1.1 Integers and Rational Numbers

www.ck12.org Chapter 1. Arithmetic Review1.2 Addition and Subtraction of Rational NumbersAddition of Rational NumbersA football team gains 11 yards on one play then loses 5 yards on another play and loses 2 yards on the third play.What is the total yardage loss or gain?A loss can be expressed as a negative integer. A gain can be expressed as a positive integer. To find the net gain orloss, the individual values must be added together. Therefore, the sum is 11+−5+−2 = 4. The team has a net gainof 4 yards.Addition can also be shown using a number line. If you need to add 2 + 3, start by making a point at the value of 2and move three integers to the right. The ending value represents the sum of the values.Example 1: Find the sum of −2 + 3 using a number line.Solution: Begin by making a point at -2 and moving three units to the right. The final value is 1, so −2 + 3 = 1When the value that is being added is positive, we “jump” to the right. If the value is negative, we jump to the left(in a negative direction).Example 2: Find 2 − 3 using a number line.Solution: Begin by making a point at 2. The expression represents subtraction, so we will count three jumps to theleft.The solution is: 2 − 3 = −19