# Lesson 14

Absolute Value Meaning

- Let’s investigate absolute values.

### 14.1: Math Talk: Closest to Zero

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

### 14.2: What is Absolute Value?

- 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?
- 37 feet
- \(|37|\) feet
- -6 feet
- \(|\text{-}6|\) feet

- 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.
- \(14^\circ \text{C}\) or \(\text{-} 15^\circ \text{C}\)
- \(\text{-} 5^\circ \text{C}\) or \(\text{-} 2^\circ \text{C}\)
- \(\text{-} 12^\circ \text{C}\) or \(18^\circ \text{C}\)

### 14.3: Absolute Value Expressions

Find the value of these expressions.

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