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 DEALING WITH NEGATIVE INTEGERS

METEOROLOGIST JEFF HABY

The integers are the whole numbers and the negative whole numbers. Mathematical challenges can be faced when adding or subtracting integers and when finding a difference between integers.

The minus sign and the negative sign use the same sign (-) and can often be used interchangeable but some calculators do make a distinction between the minus and the negative. The minus means that a subtraction is taking place while a negative indicates a number is negative. For example, the problem 7 – (-10) = 17, is read 7 minus a negative 10 is equal to 17.

When there is no number between a minus sign and a negative sign, then the two signs can be exchanged for a positive sign. The problem 7 – (-10) = 17 has the same result as 7 + 10 = 17

When two negative numbers are added, then the answer becomes more negative. For example, -8 + (– 9) = -17 is read negative 8 plus a negative 9 equals negative 17 and can be thought of as spending \$8, then spending \$9 to result in the spending of \$17 dollars (a loss of \$17). This problem can also be written as -8 -9 = -17 (negative 8 minus 9 equals -17)

When there is a plus sign next to a negative sign and there is no number between the two signs, then the two signs can be exchanged for a negative sign. The problem -3 + (-3) = -6 has the same result as -3 -3 = -6

When more is subtracted from a whole number than the value of the whole number then the answer will be negative. For example, 7 – 10 = -3. Note that often a positive number will have an understood + sign with it. This plus sign that is understood may or may not be written. In integer problems you may see the plus sign included. Thus, the previous problem can be written as +7 – (+10) = -3

In meteorology, the issue of negative integers can come from finding a temperature difference or calculating an index such as the Lifted Index (LI).

Here is an example of a temperature difference. Suppose the temperature is 12 C and then falls to -8 C and a temperature difference (temperature change) needs to be determined. Take the absolute value of each number and add them together to find the temperature difference in cases where one number is positive and the other is negative. The absolute value has the symbol of | | and the symbol means to take the positive of the number inside the lines. The problem above becomes |12| + |-8| = 12 + 8 = 20 C temperature change. A qualifier can then be added such as decrease or increase. In this case, it is a 20 degree C decrease. Note that the value of a temperature change is NOT an actual temperature. Thus, a 20 degree C temperature change has nothing to do with it being an air temperature of 20 C.

In cases where both numbers are positive or both numbers are negative, then subtract one number from the other and then take the absolute value to get the temperature difference. Suppose the temperature drops from +17 C to +5 C and thus the temperature change is |17 – 5| or |5 – 17|, which in both cases results in a temperature change of 12 C (decreasing as a qualifier of the direction of change). Suppose the temperature increases from -22 (negative 22) to -8 (negative 8). The temperature change is |-22 – (-8)| or |-8 – (-22)|, which in both cases results in a temperature change of 14 C (increasing as a qualifier of the direction of change).

The formula for the LI (Lifted Index) is Temperature (environment) – Temperature (parcel) = LI. Usually these temperature will be negative, thus solving the problem will include negative values within a subtraction problem. Suppose the temperature of the environment is -15 C (negative 15) while the temperature of the parcel is -8 C (negative 8). The LI = (-15) – (-8) = (-15) + 8 = -7, thus the LI is a negative 7 (indicating instability). In this problem, since there was a minus and a negative next to each other, they became a plus and thus the 8 was added to the -15 to result in the answer of -7