Page 10

hendricks_beginning_algebra_1e_ch1_3

8 Chapter 1 Real Numbers and Algebraic Expressions Opposites of Real Numbers A number line not only provides us a way to order real numbers, it also helps us visualize the distance between numbers. Two numbers that lie equal distances from zero and lie on opposite sides of zero are opposites or additive inverses of one another. ������������������������ Opposite of a Real Number The opposite or additive inverse of a real number a is the number that has the same distance from 0 but lies on the opposite side of 0. The opposite of a real number a is denoted as -a. –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 3 units 3 units This number line illustrates that -3 and 3 are opposites of one another since they are the same distance from zero but on opposite sides of zero. We state these facts as shown in the table. Verbal Statement Mathematical Statement The opposite of negative three is three. -(-3) = 3 The opposite of three is negative three. -(3) = -3 ������������ • The opposite of a positive real number is a negative number. • The opposite of a negative real number is a positive number. �� ������������������������ ������������������ Find the opposite of each number. Write a mathematical statement to represent the answer. Solution Problem Opposite Mathematical Statement 4a. -2 The opposite of -2 is 2. -(-2) = 2 4b. 16 The opposite of 16 is -16. -(16) = -16 3 4 4c. The opposite of 3 4 is - 3 4 . -a3 4 b = - 3 4 4d. - 9 5 The opposite of - 9 5 is 9 5 . -a- 9 5 b = 9 5 4e. π The opposite of π is -π. -(π) = -π 4f. -0.23 The opposite of -0.23 is 0.23. -(-0.23) = 0.23 Student Check 4 Find the opposite of each number. Write a mathematical statement to represent the answer. a. -7 b. 4 c. 1 2 d. - 25 6 e. 16 f. 8.2 Absolute Value We just defined numbers that are opposites as numbers that have the same distance from zero on a number line. A number’s distance from zero is called its absolute value. Objective 4 ▶ Find the opposite of a real number. Objective 5 ▶ Find the absolute value of a real number.


hendricks_beginning_algebra_1e_ch1_3
To see the actual publication please follow the link above