Lesson 6
Absolute Value of Numbers
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.](https://cms-im.s3.amazonaws.com/s8CrmJfocHpM31NbehedZ4K1?response-content-disposition=inline%3B%20filename%3D%226.7.A.PP.Image.01a.png%22%3B%20filename%2A%3DUTF-8%27%276.7.A.PP.Image.01a.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T172133Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=5f20d783178cc26b071083c71ac803448bf20f948b4aefbca55104d7fb175d7d)
Solution
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Problem 2
The temperature at dawn is \(6^\circ \text{C}\) away from 0. Select all the temperatures that are possible.
\(\text-12^\circ \text{C}\)
\(\text-6^\circ \text{C}\)
\(0^\circ \text{C}\)
\(6^\circ \text{C}\)
\(12^\circ \text{C}\)
Solution
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Problem 3
Put these numbers in order, from least to greatest.
\(|\text-2.7|\)
0
1.3
\(|\text-1|\)
2
Solution
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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?
Solution
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(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 |
- 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 \(d\).
Solution
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(From Unit 6, Lesson 16.)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 \(5^4\).
Solution
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(From Unit 6, Lesson 12.)