2.1 Basic Math Operations in Police Scenarios

Basic Math Operations in Police Scenarios

As a law enforcement officer, you will frequently rely on basic mathematics in the field. From calculating the total value of stolen property to dividing up patrol zones and estimating timeframes, fundamental arithmetic is a daily necessity. The National Police Officer Selection Test (NPOST) evaluates your proficiency in these skills. Critically, calculators are not permitted during the exam. You must be comfortable performing addition, subtraction, multiplication, and division manually with whole numbers, decimals, and fractions.

This section provides a thorough refresher on these core operations, applying them to the types of police scenarios you will encounter on the exam.

Whole Numbers

Whole numbers are the most basic building blocks of arithmetic. While you likely know how to perform these operations, the challenge on the NPOST often lies in extracting the correct numbers from a written scenario and executing the calculation flawlessly under time pressure.

Addition and Subtraction

Addition and subtraction often apply to taking inventory, compiling totals, or determining differences in quantities.

Scenario 1: Adding Property Values During a burglary investigation, Officer Chen catalogs the following stolen items: a television valued at $450, a laptop valued at $1,250, a watch valued at $325, and a camera valued at $800. What is the total estimated value of the stolen property?

Step-by-Step Solution:

1. Stack the numbers vertically, ensuring the units, tens, and hundreds columns align perfectly. 1250 800 450

• 325

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1. Add the units column: 0 + 0 + 0 + 5 = 5. Write down 5.
2. Add the tens column: 5 + 0 + 5 + 2 = 12. Write down 2 and carry over the 1.
3. Add the hundreds column: 1 (carried) + 2 + 8 + 4 + 3 = 18. Write down 8 and carry over the 1.
4. Add the thousands column: 1 (carried) + 1 = 2. Answer: The total value is $2,825.

Scenario 2: Subtracting Inventory The evidence room contains 4,520 rounds of 9mm ammunition. An instructor signs out 1,285 rounds for the week's qualification training. How many rounds remain in the evidence room?

Step-by-Step Solution:

1. Align the numbers vertically: 4520

• 1285

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1. Subtract the units: You cannot subtract 5 from 0, so you must borrow 1 from the tens column (the 2 becomes a 1, the 0 becomes 10). 10 - 5 = 5.
2. Subtract the tens: You cannot subtract 8 from 1, so you borrow from the hundreds column (the 5 becomes a 4, the 1 becomes 11). 11 - 8 = 3.
3. Subtract the hundreds: 4 - 2 = 2.
4. Subtract the thousands: 4 - 1 = 3. Answer: There are 3,235 rounds remaining.

Multiplication and Division

Multiplication is used for scaling up quantities (e.g., finding total costs for multiple identical items), while division is used for distribution or determining rates.

Scenario 3: Multiplication for Bulk Fines A municipal code enforcement officer issues 14 citations for illegal dumping in a month. If the standard fine for each citation is $350, what is the total dollar amount of the fines issued?

Step-by-Step Solution:

1. Set up the multiplication: 350 x 14

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1. Multiply 350 by 4:
   • 4 x 0 = 0
   • 4 x 5 = 20 (write 0, carry 2)
   • 4 x 3 = 12, plus 2 = 14.
   • First partial product: 1400.
2. Multiply 350 by 1 (representing 10, so add a zero placeholder):
   • 1 x 0 = 0
   • 1 x 5 = 5
   • 1 x 3 = 3
   • Second partial product: 3500.
3. Add the partial products: 1400 + 3500 = 4900. Answer: The total amount is $4,900.

Scenario 4: Division for Patrol Shifts A precinct has 156 patrol officers available. The captain wants to divide them evenly across 4 distinct shifts to ensure consistent coverage. How many officers will be assigned to each shift?

Step-by-Step Solution:

1. Set up long division: 156 ÷ 4.
2. Determine how many times 4 goes into the first digit (1). It does not, so look at the first two digits (15).
3. 4 goes into 15 three times (4 x 3 = 12). Write 3 above the 5.
4. Subtract 12 from 15 to get a remainder of 3. Bring down the 6, making the new number 36.
5. 4 goes into 36 exactly nine times (4 x 9 = 36). Write 9 above the 6.
6. The remainder is 0. Answer: There will be 39 officers per shift.

Decimals

Decimals frequently appear in police work when dealing with money, mileage, and precise weights (such as narcotics seizures). The golden rule of decimals is to align the decimal points during addition and subtraction.

Adding and Subtracting Decimals

Scenario 5: Calculating Drug Weights During a raid, officers seize three separate bags of a controlled substance. The bags weigh 4.25 grams, 12.6 grams, and 0.835 grams. What is the total weight of the seized narcotics?

Step-by-Step Solution:

1. Align the decimal points vertically. Add trailing zeros to ensure all numbers have the same number of decimal places. 4.250 12.600

• 0.835

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1. Add from right to left, just like whole numbers.
2. Bring the decimal point straight down into the answer.
   • Units: 0 + 0 + 5 = 5
   • Tens: 5 + 0 + 3 = 8
   • Hundreds: 2 + 6 + 8 = 16 (write 6, carry 1)
   • Decimal point down.
   • Ones: 1 (carried) + 4 + 2 + 0 = 7
   • Tens: 1 Answer: The total weight is 17.685 grams.

Multiplying and Dividing Decimals

When multiplying decimals, ignore the decimal points initially, multiply as whole numbers, and then count the total number of decimal places in the original problem to place the decimal in the answer.

Scenario 6: Multiplying Overtime Hours Officer Davis worked 8.5 hours of overtime this week. Her overtime pay rate is $32.40 per hour. How much overtime pay did she earn?

Step-by-Step Solution:

1. Multiply 3240 by 85 (ignoring decimals). 3240 x 85

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1. 5 x 3240 = 16200
2. 80 x 3240 = 259200
3. Add: 16200 + 259200 = 275400
4. Count the decimal places in the original problem: 8.5 has one, 32.40 has two. Total = 3 decimal places.
5. Place the decimal point three spots from the right: 275.400. Answer: She earned $275.40 in overtime pay.

Fractions

Fractions represent parts of a whole and are commonly used when discussing time (e.g., half an hour) or proportions.

Adding and Subtracting Fractions

To add or subtract fractions, you must find a common denominator (the bottom number).

Scenario 7: Combining Patrol Times Officer Miller spends 1/4 of his shift on paperwork, 1/3 of his shift on traffic detail, and the rest on community outreach. What fraction of his shift is spent on paperwork and traffic detail combined?

Step-by-Step Solution:

1. Add 1/4 + 1/3.
2. Find the lowest common denominator for 4 and 3, which is 12.
3. Convert 1/4: Multiply top and bottom by 3 to get 3/12.
4. Convert 1/3: Multiply top and bottom by 4 to get 4/12.
5. Add the numerators (top numbers): 3 + 4 = 7. Keep the denominator the same. Answer: He spends 7/12 of his shift on those duties.

Multiplying and Dividing Fractions

To multiply fractions, multiply the numerators together and the denominators together. To divide, flip the second fraction (find the reciprocal) and multiply.

Scenario 8: Multiplying Fractions for Search Areas A search and rescue grid is divided into sectors. Sector A is 3/4 of a square mile. A search team has covered 2/5 of Sector A. How much area (in square miles) have they covered?

Step-by-Step Solution:

1. Set up the multiplication: (3/4) x (2/5).
2. Multiply numerators: 3 x 2 = 6.
3. Multiply denominators: 4 x 5 = 20.
4. The result is 6/20. Simplify the fraction by dividing top and bottom by 2 to get 3/10. Answer: They have covered 3/10 of a square mile.

Mastering these manual operations is crucial. Practice them daily leading up to the exam to build speed and accuracy without a calculator.