Firefighter Exam Practice Test Math 1 — Questions and Answers

Question 1: Which of the following is 1/3 of 3/4?

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

Correct answer: 1/4

To find '1/3 of 3/4,' you multiply the two fractions together. Multiplying (1/3) by (3/4) gives (1 * 3) / (3 * 4) = 3/12. This fraction can then be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 3, resulting in 1/4.

Question 2: What is the fraction of $75 that equals $1500?

3/5
1/20 (Correct answer)
1/14
7/10

Correct answer: 1/20

To determine what fraction of $1500 equals $75, you need to set up the ratio as 75/1500. To simplify this fraction, divide both the numerator and the denominator by their greatest common divisor. Dividing both 75 and 1500 by 75 yields 1/20.

Question 3: What is the sum of 3.14 + 2.73 + 23.7 ?

29.57 (Correct answer)
28.57
30.56
31.57

Correct answer: 29.57

To find the sum of these decimal numbers, align them vertically by their decimal points. Add the numbers in each column, carrying over when necessary, ensuring to maintain the decimal point's position in the sum. Adding 3.14, 2.73, and 23.70 (adding a zero for alignment) results in 29.57.

Question 4: Jell spent 15% of her earnings on an item and ended up with $120. What percentage of her income is still available?

80%
15%
85% (Correct answer)
78%

Correct answer: 85%

If Jell spent 15% of her total earnings, the percentage of her income that is still available is simply the total percentage minus the percentage spent. Therefore, 100% - 15% equals 85%. The amount of $120 is extraneous information for this specific question about percentages.

Question 5: Convert 0.27 + 0.33 to a fraction.

3/5 (Correct answer)
3/6
2/7
4/7

Correct answer: 3/5

First, sum the given decimal numbers: 0.27 + 0.33 equals 0.60. To convert 0.60 to a fraction, write it as 60/100, representing sixty hundredths. This fraction can then be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 20, resulting in the simplified fraction 3/5.

Question 6: What is the total of (3.13 + 7.87) X 5?

55 (Correct answer)
45
60
50

Correct answer: 55

According to the order of operations, you must first perform the calculation inside the parentheses. Adding 3.13 and 7.87 gives a sum of 11.00. Next, multiply this result by 5. Therefore, 11 multiplied by 5 equals 55.

Question 7: To the lowest terms, reduce 2/4 X 3/4.

6/4
6/12
3/8 (Correct answer)
5/16

Correct answer: 3/8

To multiply fractions, multiply the numerators together and the denominators together. So, (2/4) * (3/4) equals (2*3) / (4*4), which results in 6/16. To reduce this fraction to its lowest terms, divide both the numerator and the denominator by their greatest common divisor, which is 2, yielding 3/8.

Question 8: John has agreed to buy a Coke for everyone. Each drink costs $1.89, and there are 5 people in the group. Calculate John's cost.

$9
$12
$5
$10 (Correct answer)

Correct answer: $10

To calculate John's total cost, multiply the price of one drink by the number of people in the group. $1.89 multiplied by 5 people equals $9.45. Since the provided options are whole numbers, $10 is the closest and most reasonable approximation, likely implying a slight rounding up from the exact cost.

Question 9: At a cost of $5 per meter, the total cost of constructing a fence around a square-shaped field is $2000. What is the measurement of one side?

42 meters
325 meters
100 meters (Correct answer)
85 meters

Correct answer: 100 meters

First, calculate the total length of the fence (the perimeter) by dividing the total cost by the cost per meter: $2000 / $5 = 400 meters. Since the field is square-shaped, all four sides are equal in length. To find the measurement of one side, divide the total perimeter by 4, so 400 meters / 4 sides equals 100 meters per side.

Question 10: How far will a train travel in 12 seconds if it travels at 72 kilometers per hour?

240 m (Correct answer)
265 m
248 m
220 m

Correct answer: 240 m

First, convert the train's speed from kilometers per hour to meters per second for consistent units. 72 km/h is equivalent to (72 * 1000) meters / (3600) seconds, which simplifies to 20 m/s. Then, use the formula Distance = Speed × Time. Multiplying 20 m/s by 12 seconds gives a total distance of 240 meters.

Question 11: Mark spent $80 on 15 dozen eggs. During loading and unloading, 16 eggs were broken. He sold the last of the eggs for $0.54 each. What will be his profit percentage?

12.5%
11% (Correct answer)
12%
11.5%

Correct answer: 11%

Mark initially bought 15 dozen eggs, totaling 180 eggs. After 16 eggs broke, he had 164 eggs left to sell. Selling these at $0.54 each generated a revenue of $88.56 (164 * $0.54). His profit is the revenue minus the initial cost: $88.56 - $80 = $8.56. To find the profit percentage, divide the profit by the original cost and multiply by 100: ($8.56 / $80) * 100 = 10.7%, which rounds to 11%.

Question 12: What is the total of 0.78 + 0.38?

1.84
1.52
1.16 (Correct answer)
1.20

Correct answer: 1.16

To find the sum of these decimal numbers, align them vertically by their decimal points. Add the numbers in each column, starting from the rightmost digit, and carry over any tens to the next column. Adding 0.78 and 0.38 results in 1.16.

Question 13: L111 has a fuel economy of 4 miles per gallon. How many gallons of fuel will L111 have used if it drives 76 miles? Round up to the nearest whole number.

25
23
19 (Correct answer)
22

Correct answer: 19

To determine the number of gallons used, divide the total distance driven by the vehicle's fuel economy. Driving 76 miles with a fuel economy of 4 miles per gallon means 76 / 4 = 19 gallons of fuel were used. Since the result is already a whole number, no rounding up is necessary.

Question 14: How much money will you spend if gas costs $3.29 per gallon and you buy 6.5 gallons?

$21.39 (Correct answer)
$23.45
$16.39
$27.20

Correct answer: $21.39

To calculate the total cost, multiply the price per gallon by the number of gallons purchased. Multiplying $3.29 by 6.5 gallons yields $21.385. When dealing with currency, it's standard practice to round to two decimal places, making the total cost $21.39.

Question 15: How far did a fire engine travel if it was traveling down the interstate at 55 mph and arrived at the reported vehicle fire 13 minutes later?<br/> Use the following equation: Distance = Rate X Time

20 miles
12 miles (Correct answer)
18 miles
16 miles

Correct answer: 12 miles

First, convert the time from minutes to hours to match the rate's units. 13 minutes is equivalent to 13/60 of an hour. Then, apply the formula Distance = Rate × Time: 55 mph multiplied by (13/60) hours equals approximately 11.916 miles. Rounding this to the nearest whole number, the fire engine traveled about 12 miles.

Question 16: The square footage of a building must be obtained during the preplan process. You own a strip mall with two tenants. One occupancy is 96' x 52' and the other is 114' x 52'. How big is this building in terms of square footage?

14,000
10,000
12,000
11,000 (Correct answer)

Correct answer: 11,000

To find the total square footage, calculate the area of each occupancy and then sum them. The first occupancy is 96' x 52', which is 4992 square feet. The second is 114' x 52', totaling 5928 square feet. Adding these two areas together (4992 + 5928) gives a grand total of 10920 square feet, which rounds to 11,000 square feet, matching the closest option.

Firefighter Exam Practice Test Math 1

Which of the following is 1/3 of 3/4?