https://file.aiquickdraw.com/mathbot/file/1727269348095d0cl4zdg.jpg

Let’s work through the problems on the worksheet:

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### A. Compare the following values using the symbols `<`, `>`, or `=`.
1. **10 __ 12**  
   \( 10 < 12 \)
   
2. **-34 __ 7**  
   \( -34 < 7 \)
   
3. **-28 __ -2**  
   \( -28 < -2 \)
   
4. **0 __ 45**  
   \( 0 < 45 \)
   
5. **-6 __ -83**  
   \( -6 > -83 \)
   
6. **-28 __ -(-(-28))**  
   Since \(-(-(-28)) = -28\),  
   \( -28 = -28 \)
   
7. **1 __ -100**  
   \( 1 > -100 \)
   
8. **-(24) __ -(-9)**  
   \( -24 < 9 \)
   
9. **|-3| __ -3**  
   \( |3| = 3 \) and \( -3 = -3 \),  
   \( 3 > -3 \)
   
10. **|-36| __ 36**  
   \( |36| = 36 \),  
   \( 36 = 36 \)

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### B. Arrange the following set of integers from least to greatest:
Set: **17, -16, 13, -4, -5, -20, 8, -11**  
**Ordered Set**:  
\(-20, -16, -11, -5, -4, 8, 13, 17\)

Another set: **-23, -8, -1, -37, -12, -6, -19, -10**  
**Ordered Set**:  
\(-37, -23, -19, -12, -10, -8, -6, -1\)

---

### C. Write TRUE or FALSE.
1. **The absolute value of 5 is -5.**  
   FALSE (absolute value is always non-negative)
   
2. **The opposite of (-9 + 5) is 9 - 5.**  
   TRUE
   
3. **Simplifying | - 23 | gives 23.**  
   TRUE
   
4. **Simplifying -(-(-4)) gives 4.**  
   TRUE
   
5. **On the number line, 5 units to the right of -4 is 1.**  
   TRUE
   
6. **The absolute value of -12 is 12.**  
   TRUE
   
7. **-(a - b) is equal to a + b.**  
   FALSE (it equals \(b - a\))
   
8. **| -4 | is greater than | -6 |.**  
   TRUE (\( |4| > |6| \))
   
9. **The opposite of negative 2 is 2.**  
   TRUE
   
10. **19 and -19 have the same absolute value.**  
   TRUE

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### D. Answer the following:
1. **What is the additive inverse of -17?**  
   \( 17 \)
   
2. **What is the opposite of -32?**  
   \( 32 \)
   
3. **What is -(-19) equal to?**  
   \( 19 \)
   
4. **What is the negative of (-ab)?**  
   \( ab \)
   
5. **If (-c) + k = 0, what is k equal to?**  
   \( k = c \)
   
6. **If (-c) + k = -c, then what is k equal to?**  
   \( k = 0 \)
   
7. **Fill in the blank: \( p + \underline{\ \ \ \ \ } = 0 \)**  
   \( -p \)
   
8. **What is the sum of -p and (-p)?**  
   \( -2p \)
   
9. **If -x + k = k, then what is -x?**  
   \( -x = 0 \), so \( x = 0 \)
   
10. **Fill in the blank: \( x + y + \underline{\ \ \ \ \ } = 0 \)**  
    \( -(x + y) \)

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Would you like more detailed explanations on any of these? Here are some related questions to practice:

1. What is the absolute value of -25?
2. Arrange the numbers: -3, -7, 9, 0, -12 from least to greatest.
3. Simplify: \(-(-(-5))\).
4. What is the opposite of 7?
5. If \( -a + b = 0 \), what is \( b \)?

**Tip:** Always remember, the absolute value of any number is its distance from zero, so it's always positive or zero.

Grade 7 Worksheet on Integer comparison, ordering, and properties

This worksheet covers integer comparison, ordering integers from least to greatest, absolute values, and properties of integers. Suitable for Grade 7 students.

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