# 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?

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 $$18^\circ \text{C}$$

### 14.3: Absolute Value Expressions

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. $$9 - |19 + 3|$$