Chapter 2 Number Lines and Negative Numbers Section

Chapter 2 Number Lines and Negative Numbers Section 3 Absolute Value © 2020 Marshall Cavendish: Marshall Cavendish is not responsible for content accuracy once it has been edited from its original format.

Section 3 Absolute Value • I can recognize the absolute • value of a number as its distance from 0 on the number line. I can interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. Student Edition © 2020 Marshall Cavendish: Marshall Cavendish is not responsible for content accuracy once it has been edited from its original format. 69

Section 3 Absolute Value a Tank A and tank B originally had 14 fish each. After one month, tank A had an increase of 4 fish and tank B had an increase of – 5 fish. Which tank had a greater change in the number of fish? b Tank C also originally had 14 fish. After one month, it had a change of 6 fish. What is the possible number of fish in tank C after one month? How would you represent this change on a number line? Student Edition © 2020 Marshall Cavendish: Marshall Cavendish is not responsible for content accuracy once it has been edited from its original format. 69

Section 3 a Absolute Value The current temperature is 18°C. It has dropped by 18°C. What is the new temperature? b In an experiment, the temperature reading at the start was unknown. The temperature first rose to 18°C, before dropping to – 18°C. If the temperature dropped three-quarters as much as it rose, what was the temperature reading at the start? Student Edition © 2020 Marshall Cavendish: Marshall Cavendish is not responsible for content accuracy once it has been edited from its original format. 69

Section 3 Absolute Value Write the absolute value of a number 1 The given number line shows the distance of – 5 and 5 from 0. Notice that even though – 5 is negative, its distance from 0 is still 5 units. The absolute value of a number is the distance of that number from 0 on a number line. Since distances are always positive, the absolute value of a positive or negative number is always positive. Absolute value bars are used to show the absolute value of a number. The absolute value of – 5 is 5. You can write | – 5 | = 5. The absolute value of 5 is 5. You can write | 5 | = 5. © 2020 Marshall Cavendish: Marshall Cavendish is not responsible for content accuracy once it has been edited from its original format. Student Edition 69

Section 3 Absolute Value Write the absolute value of a number 2 Use the number line to find the absolute value of each of the following numbers. |– 9|=9 – 9 is 9 units from 0. |7|=7 7 is 7 units from 0. |– 4|=4 – 4 is 4 units from 0. |2|=2 2 is 2 units from 0. © 2020 Marshall Cavendish: Marshall Cavendish is not responsible for content accuracy once it has been edited from its original format. Student Edition 70

Section 3 Absolute Value 1 At the end of a game, Team A had – 5 points and Team B had – 8 points. Use absolute values to explain which team ended the game with fewer points. Student Edition © 2020 Marshall Cavendish: Marshall Cavendish is not responsible for content accuracy once it has been edited from its original format. 71

Section 3 Absolute Value 2 Ben’s account balance shows – $216. 75. Will’s account balance shows $180. Who has more money in the bank? How much more? How do you know? Student Edition © 2020 Marshall Cavendish: Marshall Cavendish is not responsible for content accuracy once it has been edited from its original format. 71

Section 3 Absolute Value Use absolute values to interpret real-world situations 1 The figure shows a section from Mr. Carter’s bank account statement. As of May 31, Mr. Carter had $280 in his bank account. On June 24, after he withdrew $490, he had –$170 in his bank account. | – 170 | = 170 This means that Mr. Carter had overdrawn $170. © 2020 Marshall Cavendish: Marshall Cavendish is not responsible for content accuracy once it has been edited from its original format. Student Edition 71

Section 3 Absolute Value Use absolute values to interpret real-world situations 2 A dog is sitting on a cliff, 35 feet above sea level. A dolphin is swimming 6 feet below sea level. An octopus is moving along the seabed, feet below sea level. 40 You can use positive and negative numbers to show the elevation of the animals relative to sea level. Dog’s elevation = 35 ft Dolphin’s elevation = – 6 ft Octopus’s elevation = – 40 ft Student Edition © 2020 Marshall Cavendish: Marshall Cavendish is not responsible for content accuracy once it has been edited from its original format. 71

Section 3 Absolute Value (Continued) Use absolute values to interpret real-world situations To decide which animal is farthest from sea level, you do not need to think about whether the animals are above or below sea level. You can use absolute values to compare distances. Distance of dog from sea level = | 35 | = 35 ft Distance of dolphin from sea level = | – 6 | = 6 ft Distance of octopus from sea level = | – 40 | = 40 ft The octopus is the farthest from sea level. Student Edition © 2020 Marshall Cavendish: Marshall Cavendish is not responsible for content accuracy once it has been edited from its original format. 71

Section 3 Absolute Value a Tank A and tank B originally had 14 fish each. After one month, tank A had an increase of 4 fish and tank B had an increase of – 5 fish. Which tank had a greater change in the number of fish? b Tank C also originally had 14 fish. After one month, it had a change of 6 fish. What is the possible number of fish in tank C after one month? How would you represent this change on a number line? Student Edition © 2020 Marshall Cavendish: Marshall Cavendish is not responsible for content accuracy once it has been edited from its original format. 69