Lesson 6: Absolute Value of Numbers

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

$\frac{9}{11}$ or $\frac{15}{11}$

$\frac15$ or $\frac19$

$1.25$ or $\frac54$

$0.01$ or $0.001$

Move the bug to a starting point, choose a jump distance, and press the jump button. You may need to zoom in or out if your bug jumps off the screen.

1. A bug is jumping around on a number line.
   1. If the bug starts at 1 and jumps 4 units to the right, where does it end up? How far away from 0 is this?
   2. If the bug starts at 1 and jumps 4 units to the left, where does it end up? How far away from 0 is this?
   3. If the bug starts at 0 and jumps 3 units away, where might it land?
   4. If the bug jumps 7 units and lands at 0, where could it have started?
   5. The absolute value of a number is the distance it is from 0. The bug is currently to the left of 0 and the absolute value of its location is 4. Where on the number line is it?
   6. If the bug is to the left of 0 and the absolute value of its location is 5, where on the number line is it?
   7. If the bug is to the right of 0 and the absolute value of its location is 2.5, where on the number line is it?
2. We use the notation $|{\text-2}|$ to say “the absolute value of -2,” which means “the distance of -2 from 0 on the number line.”
   1. What does $|{\text-7}|$ mean and what is its value?
   2. What does $|{1.8}|$ mean and what is its value?
3. For another challenge, show a target and move it wherever you want it. Can you set the jump to land on it?

1. A part of the city of New Orleans is 6 feet below sea level. We can use “-6 feet” to describe its elevation, and “$|\text-6|$ feet” to describe its vertical distance from sea level. In the context of elevation, what would each of the following numbers describe?

   1. 25 feet
   2. $|25|$ feet
   3. -8 feet
   4. $|\text-8|$ feet
2. The elevation of a city is different from sea level by 10 feet. Name the two elevations that the city could have.

3. We write “$\text-5^\circ \text{C}$” to describe a temperature that is 5 degrees Celsius below freezing point and “$5^\circ \text{C}$” for a temperature that is 5 degrees above freezing. In this context, what do each of the following numbers describe?

   1. $1^\circ \text{C}$
   2. $\text-4^\circ \text{C}$
   3. $|12|^\circ \text{C}$
   4. $|\text-7|^\circ \text{C}$

4. 1. Which temperature is colder: $\text-6^\circ \text{C}$ or $3^\circ \text{C}$?

   2. Which temperature is closer to freezing temperature: $\text-6^\circ \text{C}$ or $3^\circ \text{C}$?

   3. Which temperature has a smaller absolute value? Explain how you know.