CHAPTER 1. Mathematics Finding a Number When a Percentage of It Is Known Example: Eighty ohms represents 52% of a microphone’s total resistance. Find the total resistance of this microphone. Positive and Negative Numbers (Signed Numbers) Positive numbers are numbers that are greater than zero. Negative numbers are numbers less than zero. [Figure 1-8] Signed numbers are also called integers. Addition of Positive and Negative Numbers The sum (addition) of two positive numbers is positive. The sum (addition) of two negative numbers is negative. The sum of a positive and a negative number can be positive or negative, depending on the values of the numbers. A good way to visualize a negative number is to think in terms of debt. If you are in debt by \$100 (or, -100) and you add \$45 to your account, you are now only \$55 in debt (or -55). Therefore: - 100 + 45 = - 55. Example: The weight of an aircraft is 2,000 pounds. A radio rack weighing 3 pounds and a transceiver weighing 10 pounds are removed from the aircraft. What is the new weight? For weight and balance purposes, all weight removed from an aircraft is given a minus sign, and all weight added is given a plus sign. 2,000 + - 3 + - 10 = 2,000 + - 13 = 1987 Therefore, the new weight is 1,987 pounds. Subtraction of Positive and Negative Numbers To subtract positive and negative numbers, first change the “–" (subtraction symbol) to a “+" (addition symbol), and change the sign of the second number to its opposite (that is, change a positive number to a negative number or vice versa). Finally, add the two numbers together. Example: The daytime temperature in the city of Denver was 6° below zero (-6°). An airplane is cruising at 15,000 feet above Denver. The temperature at 15,000 feet is 20° colder than in the city of Denver. What is the temperature at 15,000 feet? Subtract 20 from - 6: - 6 – 20 = - 6 + - 20 = - 26 The temperature is - 26°, or 26° below zero at 15,000 feet above the city. Multiplication of Positive and Negative Numbers The product of two positive numbers is always positive. The product of two negative numbers is always positive. The product of a positive and a negative number is always negative. Examples: 3 x 6 = 18 - 3 x 6 = -18 - 3 x - 6 = 18 3 x - 6 = - 18 Division of Positive and Negative Numbers The quotient of two positive numbers is always positive. The quotient of two negative numbers is always positive. The quotient of a positive and negative number is always negative.