Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Chapter 1 Introduction to Algebraic Expressions

1-2 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Addition of Real Numbers Adding with the Number Line Adding Without the Number Line Problem Solving Combining Like Terms 1.5

1-3 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Adding with a Number Line To add a + b on a number line, we start at a and move according to b. a) If b is positive, we move to the right (the positive direction). b) If b is negative, we move to the left (the negative direction). c) If b is 0, we stay at a.

1-4 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Example Add: − Solution Locate the first number −3, and then move 7 units to the right −3 + 7 = Start at −3 Move 7 units to the right.

1-5 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Example Add: −2 + (−3). Solution After locating −2, we move 3 units to the left Start at −2 Move 3 units to the left. −2 + (−3) = −5

Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Rules for Addition of Real Numbers 1.Positive numbers: Add as usual. The answer is positive. 2.Negative numbers: Add the absolute values and make the answer negative. 3.A positive and a negative number: Subtract the smaller absolute value from the greater absolute value. a) If the positive number has the greater absolute value, the answer is positive. b) If the negative number has the greater absolute value, the answer is negative. c) If the numbers have the same absolute value, the answer is 0. 4.One number is zero: The sum is the other number.

1-7 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Example Add without using the number line. a) −9 + (−11) b) − Two negatives, add the absolute value, answer is −20. A negative and a positive, subtract and the answer is negative, −19.

1-8 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Example Add without using the number line. c) − d) (−2.4) A negative and a positive, subtract and the answer is positive, 5.1. A negative and a positive, subtract and the answer is 0.

1-9 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Example Add: 17 + (−3) (−4) + (−12). Solution 17 + (−3) (−4) + (−12) = (−3)+ (−4) + (−12) Using the commutative law = ( ) +[(−3)+ (−4) + (−12)] Using the associative law = 42 + (−19) = 23

1-10 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Example During the first two weeks of the semester, 6 students withdrew from Mr. Lange’s algebra class, 9 students were added to the class, and 4 students were dropped as “no- shows.” By how many students did the original class size change? The original class size dropped by one.

1-11 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Combining Like Terms When two terms have variable factors that are exactly the same, the terms are called like or similar terms.

1-12 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Example Combine like terms −5x + 7x. Solution −5x + 7x = (−5 + 7)x = 2x

1-13 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Example Combine like terms: 3a + (−4b) + (−8a) + 10b Solution 3a + (−4b) + (−8a) + 10b = 3a + (−8a) + (−4b) + 10b = (3 +(−8))a + (−4 + 10)b = −5a + 6b