Chapter 1 1. Write the following as a mixed number: 17/4. 1. 4 1/4 2. 4 3. 64 4. 20 Answer: 1 Rationale: Divide the numerator by the denominator or 17 ÷ 4 = 4 with 1 left over so the answer is 4 with the 1 remainder over 4 or ¼ 2. Write the following as a mixed number: 36/7. 1. 4 6/7 2. 5 1/7 3. 4 1/7 4. 5 Answer: 2 Rationale: Divide the numerator by the denominator: 36 ÷ 7 = 5 with a remainder of 1 or 5 1/7 3. Write the following as a mixed number: 7/2. 1. 4 1/2 2. 5 1/2 3. 3 1/2 4. 3 Answer: 3 Rationale: Divide the numerator by the denominator: 7 ÷ 2 = 3 with 1 remaining or 3 1/2 4. Write the following number as an improper fraction: 8 5/6. 1. 53/6 2. 40/6 3. 53/8 4. 45/6 Answer: 1 Rationale: Multiply the whole number by the denominator, and add the numerator. 8 × 6 = 48 + 5 = 53. Place this number over the denominator or 53/6 5. Write the following number as an improper fraction: 5 5/6. 1. 35/6 2. 30/6 3. 25/6 4. 41/6 Answer: 1 Rationale: Multiply the whole number by the denominator and add the numerator: 5 × 6 = 30 + 5 = 35. Place this number over the denominator: 35/6 6. Write the following number as an improper fraction: 8 1/3. 1. 11/3 2. 24/3 3. 8/3 4. 25/3 Answer: 4 Rationale: Multiply the whole number by the denominator and add the numerator: 8 × 3 = 24 + 1 = 25 Place this number over the denominator: 25/3 7. Write 0.125 as a fraction in lowest terms and as a percentage. 1. 125/100; 1.25% 2. 25/100; 25% 3. 1/6; 12.5% 4. 1/8; 12.5% Answer: 4 Rationale: Write one hundred twenty-five thousandths as 125/1000, and then reduce the fraction to 1/8. Move the decimal two places to the right yielding 12.5% 8. Write 0.2 as a fraction in lowest terms and as a percentage. 1. 1/50; 2% 2. 1/5; 20% 3. 2/100; 0.2% 4. 1/500; 0.002% Answer: 2 Rationale: Write 2 tenths as 2/10 and reduce to 1/5. Move the decimal point 2 places to the right yielding 20% 9. Write 0.49 as a fraction in lowest terms and as a percentage. 1. 49/100; 49% 2. 7/15; 49% 3. 49/100; 4.9% 4. ½; 4.9% Answer: 1 Rationale: Write 0.49 as 49/100 which cannot be reduced further. Move the decimal point 2 places to the right to yield 49% 10. Write 0.75 as a fraction in lowest terms and as a percentage. 1. 75/100; 75% 2. 15/20; 7.5% 3. 15/20; 75% 4. ¾; 75% Answer: 4 Rationale: Write 0.75 as 75/100 and reduce to ¾. Move the decimal point 2 places to the right to yield 75% 11. Write 0.06 as a fraction in lowest terms and as a percentage. 1. 3/50; 60% 2. 6/10; 6% 3. 3/50; 6% 4. 3/5; 6% Answer: 3 Rationale: Write 0.06 as 6/100 and reduce to 3/50. Move the decimal point 2 places to the right to yield 6%. 12. Write 55% as a decimal number and a proper fraction in lowest terms. 1. 5.5; 55/100 2. 0.055; 55/1000 3. 0.55; 11/20 4. 0.0055; 11/200 Answer: 3 Rationale: Move the decimal 2 places to the left or 0.55, place 55 over 100 and reduce to 11/20 13. Write 72% as a decimal number and a proper fraction in lowest terms. 1. 7.2; 72/1000 2. 7.2; 72/100 3. 0.72; 36/50 4. 0.72; 18/25 Answer: 4 Rationale: Move the decimal 2 places to the left or 0.72. Place 72 over 100 and reduce to 18/25 14. Write 0.6% as a decimal number and a proper fraction in lowest terms. 1. 3/50; 0.06 2. 6/100; 0.60 3. 1/17; 0.06 4. 3/500; 0.006 Answer: 4 Rationale: Move the decimal 2 places to the left or 0.006, place 6 over 1000 and reduce to 3/500 15. Write 4.5% as a decimal number and a proper fraction in lowest terms. 1. 0.45; 45/100 2. 0.045; 9/200 3. 0.0045; 45/10,000 4. 0.045; 45/1,000 Answer: 2 Rationale: Move the decimal 2 places to the left or 0.045, place 45 over 1000 and reduce to 9/200 16. Write 25% as a decimal number and a proper fraction in lowest terms. 1. 2.5; 1/40 2. 0.025; 5/200 3. 0.25; 1/4 4. 0.25; 25/100 Answer: 3 Rationale: Move the decimal 2 places to the left or 0.25, place 25 over 100 and reduce to 1/4 17. Write 3/5 as a decimal number and a percent. 1. 0.0166; 1.66% 2. 0.6; 60% 3. 0.15; 15% 4. 0.3; 30% Answer: 2 Rationale: Divide the denominator into the numerator: 3 ÷ 5 = 0.6. Move the decimal point two places to the right yielding 60% 18. Convert 5/8 to a decimal number and a percent. 1. 1.6; 160% 2. 0.4; 40% 3. 0.625; 62.5% 4. 0.45; 45% Answer: 3 Rationale: Dividing the denominator into the numerator: 5 ÷ 8 = 0.625. Move the decimal point two places to the right yielding 62.5% 19. Convert 9/19 to a decimal number rounded off to the nearest tenth, and to a percentage rounded off to the nearest tenth of a percent. 1. 0.5; 47.4% 2. 0.47; 4.8% 3. 0.02; 2.1% 4. 0.4; 47.4% Answer: 1 Rationale: Divide the denominator into the numerator. 9 ÷ 19 = 0.4736… rounded off to 0.5. Move the decimal point two places to the right yielding 47.4% 20. Write 3/5 as a decimal number and a percent. 1. 1.67; 167% 2. 0.6; 60% 3. 0.167; 16.7% 4. 0.06; 6% Answer: 2 21. Reduce 36/48 to lowest terms. 1. 12/18 2. 18/24 3. 9/12 4. 3/4 Answer: 4 Rationale: Divide numerator and denominator by 12 yielding 3/4. 22. Reduce 95/100 to lowest terms. 1. 4/5 2. 19/20 3. 24/25 4. 9.5/10 Answer: 2 Rationale: Divide numerator and denominator by 5 yielding 19/20. 23. Reduce 24/36 to lowest terms. 1. 12/18 2. 3/4 3. 2/3 4. 6/9 Answer: 3 Rationale: Divide numerator and denominator by 12 yielding 2/3. 24. Reduce the ratio 18:54 to a fraction in lowest terms. 1. 18/54 2. 1/3 3. 3/4 4. 1/2 Answer: 2 Rationale: Convert the ratio to 18/54 and reduce to 1/3. 25. Reduce the ratio 10:75 to a fraction in lowest terms. 1. 1/7.5 2. 5/15 3. 2/15 4. 1/3 Answer: 3 Rationale: Convert the ratio to 10/75 and reduce to 2/15. 26. Reduce the ration 12:24 to a fraction in lowest terms. 1. 1/3 2. 6/18 3. 2/4 4. 1/2 Answer: 4 Rationale: Convert the ratio to 12/24 and reduce to 1/2. 27. Write 5/8 as an equivalent fraction with 96 in the denominator. 1. 96/154 2. 65/96 3. 60/96 4. 5/96 Answer: 3 Rationale: 5/8 × 12/12 = 60/96 28. Write 4/5 as an equivalent fraction with 100 in the denominator. 1. 100/80 2. 5/100 3. 75/100 4. 80/100 Answer: 4 Rationale: 4/5 × 20/20 = 80/100 29. Write 17/20 as an equivalent fraction with 100 in the denominator. 1. 85/100 2. 34/100 3. 4/100 4. 100/85 Answer: 1 Rationale: 17/20 × 5/5 = 85/100 30. Write 1/5 as an equivalent fraction with 25 in the denominator. 1. 25/5 2. 25/20 3. 5/25 4. 1/25 Answer: 3 Rationale: 1/5 × 5/5 = 5/25 31. Write 3/4 as an equivalent fraction with 100 in the denominator. 1. 75/100 2. 80/100 3. 100/25 4. 100/75 Answer: 1 Rationale: ¾ × 25/25 = 75/100 32. Round off 6.892489 to the hundredths place. 1. 6.9 2. 6.89 3. 6.8 4. 6.892 Answer: 2 Rationale: The digit following the hundredths place is 2, so leave 6.89 alone 33. Round off 17.456 to the tenths place. 1. 17.5 2. 17.4 3. 17.46 4. 17.56 Answer: 1 Rationale: The digits following the tenths place is 5 so add 1 to 4 yielding 17.5 34. Round off 3.5243 to the tenths place. 1. 3.6 2. 3.4 3. 3.5 4. 3.52 Answer: 3 Rationale: The digit following the tenths place is 2 so leave the 5 alone yielding 3.5 35. Round down 9.6723 to the tenths place. 1. 9.7 2. 9.6 3. 9.67 4. 9.72 Answer: 2 Rationale: The digit in the tenths place is 6, delete the remaining digits. 36. Round down 4.2894 to the hundredths place. 1. 4.3 2. 4.29 3. 4.28 4. 4.2 Answer: 3 Rationale: The digit in the hundredths place is 8, delete the remaining digits. 37. Round down 4.0678 to the tenths place. 1. 4 2. 4.1 3. 4.06 4. 4.07 Answer: 2 Rationale: The digit in the tenths place is 1, delete the remaining digits. 38. Add 4.55 and 0.035. 1. 4.9 2. 4.5035 3. 4.585 4. 4.515 Answer: 3 Rationale: Line up the decimal points and add. 39. Add the following decimal numbers: 10.1 + 3.964. 1. 14.064 2. 13.974 3. 13.064 4. 14.974 Answer: 1 Rationale: Line up the decimal points and add. 40. Add 4.834 + 3.962 + 1.083. 1. 8.879 2. 9.793 3. 9.879 4. 8.793 Answer: 3 Rationale: Line up the decimal points and add. 41. Subtract 1.864 from 3.691. 1. 1.827 2. 1.823 3. 2.827 4. 0.827 Answer: 1 Rationale: Line up the decimal points and subtract. 42. Subtract 0.068 from 5.543. 1. 4.863 2. 5.475 3. 5.863 4. 5.5362 Answer: 2 Rationale: Line up the decimal points and subtract. 43. Subtract 2.4 from 10. 1. 7.6 2. 12.40 3. 9.76 4. 12.4 Answer: 1 Rationale: Line up the decimal points and subtract. 44. Solve the following problem: 3.29 × 1.64. Round off the answer to the tenths place. 1. 5.4 2. 5.3 3. 53.4 4. 54.2 Answer: 1 Rationale: 3.29 × 1.64 = 5.3956 then round off to 5.4 45. Multiply 2.87 by 0.064 and round off to the hundredths place. 1. 0.19 2. 0.183 3. 0.1837 4. 0.18 Answer: 4 Rationale: 2.87 × 0.064 = 0.18368 rounded off to the hundredth place is 0.18 46. Multiply 2.4 by 0.5. 1. 1.2 2. 12 3. 0.12 4. 120 Answer: 1 Rationale: 2.4 × 0.5 = 1.2 47. Solve the following problem: 0.68 ÷ 0.4. 1. 170 2. 17 3. 1.7 4. 0.17 Answer: 3 Rationale: Move the decimal point one place to the right on each number, then divide 6.8 by 4 = 1.7 48. Divide 8.6 by 0.5. 1. 1.72 2. .172 3. 17.2 4. 172 Answer: 3 Rationale: Move the decimal point one place to the right on each number then divide 86 by 5 = 17.2 49. Divide 8.6 by 0.02. 1. 0.172 2. 4.3 3. 430 4. 0.43 Answer: 3 Rationale: Move the decimal point two places to the right and then divide 860 by 2 = 430 50. Multiply 0.089 by 1,000. 1. 89 2. 8.9 3. 0.89 4. 0.089 Answer: 1 Rationale: Move the decimal point three places to the right 51. Multiply 0.84 by 100. 1. 8.4 2. 84 3. 840 4. 0.084 Answer: 2 Rationale: Move the decimal point two places to the right yielding 84. 52. Multiply 34.2 by 100. 1. 3.42 2. 342 3. 3,420 4. 34,200 Answer: 3 Rationale: Move the decimal point two places to the right yielding 3420 53. Divide 0.89 by 100. 1. 8.9 2. 0.89 3. 0.089 4. 0.0089 Answer: 4 Rationale: Move the decimal point two places to the left yielding 0.0089 54. Divide 1.24 by 10. 1. 0.0124 2. 0.124 3. 12.4 4. 124 Answer: 2 Rationale: Move the decimal point one place to the left yielding 0.124 55. Divide 566.8 by 1,000. 1. 5,668 2. 56.68 3. 5.668 4. 0.5668 Answer: 4 Rationale: Move the decimal point three places to the left. 56. Write the numbers 0.289, 0.395, 0.0289, and 0.0395 in order of size from smallest to largest. ______ Answer: 0.0289; 0.0395; 0.289; 0.395 Rationale: Put in a column and line up the decimal points. 57. Write the numbers 0.003, 0.034, 0.38, and 0.0003 in order of size from smallest to largest. ______ Answer: 0.0003; 0.003; 0.034; 0.38 Rationale: Place the numbers in a column and line up the decimal points. 58. Write the numbers 0.3, 0.4, 0.33, and 0.111 in order of size from smallest to largest. ______ Answer: 0.111; 0.3; 0.33; 0.4 Rationale: Place the numbers in a column and line up the decimal points. 59. Which is larger: 0.21 or 0.7? ______ Answer: 0.7 Rationale: 0.7 is larger than 0.21. 60. Which is larger: 2.45 or 2.6? ______ Answer: 2.6 Rationale: 2.6 is larger than 2.45. 61. Which is largest: 0.3, 0.33, or 0.198? ______ Answer: 0.33 Rationale: 0.33 is larger than both 0.3 and 0.198. 62. Add 5 7/8 and 3 1/4. 1. 8 3/4 2. 9 1/8 3. 9 1/4 4. 8 1/4 Answer: 2 Rationale: Convert both denominators to 8 then add 5 7/8 + 3 2/8 = 8 9/8 = 9 1/8 63. Add 6 1/2 and 2 3/8. 1. 8 7/8 2. 9 3. 8 12/16 4. 9 1/4 Answer: 1 Rationale: Convert both denominators to 8 then add 6 4/8 + 2 3/8 = 8 7/8 64. Add 3 3/4 and 7 1/2. 1. 10 1/4 2. 10 3/4 3. 11 1/2 4. 11 1/4 Answer: 4 Rationale: Convert both denominators to 4 then add: 3 ¾ + 7 2/4 = 10 5/4 or 11 1/4 65. Subtract 1 3/4 from 2 3/8. 1. 1 3/8 2. 1 5/8 3. 5/8 4. 1 Answer: 3 Rationale: Convert both denominators to 8, then subtract 2 3/8 – 1 6/8 = 5/8 66. Subtract 1½ from 4 3/4. 1. 4 1/4 2. 3 1/2 3. 2 3/4 4. 3 1/4 Answer: 4 Rationale: Convert both denominators to 4, then subtract 4 ¾ – 1 2/4 = 3 ¼ 67. Subtract 2 7/8 from 7 1/4. 1. 5 5/8 2. 4 5/8 3. 4 3/8 4. 5 3/8 Answer: 3 Rationale: Convert both denominators to 8 then subtract 7 2/8 – 2 7/8 68. Solve the following problem and write the answer in lowest terms: 16/21 × 7/8 × 1/2. 1. 112/336 2. 64/147 3. 1/3 4. 1 109/147 Answer: 3 Rationale: Cancel before multiplying yielding 1/3 69. Solve the following problem and write the answer as a mixed number in lowest terms: 7/8 × 3/4 × 3/16. 1. 63/576 2. 7/64 3. 7/64 4. 63/512 Answer: 4 Rationale: Multiply the numerators (7 × 3 × 3) = 63. Multiply the denominators (8 × 4 × 16) = 512 and place the numerator over the denominator yielding 63/512. 70. Solve the following problem and write the answer in lowest terms: 3/5 × 4/15 × 25/24. 1. 300/1,800 2. 30/180 3. 3/18 4. 1/6 Answer: 4 Rationale: Cancel before multiplying yielding 1/6 71. Solve the following problem and write the answer as a mixed number in lowest terms: 8/11 ÷ 4/9. 1. 36/99 2. 2/11 3. 1 7/11 4. 1 28/44 Answer: 3 Rationale: Invert the second fraction and multiply (8/11 × 9/4 = 18/11) and change to 1 7/11 72. Solve the following problem and write the answer in lowest terms: 3/4 ÷ 7/8. 1. 21/32 2. 24/32 3. 6/7 4. 24/28 Answer: 3 Rationale: Invert the second fraction and multiply. 73. Solve the following problem and write the answer as a whole number or fraction in the lowest terms: 3/200 ÷ 11/300. 1. 9/22 2. 3/7 3. 33/6,000 4. 900/2,200 Answer: 1 Rationale: Invert the second fraction and multiply. 74. Simplify the following complex fraction: 3/4/7/8 1. 1/2 2. 2/3 3. 3/4 4. 6/7 Answer: 4 Rationale: Write as a division problem: ¾ ÷ 7/8 invert the second fraction and multiply: ¾ × 8/7 = 6/7 75. Simplify the following complex fraction: 4/5/8/9 1. 2/35 2. 9/10 3. 36/40 4. 32/45 Answer: 2 Rationale: Write as a division problem: 4/5 ÷ 8/9, invert the second fraction and multiply. 76. Simplify the following complex fraction: 1/4/1/2 1. 1/8 2. 1/4 3. 2 4. 1/2 Answer: 4 Rationale: Write as a division problem: 1/4 ÷ 1/2, invert the second fraction and multiply. 77. Simplify the following complex fraction and write as a mixed number in lowest terms: 4/5/3/4 1. 1 1/15 2. 3/5 3. 16/15 4. 12/20 Answer: 1 Rationale: Write as a division problem: 4/5 ÷ 3/4, invert the second fraction and multiply. 78. Simplify the following complex fraction and write in lowest terms: 1/2/3/4 1. 3/8 2. 4/6 3. 2/3 4. 1 1/3 Answer: 3 Rationale: Write as a division problem: 1/2 ÷ 3/4, invert the second fraction and multiply. 79. What is 32% of 25? 1. 800 2. .78 3. 7.8 4. 8 Answer: 4 Rationale: Multiply 0.32 by 25 yielding 8 80. What is 20% of 19? 1. 38 2. 3.8 3. 98 4. 0.95 Answer: 2 Rationale: Multiply 0.2 by 19 yielding 3.8 81. What is 80% of 110? 1. 88 2. 1.375 3. 0.72 4. 8800 Answer: 1 Rationale: Multiply 0.8 by 110 yielding 88 82. What is 0.87% of 30? 1. 26.1 2. 0.261 3. 2.9 4. 0.34 Answer: 2 Rationale: Multiply 0.0087 by 30 yielding 0.261 83. What is 20% of 50? 1. 0.4 2. 100 3. 10 4. 2.5 Answer: 3 Rationale: Multiply 0.2 by 50 yielding 10 84. The client was taking 250 mg of ampicillin every six hours. The doctor increased the dosage to 400 mg every six hours. What percentage of change was made in the dosage? ______% Answer: 60 Rationale: Fraction of change = change in dose/old dose = 150/250 = .6, or 60% increase in dosage. 85. The client's dosage of Lanoxin (digoxin) was changed from 0.125 mg to 0.5 mg. What percentage was the dosage increased? 1. 0.25 % 2. 40% 3. 400% 4. 300% Answer: 4 Rationale: Fraction of change = change in dose/old dose = 0.375/0.125 = 3 0r 300% increase in dosage. 86. A dosage is changed from 4 mg per day to 6 mg per day. Find the percentage of increase. 1. 150% 2. 67% 3. 50% 4. 33% Answer: 3 Rationale: Fraction of change = change in dose/old dose = 2/4 = .5 or 50% increase in dosage. 87. The old price was $19.95. The sale price is $11.97. What is the percentage discount? 1. 20% 2. 40% 3. 60% 4. 80% Answer: 2 Rationale: Fraction of discount = Change in price/old price = 7.98/19.95 = 0.4 or 40% 88. The client's dosage of Tenormin (atenolol) is reduced from 75 mg to 60 mg. What is the percentage decrease? 1. 67% 2. 15% 3. 150% 4. 20% Answer: 4 Rationale: Fraction of change = change in dose/old dose = 15/75 = .2 or 20% decrease in dosage. 89. A dosage is changed from 12 mg per day to 9 mg per day. What is the percentage decrease? 1. 25% 2. 13% 3. 75% 4. 33% Answer: 1 Rationale: Fraction of change = change in dose/old dose = 3/12 = .25 or 25% decrease in dosage. Test Bank for Dosage Calculations: A Multi-Method Approach Anthony Patrick Giangrasso, Dolores M. Shrimpton 9780132158626
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