5.2 The Integers 227 The rule for subtraction indicates that to subtract b from a, add the additive inverse of b to a. For example, − = + − 3 5 3 ( 5) Subtraction − = + − a b a b ( ) Subtraction Addition Additive inverse of 5 Now we can determine the value of + − 3 ( 5). 23 22 25 21 0 1 2 3 3 4 5 Thus, − = + − = − 3 5 3 ( 5) 2. Adding and Subtracting Integers Example 4 Subtracting Integers Evaluate 4 (3) − − − using the number line. Solution We are subtracting −3 from 4. − The additive inverse of −3 is 3; therefore, we add 3 to 4. − We now add 4 3 − + on the number line to obtain the answer −1. 24 3 22 21 24 23 25 0 1 2 3 4 5 6 Thus, 4 (3) 4 3 1. − − − = − + = − 7 Now try Exercise 19 In Example 4, we determined that 4 ( 3) 4 3. − − − = − + In general, a b ( ) − − = + a b. As you get more proficient in working with integers, you should be able to answer questions involving them without drawing a number line. Did You Know? Earthly Extremes M ore than 8300 people have stood on the top of Nepal’s 29,035-foot-high Mount Everest. Very few people have visited the Pacific Ocean’s 36,198-foot-deep Mariana Trench. In 1960, Jacques Piccard and Don Walsh were the first to make the journey in a vessel designed to withstand the immense pressure: 7 tons per square inch. The diving time was 81 2 hours, of which only 20 minutes were spent on the ocean floor. m Mount Everest Example 5 Subtracting Integers: Adding the Inverse Evaluate: a) 6 2 − − b) 6 (2) − − − c) − − 6 ( 2) d) − 6 2 Solution a) 6 2 6 (2) 8 − − = − + − = − b) 6 (2) 6 2 4 − − − = − + = − Now try Exercise 21 c) − − = + = 6 ( 2) 6 2 8 d) − = + − = 6 2 6 ( 2) 4 7 Example 6 Elevation Difference The highest point in the United States is Denali in Alaska at a height of 20,237 ft above sea level. The lowest point in the United States is Death Valley in California and Nevada at a depth of 282 ft below sea level −( 282 ft). Determine the vertical height difference between Denali and Death Valley. Vixit/Shutterstock
RkJQdWJsaXNoZXIy NjM5ODQ=