Ways We Use Integers Problem Solving: Negative Numbers in Bar Graphs Ways We Use Integers When do we use negative integers? We use negative integers in several different ways. Most of the time, they are part of higher mathematics. We will work with negative integers a lot when we start algebra. However, there are common ways we use negative integers in everyday life. Probably the most common example is temperature, particularly in cold parts of the world. On a thermometer, the temperature will drop or go down to the point of zero and then below that into negative numbers. Notice that zero is an important dividing line on the thermometer just like it is on the number line. The graphics show how movement on the thermometer is similar to movement on the number line. We can show this movement on a number line. 1 9 7 6 5 4 3 2 1 1 2 3 4 1 9 7 6 5 4 3 2 1 1 2 3 4 We see that the temperature moves from 1 degrees above zero (a positive integer) to 4 degrees below zero (a negative integer). 54 Unit Lesson 3
Example 1 Use a number line to show the temperature changing from 1 degrees to 4 degrees. 14 degrees 4 3 2 1 1 2 3 4 5 6 7 9 1 The temperature changed 14 degrees. Improve Your Skills Your friend wants to know how much the temperature changed from morning to afternoon. In the morning, the temperature was 5 degrees. Later that afternoon, the temperature was 22 degrees. Your friend says that the temperature increased 17 degrees from morning to afternoon. ERROR When we look at this problem on a number line, we see the answer. 27 degrees 7 9 1 11 12 13 14 15 16 17 1 19 2 21 22 23 Your friend started counting at 5. He should have started at 5. The temperature increased 27 degrees from morning to afternoon. CORRECT Unit Lesson 3 549
Elevation is a second way to think about negative integers. When we say that something is at sea level, we understand that its elevation is feet. The diver dove 5 feet. If we move higher up from sea level, we are going in a positive direction. If we go under water at sea, we are moving in a negative direction. Once again, zero is an important dividing line, just like it is on the number line. The graphic shows a diver underwater. As soon as the diver goes under the water, she is below sea level. This means that she is at a negative elevation. sea level 1 ft. 2 ft. 3 ft. 4 ft. 5 ft. Example 2 Use a number line to show the change in elevation when the diver went down 5 feet. 5 feet 5 4 3 2 1 1 Apply Skills Turn to Interactive Text, page 24. Reinforce Understanding Use the mbook Study Guide to review lesson concepts. 55 Unit Lesson 3
Problem Solving: Negative Numbers in Bar Graphs How do we use negative numbers in bar graphs? Another way we use negative integers is when we talk about money. The bar graph shows the amount of money that the company Crash Bang Entertainment made from September to February. Crash Bang makes video games. The numbers in the graph have been rounded to the nearest integer to make the graph easier to read. We see from the graph that in the months of September, December, and February, the company made money, or had a positive cash flow. That is what the black bars in the graph indicate. For example, Crash Bang made $7 million in September. The company lost money, or had a negative cash flow, in October, November, and January. That is what the red bars indicate. For example, the company lost $5 million in October. Income (millions of dollars) 6 4 2 2 4 Crash Bang Entertainment Income for Six Months When we say, We re in the black, it means that we are making a profit. When we say, We re in the red, it means that we are losing money. 6 Sept. Oct. Nov. Dec. Jan. Feb. Month Crash Bang went from $7 million profit in September to $5 million in loss in October. Notice what is happening on the vertical axis of the bar graph. The zero is the dividing line in the bar graph, and we can see that the positive and negative integers go in opposite directions. This means that opposite integers, such as 4 and 4, are equal distances from the point on the graph. Problem-Solving Activity Turn to Interactive Text, page 25. Reinforce Understanding Use the mbook Study Guide to review lesson concepts. Unit Lesson 3 551
Homework Activity 1 Complete the statements using the number line. Make sure to copy the entire statement onto your paper. Model 3 6 = 3 1. 2. 3. 4. 2 = 4 2 + = 5 5 + = 2 1 = 4 Activity 2 Tell whether the change described in the problem is (a) positive or (b) negative. Just write a or b on your paper. 1. After three years operating in the red, Joe s business finally made a profit this year. 2. The temperature was 5 degrees at midnight and 1 degrees at 3: a m. 3. The scuba diver swam to more shallow waters. 4. The scuba diver dove to 2 feet below sea level. 5. The temperature was 65 degrees at noon and 73 degrees two hours later. 552 Unit Lesson 3 Copyright 21 by Cambium Learning Sopris West. All rights reserved. Permission is granted to reproduce this page for student use.
Homework Activity 3 Use the bar graph to help you answer the questions. Income (in thousands of dollars) 1 5-5 -1 BB s Mowing Service Dec. Jan. Feb. Mar. Apr. May Jun. Jul. Aug. Month 1. In what month did BB s Mowing make the most money? (a) January (b) August (c) May 2. In what month did BB s Mowing lose the most money? (a) February (b) March (c) January 3. In what month did BB s Mowing neither gain nor lose money? (a) December (b) March (c) July 4. In which three-month period was BB s Mowing operating in the red? (a) Mar. Apr. May (b) June July Aug. (c) Dec. Jan. Feb. Activity 4 Distributed Practice Solve. 1. Convert 75% to a fraction. 3 4 2. Convert.2 to a percent. 3. Convert 3 5 to a decimal number. 4. 2.22 + 1.35 + 4.29 + 3.7 + 1.6 5. 1.6.99 6. 7. 9 1 3 5 9 3 5 + 1 4 17 2. 7.77.11 Copyright 21 by Cambium Learning Sopris West. All rights reserved. Permission is granted to reproduce this page for student use. Unit Lesson 3 553