ASVAB Mathematics: Fractions, Decimals and Percentages — Questions and Answers

Question 1: What is 3/4 expressed as a decimal?

0.34
0.75 (Correct answer)
0.43
0.80

Correct answer: 0.75

Divide the numerator by the denominator: 3 ÷ 4 = 0.75.

To convert a fraction to a decimal, divide the numerator by the denominator. 3 ÷ 4 = 0.75. This can also be remembered as a benchmark: 1/4 = 0.25, so 3/4 = 3 × 0.25 = 0.75.

Question 2: What is 45% expressed as a decimal?

4.5
0.045
0.45 (Correct answer)
45.0

Correct answer: 0.45

To convert a percent to a decimal, divide by 100: 45 ÷ 100 = 0.45.

Percent means 'per hundred.' To convert a percent to a decimal, divide by 100 or simply move the decimal point two places to the left. 45% becomes 0.45.

Question 3: What is 2/5 expressed as a percentage?

25%
40% (Correct answer)
20%
50%

Correct answer: 40%

2 ÷ 5 = 0.40; multiply by 100 to get 40%.

To convert a fraction to a percentage: 2 ÷ 5 = 0.40, then 0.40 × 100 = 40%. Alternatively, multiply numerator and denominator to get a denominator of 100: 2/5 = 40/100 = 40%.

Question 4: What is 1/3 + 1/6?

1/2 (Correct answer)
2/9
1/4
2/6

Correct answer: 1/2

Convert to common denominator: 2/6 + 1/6 = 3/6 = 1/2.

To add fractions, find a common denominator. LCD of 3 and 6 is 6. Convert 1/3 to 2/6. Then 2/6 + 1/6 = 3/6. Simplify 3/6 to 1/2.

Question 5: What is 30% of 150?

30
45 (Correct answer)
50
60

Correct answer: 45

30% of 150 = 0.30 × 150 = 45.

To find 30% of 150: convert 30% to 0.30, then multiply: 0.30 × 150 = 45. Alternatively, 10% of 150 = 15, and 30% = 3 × 15 = 45.

Question 6: Reduce the fraction 18/24 to lowest terms.

9/12
3/4 (Correct answer)
6/8
2/3

Correct answer: 3/4

GCF of 18 and 24 is 6. 18÷6 = 3, 24÷6 = 4, so 3/4.

The greatest common factor (GCF) of 18 and 24 is 6. Dividing both by 6 gives 3/4. While 9/12 and 6/8 are equivalent, they are not in lowest terms because they can still be simplified.

Question 7: What is 0.625 expressed as a fraction in lowest terms?

625/1000
5/8 (Correct answer)
6/10
62/100

Correct answer: 5/8

0.625 = 625/1000. GCF is 125, giving 5/8.

0.625 = 625/1000. Find GCF(625, 1000) = 125. Divide both: 625 ÷ 125 = 5; 1000 ÷ 125 = 8. So 0.625 = 5/8.

Question 8: A store item is marked up 20% from its cost of $80. What is the selling price?

$90
$96 (Correct answer)
$100
$88

Correct answer: $96

20% of $80 = $16. $80 + $16 = $96.

A 20% markup means you add 20% of the cost to the original price. 20% of $80 = 0.20 × $80 = $16. Selling price = $80 + $16 = $96.

Question 9: What is 3/8 × 4/9?

7/17
1/6 (Correct answer)
12/24
4/8

Correct answer: 1/6

Multiply numerators and denominators: (3×4)/(8×9) = 12/72 = 1/6.

To multiply fractions, multiply numerators together and denominators together: 3×4 = 12; 8×9 = 72. So 12/72. Simplify: GCF(12, 72) = 12, giving 1/6.

Question 10: What is 5/6 ÷ 2/3?

10/18
5/4 (Correct answer)
3/4
2/5

Correct answer: 5/4

Multiply by the reciprocal: 5/6 × 3/2 = 15/12 = 5/4.

To divide fractions, multiply by the reciprocal of the divisor: 5/6 ÷ 2/3 = 5/6 × 3/2 = 15/12. Simplify: GCF(15,12) = 3, giving 5/4.

Question 11: A soldier scores 72 out of 90 on a test. What percentage did she score?

72%
80% (Correct answer)
78%
75%

Correct answer: 80%

72 ÷ 90 = 0.80 = 80%.

Percentage score = (score ÷ total) × 100 = (72 ÷ 90) × 100 = 0.80 × 100 = 80%.

Question 12: What is 7/10 + 3/5?

10/15
13/10
1 3/10 (Correct answer)
4/5

Correct answer: 1 3/10

Convert 3/5 to 6/10. 7/10 + 6/10 = 13/10 = 1 3/10.

LCD of 10 and 5 is 10. Convert: 3/5 = 6/10. Add: 7/10 + 6/10 = 13/10. As a mixed number: 1 3/10.

Question 13: An item originally costs $120. After a 15% discount, what is the new price?

$102 (Correct answer)
$105
$108
$18

Correct answer: $102

15% of $120 = $18. $120 - $18 = $102.

Discount = 15% × $120 = 0.15 × 120 = $18. New price = $120 - $18 = $102.

Question 14: What is 0.35 expressed as a percentage?

3.5%
0.35%
35% (Correct answer)
350%

Correct answer: 35%

Multiply the decimal by 100: 0.35 × 100 = 35%.

To convert a decimal to a percentage, multiply by 100 (move decimal right two places): 0.35 × 100 = 35%.

Question 15: What is 2 1/4 - 3/4?

1 1/2 (Correct answer)
1 1/4
2
1 3/4

Correct answer: 1 1/2

Convert 2 1/4 to 9/4. 9/4 - 3/4 = 6/4 = 1 1/2.

Convert 2 1/4 to improper fraction: (2×4+1)/4 = 9/4. Subtract: 9/4 - 3/4 = 6/4. Simplify: 6/4 = 3/2 = 1 1/2.

Question 16: What percent of 200 is 50?

15%
20%
25% (Correct answer)
30%

Correct answer: 25%

50 ÷ 200 = 0.25 = 25%.

Percentage = (part ÷ whole) × 100 = (50 ÷ 200) × 100 = 0.25 × 100 = 25%.

Question 17: What is 1.2 × 0.5?

0.6 (Correct answer)
6.0
0.06
1.7

Correct answer: 0.6

1.2 × 0.5 = 0.6. Multiply as whole numbers (12 × 5 = 60), then place decimal.

Multiply 12 × 5 = 60. The total decimal places in 1.2 (one) and 0.5 (one) = two places. Place decimal two from right: 0.60 = 0.6.

Question 18: A vehicle travels 3/5 of a 200-mile route. How many miles does it cover?

100
120 (Correct answer)
150
60

Correct answer: 120

3/5 × 200 = 120 miles.

3/5 of 200 = (3 × 200) ÷ 5 = 600 ÷ 5 = 120 miles.

Question 19: Which fraction is greatest: 2/3, 3/5, 5/8?

3/5
5/8
2/3 (Correct answer)
They are equal

Correct answer: 2/3

Convert to decimals: 2/3 ≈ 0.667, 3/5 = 0.60, 5/8 = 0.625. So 2/3 is greatest.

2/3 ≈ 0.667; 3/5 = 0.600; 5/8 = 0.625. The largest decimal is 0.667, corresponding to 2/3.

Question 20: What is 12.5% expressed as a fraction in lowest terms?

1/8 (Correct answer)
12/50
1/4
5/40

Correct answer: 1/8

12.5% = 12.5/100 = 125/1000 = 1/8.

12.5% = 12.5/100. Multiply numerator and denominator by 8: 12.5 × 8 = 100; 100 × 8 = 800. Wait — simpler: 12.5/100 = 125/1000. GCF = 125. 125/125 = 1; 1000/125 = 8. So 1/8.

Question 21: What is the decimal equivalent of 7/8?

0.78
0.875 (Correct answer)
0.87
0.88

Correct answer: 0.875

7 ÷ 8 = 0.875.

7 ÷ 8: 8 goes into 70 eight times (64), remainder 6. 8 goes into 60 seven times (56), remainder 4. 8 goes into 40 five times. Result: 0.875.

Question 22: A squad uses 2/3 of its 60 MREs in the field. How many MREs remain?

20 (Correct answer)
40
30
45

Correct answer: 20

2/3 × 60 = 40 used. 60 - 40 = 20 remaining.

MREs used = 2/3 × 60 = 40. Remaining = 60 - 40 = 20.

Question 23: Increase 80 by 25%. What is the result?

95
100 (Correct answer)
105
110

Correct answer: 100

25% of 80 = 20. 80 + 20 = 100.

25% × 80 = 0.25 × 80 = 20. New value = 80 + 20 = 100.

Question 24: What is 5/12 - 1/4?

4/8
1/6 (Correct answer)
2/12
1/3

Correct answer: 1/6

Common denominator 12: 5/12 - 3/12 = 2/12 = 1/6.

Convert 1/4 to 3/12 (multiply by 3/3). Subtract: 5/12 - 3/12 = 2/12. Simplify: GCF(2,12) = 2, giving 1/6.

Question 25: What is 3.6 ÷ 0.4?

0.9
9 (Correct answer)
36
0.09

Correct answer: 9

Multiply both by 10: 36 ÷ 4 = 9.

To divide by a decimal, multiply both dividend and divisor by the same power of 10 to make the divisor a whole number: 3.6 ÷ 0.4 = 36 ÷ 4 = 9.

Question 26: A soldier completes 60% of a 15-mile run. How many miles has she run?

8
9 (Correct answer)
10
12

Correct answer: 9

60% × 15 = 0.60 × 15 = 9 miles.

60% of 15 = 0.60 × 15 = 9 miles.

Question 27: What is 1/2 + 2/3 + 1/6?

3/11
1 1/3 (Correct answer)
4/11
1 1/2

Correct answer: 1 1/3

LCD = 6: 3/6 + 4/6 + 1/6 = 8/6 = 1 2/6 = 1 1/3.

LCD = 6. Convert: 1/2 = 3/6; 2/3 = 4/6; 1/6 stays. Add: 3/6 + 4/6 + 1/6 = 8/6. Convert to mixed: 1 2/6 = 1 1/3.

Question 28: What percentage is 18 out of 24?

65%
70%
75% (Correct answer)
80%

Correct answer: 75%

18 ÷ 24 = 0.75 = 75%.

18 ÷ 24 = 0.75. Multiply by 100 = 75%.

Question 29: What is 0.125 as a fraction?

1/4
1/8 (Correct answer)
1/5
1/6

Correct answer: 1/8

0.125 = 125/1000. GCF = 125. 125/1000 = 1/8.

0.125 = 125/1000. Simplify: 125 ÷ 125 = 1; 1000 ÷ 125 = 8. Result: 1/8.

Question 30: A tank is 3/8 full. If it holds 240 gallons, how many gallons are currently in it?

60
80
90 (Correct answer)
120

Correct answer: 90

3/8 × 240 = 720/8 = 90 gallons.

3/8 of 240 = (3 × 240) ÷ 8 = 720 ÷ 8 = 90 gallons.

Question 31: If a price decreases from $50 to $40, what is the percent decrease?

10%
20% (Correct answer)
25%
15%

Correct answer: 20%

Decrease = $10. Percent = (10/50) × 100 = 20%.

Percent change = [(original - new) ÷ original] × 100 = [(50 - 40) ÷ 50] × 100 = [10 ÷ 50] × 100 = 0.20 × 100 = 20%.

Question 32: What is 9/10 × 5/3?

3/2 (Correct answer)
45/30
14/30
5/4

Correct answer: 3/2

9×5 = 45; 10×3 = 30. 45/30 = 3/2.

Multiply numerators: 9 × 5 = 45. Multiply denominators: 10 × 3 = 30. Fraction = 45/30. GCF(45,30) = 15. 45÷15 = 3; 30÷15 = 2. Result: 3/2.

Question 33: What is 33 1/3% expressed as a fraction?

1/4
1/3 (Correct answer)
2/3
3/10

Correct answer: 1/3

33 1/3% = (100/3)% = 100/(3×100) = 1/3.

33 1/3% means 33.333…/100. As a fraction: (100/3)/100 = 1/3. Memorize: 33 1/3% = 1/3; 66 2/3% = 2/3.

Question 34: Evaluate: 0.4 + 3/5.

0.9
1.0 (Correct answer)
0.7
3.4

Correct answer: 1.0

3/5 = 0.6. 0.4 + 0.6 = 1.0.

Convert 3/5 to decimal: 3 ÷ 5 = 0.6. Add: 0.4 + 0.6 = 1.0.

Question 35: What is 2 3/4 expressed as an improper fraction?

6/4
9/4
11/4 (Correct answer)
8/4

Correct answer: 11/4

Multiply whole number by denominator and add numerator: (2×4)+3 = 11. Answer: 11/4.

To convert a mixed number: (whole × denominator) + numerator, over denominator. 2 3/4: (2×4) + 3 = 8 + 3 = 11; denominator stays 4. Result: 11/4.

Question 36: What is 5% of 340?

15
17 (Correct answer)
20
34

Correct answer: 17

5% of 340 = 0.05 × 340 = 17.

5% = 0.05. 0.05 × 340 = 17. Shortcut: 10% = 34; 5% = 34 ÷ 2 = 17.

ASVAB Mathematics: Fractions, Decimals and Percentages

What is 3/4 expressed as a decimal?

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