1. Subtracting 0.025 from 0.10 results in a difference of:
a.
.0125
b.
1.25
c.
0.125
d.
0.075
ANS: D
Feedback
A
This is an addition of the numbers with the decimal points not aligned.
B
This is an addition of the numbers with the decimal points not aligned.
C
This is a sum of the numbers.
D
Aligning the decimal points and subtracting results in a difference of 0.075.
DIF: Cognitive Level: Apply REF: Page 8
2. A temperature of 104° F converts to a Celsius temperature of:
a.
40° C
b.
75.6° C
c.
129.6° C
d.
72° C
ANS: A
Feedback
A
104 – 32 = 72
72 5 = 360
360/9 = 40
B
This answer (75.6° C) is the result of adding 32 to the Fahrenheit temperature instead of subtracting it.
C
This answer (129.6° C) is the result of multiplying by 9/5 instead of 5/9.
D
This answer (72° C) is the result of subtracting 32 from the Fahrenheit temperature without multiplying by the fraction 5/9.
DIF: Cognitive Level: Apply REF: Page 13
3. What is the lowest common denominator among the fractions 1/3, 1/2, and 1/4?
a.
12
b.
6
c.
5
d.
24
ANS: A
Feedback
A
The smallest number that is divisible by all three denominators (3, 2, 4) is 12.
B
Four does not divide evenly into 6.
C
None of the denominators divide evenly into 5.
D
Although all of the denominators divide evenly into 24, it is not the smallest common denominator.
DIF: Cognitive Level: Remember REF: Page 4
4. Dividing 0.75 by 0.25 results in a quotient of:
a.
30
b.
3.00
c.
0.1875
d.
0.50
ANS: B
Feedback
A
This answer is the result of dividing 0.75 by 0.025.
B
After moving the decimal places over two positions in the divisor and the dividend, then proceeding with division, the result is the whole number 3.
C
This is the product of the two numbers, not the quotient.
D
This is the result of subtracting 0.25 from 0.75.
DIF: Cognitive Level: Apply REF: Page 9
5. One centimeter is equal to how many millimeters?
a.
100 mm
b.
1000 mm
c.
1/10 mm
d.
10 mm
ANS: D
Feedback
A
1 cm = 10 mm, not 100 mm.
B
1 cm = 10 mm, not 1000 mm.
C
1 cm = 10 mm, not 1/10 mm.
D
1 cm = 10 mm.
DIF: Cognitive Level: Remember REF: Page 13
6. Eighteen is 30% of:
a.
540
b.
60
c.
0.06
d.
54
ANS: B
Feedback
A
This answer (540) is the result of multiplying 18 by 30. (This is not the correct way to determine percentage.)
B
18 = 30%x
18 = 0.30x
18/0.30 = x
18/0.30 = 60
C
This answer (0.06) is the result of dividing 0.018 by 0.30. (This eliminates the step of moving the decimal to the right to create a divisor that is a whole number.)
D
This answer (54) is the result of multiplying 18 by 3 instead of dividing by 0.30.
DIF: Cognitive Level: Apply REF: Page 11
7. The ratio 3:100 would properly be expressed in fraction form as:
a.
0.003
b.
3/100
c.
100/3
d.
33 1/3%
ANS: B
Feedback
A
This is decimal form and not expressed as a fraction.
B
Ratio indicates division, and the fraction 3/100 also represents the same operation of three parts of 100.
C
This fraction represents 100 3.
D
This is percentage form and not a fraction.
DIF: Cognitive Level: Remember REF: Page 7
8. Three teaspoons equal how many milliliters?
a.
30 mL
b.
45 mL
c.
100 mL
d.
15 mL
ANS: D
Feedback
A
30 mL = 6 teaspoons.
B
45 mL = 9 teaspoons.
C
100 mL = 20 teaspoons.
D
1 teaspoon = 5 mL; 3 teaspoons = 15 mL.
DIF: Cognitive Level: Remember REF: Page 14
9. In the proportion 2.5 : x :: 500 : 600, the unknown is:
a.
120,000
b.
–40
c.
3
d.
2.08
ANS: C
Feedback
A
This answer (120,000) is the result of multiplying the two terms on the right (500, 600) and dividing by the numeric term on the left (2.5).
B
This answer (–40) is the result of subtracting the two terms on the right (500, 600) and dividing by the numeric term on the left (2.5).
C
This answer (3) is the result of multiplying the means and the extremes and then dividing to find the unknown.
D
This answer (2.08) is the result of multiplying an extreme (2.5) by a mean (500) and dividing by the other extreme (600).
DIF: Cognitive Level: Remember REF: Page 12
10. Expressed in Roman numerals, the number 2009 is:
a.
IIIV
b.
MMIIII
c.
MMIX
d.
IVMM
ANS: C
Feedback
A
This Roman numeral is not consistent with the syntax for the numbering system.
B
This Roman numeral is not consistent with the syntax for the numbering system.
C
The symbols for 1000 (M) are added, making 2000, and the number for 1 (I) is subtracted from the number for 10 (X), giving 9.
D
This Roman numeral is not consistent with the syntax for the numbering system.
DIF: Cognitive Level: Apply REF: Page 1 and 2
PROBLEM
1. Convert 1/500 to a decimal.
ANS:
0.002
1 500 = 0.002
DIF: Cognitive Level: Apply REF: Page 10
2. Convert 0.375 to a fraction.
ANS:
3/8
0.375 = 375/1000; reduced by dividing both numbers by 125 = 3/8
DIF: Cognitive Level: Apply REF: Page 10
3. Convert the following: 293° F = x° C.
ANS:
145° C
(5/9) (293 – 32) = 145
DIF: Cognitive Level: Apply REF: Page 13
4. Solve for x in the following proportion: 1/4 : 6 :: 3 : x.
ANS:
72
6 3 = 1/4x; 18 = 1/4x; (1/4)(18) = 72
DIF: Cognitive Level: Apply REF: Page 12
5. Change 4 3/4 to an improper fraction.
ANS:
19/4
(4 = 16/4) + 3/4 = 19/4
DIF: Cognitive Level: Apply REF: Page 3
6. Solve for x in the following equivalent fraction: 100/x = 50/25
ANS:
x = 50
100 25 = 2500; 50 x = 50x; 2500/50 = 50
DIF: Cognitive Level: Apply REF: Page 4
7. Solve for x in the following proportion: 0.25 : 10 :: x : 1
ANS:
0.025
10x = (1 0.25); x = 0.25/10 = 0.025
DIF: Cognitive Level: Apply REF: Page 12
8. What is 1/4% of 20?
ANS:
0.05
1/4% = 0.0025; 0.0025 20 = 0.05
DIF: Cognitive Level: Apply REF: Page 10 and 11
9. Convert the following units: 143 lb = x kg
ANS:
65 kg
1 kg = 2.2 lb; 143/2.2 = 65
DIF: Cognitive Level: Apply REF: Page 14
10. Convert 16/100 to a decimal.
ANS:
0.16
16 100 = 0.16
DIF: Cognitive Level: Apply REF: Page 10
11. Write CXLVII as an Arabic numeral.
ANS:
147
C = 100, X = 10, L = 50, V = 5, I = 1
100 + (50 – 10) + (5 + 2)
DIF: Cognitive Level: Apply REF: Page 1 and 2
12. Solve for x in the following proportion: 1/5 :1 :: 20 : x
ANS:
100
1/5x = 20 1; x = 5 20
DIF: Cognitive Level: Apply REF: Page 12
13. Solve for x in the following equivalent fraction: x/16 = 6/32
ANS:
x = 3
16 6 = 96; 32 x = 32x (Dividing both sides by 32 yields x = 3.)
DIF: Cognitive Level: Apply REF: Page 4
14. Convert the following units: 1 tablespoon = x mL
ANS:
15 mL
1 teaspoon = 5 mL; 1 tablespoon = 3 teaspoons
3 5 = 15
DIF: Cognitive Level: Apply REF: Page 14
15. Convert the following: 38° C = x° F
ANS:
100.4° F
(9 × 38 + 160)/5 = 100.4
DIF: Cognitive Level: Apply REF: Page 13
16. Write MDCCLXXVI as an Arabic numeral.
ANS:
1776
M = 1000, D = 500, C = 100, L = 50, X = 10, V = 5, I = 1
1000 + (1000 – 300) + (50 + 20) + (5 + 1)
DIF: Cognitive Level: Apply REF: Page 1
17. Find the lowest common denominator: 1/3, 5/4, 3/5
ANS:
LCD = 60
3 4 = 12; 12 5 = 60 (Sixty is the smallest number divisible by all three denominators.)
DIF: Cognitive Level: Apply REF: Page 4
18. Convert 1/8 to a decimal.
ANS:
0.125
1 8 = 0.125
DIF: Cognitive Level: Apply REF: Page 10
19. Three is what percent of 5?
ANS:
60%
3 is 3/5 of 5; 3 divided by 5 = 0.60 or 60%
DIF: Cognitive Level: Apply REF: Page 11
20. Solve for x in the following proportion: 9 : 6 :: x : 30
ANS:
45
6x = 9 30; 6x = 270; 270 6 = 45
DIF: Cognitive Level: Apply REF: Page 12
21. Solve for x in the following equivalent fraction: 3/6 = x/12
ANS:
x = 6
3 12 = 36; 6 x = 6x (Dividing both sides of 36 = 6x by 6 yields 6 = x.)
DIF: Cognitive Level: Apply REF: Page 4
22. Write 1888 as a Roman numeral.
ANS:
MDCCCLXXXVIII
M = 1000, D = 500, C = 100, L = 50, X = 10
1000 + 500 + 100 + 100 + 100 + 50 + 10 + 10 + 10 + 5 + 1 + 1 + 1
DIF: Cognitive Level: Apply REF: Page 1 and 2
23. Change 15 3/8 to an improper fraction.
ANS:
123/8
(15 = 120/8) + 3/8
DIF: Cognitive Level: Apply REF: Page 3
24. Convert the following: 68° F = x° C
ANS:
20° C
(5/9) (68 – 32) = 20
DIF: Cognitive Level: Apply REF: Page 13
25. Find the lowest common denominator: 1/8, 1/4, 1/32
ANS:
LCD = 32
8 4 = 32 (Thirty-two is the smallest number divisible by all three denominators.)
DIF: Cognitive Level: Apply REF: Page 4
26. Convert the following units: 30 mL = x fl oz
ANS:
1 fl oz
1 fl oz = 30 mL
DIF: Cognitive Level: Apply REF: Page 14
27. What percent of 25 is 5?
ANS:
20%
5 is 1/5 of 25; 1 divided by 5 = 0.20 or 20%
DIF: Cognitive Level: Apply REF: Page 11
28. Convert 6.25 to a fraction.
ANS:
25/4 or 6 1/4
0.25 is the same as 25/100; dividing the numerator and denominator by 25 = 1/4
DIF: Cognitive Level: Apply REF: Page 10
29. Solve for x in the following proportion: 5 : 25 :: x : 100
ANS:
20
25x = 5 100; x = 500/25
DIF: Cognitive Level: Apply REF: Page 12
