Dealing with Negative Numbers

Fundamentals of Social Statistics by Adam J. McKee

In our day-to-day activities, we predominantly encounter positive numbers. However, when diving into the realm of statistics, the use of negative numbers becomes more prevalent. Given that many might not have engaged with negative numbers for some time, it’s essential to revisit and hone our understanding. To kick things off, let’s revisit a familiar concept—the number line.

Reintroducing the Number Line

Understanding the Number Line

  -4  -3  -2  -1    0   1   2   3   4
  • Negative numbers are placed to the left of zero.
  • Positive numbers are located to the right.
  • As negative numbers increase in magnitude (like from -1 to -6), we move further away from zero, often referred to as going “deeper in the hole.”

In general mathematics, numbers without a sign are inherently positive. However, negative numbers always come prefixed with a negative sign (-).

Key Rules for Handling Negative Numbers

Rule 1: Multiplying or Dividing Different Signs
Multiplying or dividing numbers with differing signs (positive and negative) results in a negative number.

Rule 2: Multiplying or Dividing Same Signs
Numbers with identical signs, when multiplied or divided, yield a positive outcome. This is why squaring (multiplying a number by itself) a negative number always gives a positive result.

Rule 3: Summing Negative Numbers
Adding a series of negative numbers will produce a negative result.

Rule 4: Mixing Positive and Negative in Addition
When combining a positive and negative number, drop the signs and treat it like subtraction—deduct the smaller number from the larger. The resulting number inherits the sign of the larger number.

Rule 5: Series of Mixed Signs
For a series with mixed signs, sum all the positive numbers first. Then, sum the negatives. Lastly, apply Rule 4 to get the final sum.

Rule 6: Subtracting Negatives from Negatives
When you take away a negative from another negative, drop the signs and simply subtract. The outcome is negative.

Example:  -10 - -4 = -6

Rule 7: Subtracting Negative from Positive
Subtracting a negative from a positive turns the negative into a positive, and you then sum the numbers.

Example:  5 - -5 = 10

Rule 8: Subtracting Positive from Negative
When taking a positive from a negative, drop the signs and add. The result is always negative.

Example:  -6 – 4 = -10

Wrapping Up

Statistics often requires a fine balance of both theoretical and mathematical understanding. Negative numbers, although seemingly simple, can become complex when used in various operations. But with these rules as a guide, handling them becomes far more straightforward. So, the next time you encounter negative numbers in your statistical endeavors, be confident in your approach!

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Last Modified:  08/18/2023

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