Lesson 14

For each pair of values, decide mentally which one has a value that is closer to 0.

\(\text{-}\frac{4}{5}\) or \(\frac{5}{4}\)

\(\frac{1}{12}\) or \(\frac{1}{14}\)

-0.001 or 0.0001

1.3 or \(\frac{4}{3}\)

1. One of the lowest places in Europe is 23 feet below sea level. We can use “-23 feet” to describe its elevation, and “\(|\text{-}23|\) feet” to describe its vertical distance from sea level. In the context of elevation, what would each of the following numbers describe?
   1. 37 feet
   2. \(|37|\) feet
   3. -6 feet
   4. \(|\text{-}6|\) feet
2. Water freezes at 0 degrees Celsius. For each pair of temperatures, which temperature is closest to the freezing point of water? Use absolute value to explain your reasoning.
   1. \(14^\circ \text{C}\) or \(\text{-} 15^\circ \text{C}\)
   2. \(\text{-} 5^\circ \text{C}\) or \(\text{-} 2^\circ \text{C}\)
   3. \(\text{-} 12^\circ \text{C}\) or \(18^\circ \text{C}\)

Find the value of these expressions.

1. \(|10-12|\)
2. \(|\text{-}16 + 5|\)
3. \(3|9 - 4|\)
4. \(|8 - 10| - 16\)
5. \(2|\text{-}13 - 2| + 18\)
6. \(9 - |19 + 3|\)