Lesson 6

Absolute Value of Numbers

Let’s explore distances from zero more closely.

Problem 1

On the number line, plot and label all numbers with an absolute value of \(\frac32\).

A number line with 5 evenly spaced tick marks. The numbers negative 2 through 2 are indicated.

Problem 2

The temperature at dawn is \(6^\circ \text{C}\) away from 0. Select all the temperatures that are possible.


\(\text-12^\circ \text{C}\)


\(\text-6^\circ \text{C}\)


\(0^\circ \text{C}\)


\(6^\circ \text{C}\)


\(12^\circ \text{C}\)

Problem 3

Put these numbers in order, from least to greatest.







Problem 4

Lin’s family needs to travel 325 miles to reach her grandmother’s house.

  1. At 26 miles, what percentage of the trip’s distance have they completed?

  2. How far have they traveled when they have completed 72% of the trip’s distance?
  3. At 377 miles, what percentage of the trip’s distance have they completed?
(From Unit 5, Lesson 11.)

Problem 5

Elena donates some money to charity whenever she earns money as a babysitter. The table shows how much money, \(d\), she donates for different amounts of money, \(m\), that she earns.

\(d\) 4.44 1.80 3.12 3.60 2.16
\(m\) 37 15 26 30 18
  1. What percent of her income does Elena donate to charity? Explain or show your work.
  2. Which quantity, \(m\) or \(d\), would be the better choice for the dependent variable in an equation describing the relationship between \(m\) and \(d\)? Explain your reasoning.
  3. Use your choice from the second question to write an equation that relates \(m\) and \(d\).
(From Unit 6, Lesson 16.)

Problem 6

How many times larger is the first number in the pair than the second?

  1. \(3^4\) is _____ times larger than \(3^3\).
  2. \(5^3\) is _____ times larger than \(5^2\).
  3. \(7^{10}\) is _____ times larger than \(7^8\).
  4. \(17^6\) is _____ times larger than \(17^4\).
  5. \(5^{10}\) is _____ times larger than \(5^4\).
(From Unit 6, Lesson 12.)