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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

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