Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Math 52 1.3 "Addition of Real Numbers" Objectives: * Add real numbers without using a number line. * Find the opposite, or additive inverse, of a real number. Preliminaries: In this section, we consider addition of real numbers. First, to gain an understanding, we add using a number line. Then we consider rules for addition. Addition on a Number Line: To do the addition a + b on a number line, we start at 0. Then we move to a and then move according to b a) If b is positive, we move from a to the right b) If b is negative, we move from a to the left c) If b is zero, we stay at a Example 1: (Adding using a number line) Add: a) 3 7 b) 5 1 + 2 2 Adding Without a Number Line Rules for Addition of Real Numbers: 1: Positive numbers: Add the numbers (the answer is positive) 2: Negative numbers: Add absolute values (the answer is negative) 3: A positive and a negative number: Subtract the smaller absolute value from the larger (the answer has the sign of the larger number). 4: One number is zero: The sum is the other number. Note: Rule 4 is known as the identity property of 0. (it says that for any real number a, a + 0 = a) Example 2: (Adding without using a number line) Add without using a number line: a) 5 + ( 6) b) 1:5 + ( 1:5) c) 2:8 + 0 d) f) 1 + 5 0:17 + 0:7 e) 36 + 21 Page: 1 3 4 Notes by Bibiana Lopez Introductory Algebra by Marvin L. Bittinger 1.3 Example 2: (Adding without using a number line) Add without using a number line. a) 2:5 + ( 10) + 6 + ( 7:5) + 3:5 + ( 1:5) b) 15 + ( 2) + 7 + 14 + ( 5) + ( 12) Opposites or Additive Inverses De…nition: "Opposites or Additive Inverses" Two numbers whose sum is 0 are called opposites, or additive inverses, of each other. The opposite of a number a can be named a: Example 3: (Finding the opposite) Find the opposite, or additive inverse, of each number. a) 4 b) 0 c) 7:74 d) 8 9 De…nition: "The Opposite of an Opposite" kThe opposite of the opposite of a number is the number itself. That is, for any number a; Example 4: (Finding the opposite and the opposite of an opposite) Evaluate x and ( x) when: b) x= a) x = 32 The Sum of Opposites: kFor any real number a, the opposite of a expressed as ( a) = a:k 3 a, is such that a + ( a) = ( a) + a = 0k Page: 2 Notes by Bibiana Lopez