and 3/8 of them play an instrument. How many play an instrument?

  66. 66.A meal costs $20. A 15% tip is added. How many dollars is the tip?

  67. 67.A $50 purchase has 8% sales tax. What is the total paid?

  68. 68.A student finds 10% of 250, which is 25, and then says 30% is 25 + 3 = 28. What is 30% of 250?

  69. 69.Which ratio is equivalent to 6:9?

  70. 70.Which pair of ratios is not equivalent?

  71. 71.A student reads 45 pages in 90 minutes. What is the rate in pages per minute?

  72. 72.One shop sells 3 notebooks for $6. Another sells 5 notebooks for $9. Which is the lower price per notebook?

  73. 73.What is (−20) ÷ (−4)?

  74. 74.What is −15 − 6?

  75. 75.What is the distance on a number line between −3 and 4?

  76. 76.What is the opposite of −9?

  77. 77.A student says the opposite of every number is negative. Which counterexample should the teacher accept?

  78. 78.Which expression is a prime factorization of 36?

  79. 79.A student says 1 is prime because its only factor is 1. What is the right classification?

  80. 80.What is the greatest common factor of 20 and 28?

  81. 81.What is the least common multiple of 5 and 7?

  82. 82.What is 2/3 of 18?

  83. 83.A ribbon is 2.5 meters long and is cut into pieces of 0.5 meter. How many pieces are there?

  84. 84.What is 7.2 ÷ 0.8?

  85. 85.A student computes 7.2 ÷ 0.8 by shifting the decimal in only the dividend and gets 0.9. What is the quotient?

  86. 86.Twenty minutes is what fraction of an hour?

  87. 87.What is 150% of 40?

  88. 88.A price falls from $80 to $60. What is the percent decrease?

  89. 89.A student computes the percent decrease from 80 to 60 as 20/60. Why is that comparison the wrong base?

  90. 90.Which list orders 0.2, 1/4, and 0.22 from least to greatest?

  91. 91.Which expression equals 18?

  92. 92.What is 1,000 × 0.001?

  93. 93.What is (−12) ÷ (−3)?

  94. 94.Which estimate is closest to 19 × 21?

  95. 95.What is 5/6 of a dozen eggs?

  96. 96.A student adds 1/2 + 1/2 and gets 2/4, then simplifies to 1/2. What is the sum?

  97. 97.What is |−15|?

  98. 98.What is (−2) × (−3) × (−1)?

  99. 99.What is 4.05 × 10^2?

  100. 100.Which decimal equals 7/20?

  101. 101.A crate holds 12 apples, and 1/3 of them are green. How many apples are green?

  102. 102.A 12-ounce box costs $3.60. What is the price per ounce?

  103. 103.Four pencils cost $2. At the same rate, what do 10 pencils cost?

  104. 104.A student solves 3/4 = x/12 by writing 3 × 4 = 12x. What is x?

  105. 105.A student multiplies 2^3 × 2^2 and gets 2^6 by multiplying the exponents. What is the product?

  106. 106.A scoreboard changes by −5, then +12, then −4. What is the combined change?

  107. 107.A student says the greatest common factor of 8 and 12 is 24. Which idea was swapped?

  108. 108.A checkout starts at 0, records −5, and then records a payment that brings the balance to 3. What was that second change?