Lesson 4
Absolute Value of Numbers
Let’s explore distances from zero more closely.
Problem 1
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 2
On the number line, plot and label all numbers with an absolute value of \(\frac32\).
Problem 3
Put these numbers in order, from least to greatest.
\(|\text-2.7|\)
0
1.3
\(|\text-1|\)
2
Problem 4
Lin’s family needs to travel 325 miles to reach her grandmother’s house.
-
At 26 miles, what percentage of the trip’s distance have they completed?
- How far have they traveled when they have completed 72% of the trip’s distance?
- At 377 miles, what percentage of the trip’s distance have they completed?
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 |
- What percent of her income does Elena donate to charity? Explain or show your work.
- 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.
- Use your choice from the second question to write an equation that relates \(m\) and \(d\).
Problem 6
How many times larger is the first number in the pair than the second?
- \(3^4\) is _____ times larger than \(3^3\).
- \(5^3\) is _____ times larger than \(5^2\).
- \(7^{10}\) is _____ times larger than \(7^8\).
- \(17^6\) is _____ times larger than \(17^4\).
- \(5^{10}\) is _____ times larger than \(5^4\).