Question

grade 6 unit 7 georgias k-12 mathematics standards 6. mark the number line to show how you would find or illustrate | - 4 | and | 3 |. 7. put the correct sign between each pair of numbers: >, ≥, <, ≤, = a. \\(\frac{3}{4}\\) \\(\square\\) -2 b. 5 \\(\square\\) \\(\frac{10}{2}\\) c. -1 \\(\square\\) 0 d. -3 \\(\square\\) -1 this work is licensed under a creative commons attribution - noncommercial - sharealike 4.0 international license © 2023 georgia department of education, all rights reserved last updated july 2024 page 2 of 12

Explanation:

Part 6: Mark the number line for \(|-4|\) and \(|3|\)

Step 1: Recall absolute value definition

The absolute value of a number \(x\), denoted \(|x|\), is its distance from 0 on the number line. So \(|-4| = 4\) (distance of -4 from 0 is 4) and \(|3| = 3\) (distance of 3 from 0 is 3).

Step 2: Mark on the number line

• For \(|-4|\): Find the point labeled \(+4\) on the number line (since \(|-4| = 4\)) and mark it (e.g., with a dot or an 'X').
• For \(|3|\): Find the point labeled \(+3\) on the number line (since \(|3| = 3\)) and mark it.

Part 7: Compare the numbers

7a: \(\frac{3}{4}\) vs \(-2\)

Step 1: Analyze number types

\(\frac{3}{4}\) is a positive fraction (greater than 0), and \(-2\) is a negative integer (less than 0).

Step 2: Apply number line order

On the number line, positive numbers are to the right of 0, and negative numbers are to the left. So positive numbers are greater than negative numbers. Thus, \(\frac{3}{4} > -2\).

7b: \(5\) vs \(\frac{10}{2}\)

Step 1: Simplify \(\frac{10}{2}\)

Calculate \(\frac{10}{2} = 5\) (since 10 divided by 2 is 5).

Step 2: Compare the values

Since both \(5\) and \(\frac{10}{2}\) equal 5, we use the '=' sign. So \(5 = \frac{10}{2}\).

7c: \(-1\) vs \(0\)

Answer:

s:

1. Mark \(+4\) (for \(|-4|\)) and \(+3\) (for \(|3|\)) on the number line.

7a. \(\boldsymbol{\frac{3}{4} > -2}\)
7b. \(\boldsymbol{5 = \frac{10}{2}}\)
7c. \(\boldsymbol{-1 < 0}\)
7d. \(\boldsymbol{-3 < -1}\)