Compare and Order integers with absolute value online exercise for ... - Free Printable

Let's solve each part of this worksheet step by step and explain the reasoning.

---

Part 1: Compare the integers using <, >, or =

We compare integers directly or using absolute values as needed.

1. 8 ○ 10
→ 8 is less than 10
✔ 8 < 10

2. -4 ○ 6
→ Negative numbers are less than positive numbers
✔ -4 < 6

3. 5 ○ -9
→ Positive number is greater than negative
✔ 5 > -9

4. -4 ○ -6
→ On a number line, -4 is to the right of -6 → so -4 is greater
✔ -4 > -6

5. -7 ○ -5
→ -7 is to the left of -5 → so it's smaller
✔ -7 < -5

6. |7| ○ |-10|
→ |7| = 7, |-10| = 10 → 7 < 10
✔ |7| < |-10|

7. |-5| ○ |-3|
→ |-5| = 5, |-3| = 3 → 5 > 3
✔ |-5| > |-3|

8. |-15| ○ |-18|
→ |-15| = 15, |-18| = 18 → 15 < 18
✔ |-15| < |-18|

9. |9| ○ |-9|
→ |9| = 9, |-9| = 9 → they are equal
✔ |9| = |-9|

---

Part 2: Order the integers from least to greatest

We arrange them on the number line from left to right.

10. -5, 8, -3, 10, -9, 0
→ Order: -9, -5, -3, 0, 8, 10
✔ -9, -5, -3, 0, 8, 10

11. -10, -17, -12, -9, -2, -5
→ Most negative first: -17, -12, -10, -9, -5, -2
✔ -17, -12, -10, -9, -5, -2

12. -7, -9, -8, -5, 0, -3
→ Order: -9, -8, -7, -3, -5 → Wait! Let's fix:
→ From smallest to largest: -9, -8, -7, -5, -3, 0
✔ -9, -8, -7, -5, -3, 0

13. |-6|, |-3|, |0|, |9|, |-2|, |-15|
→ First evaluate absolute values:
→ |-6| = 6, |-3| = 3, |0| = 0, |9| = 9, |-2| = 2, |-15| = 15
→ Now order: 0, 2, 3, 6, 9, 15
✔ |0|, |-2|, |-3|, |-6|, |9|, |-15|

14. |-8|, |-14|, |17|, |4|, |2|, |-7|
→ Evaluate:
→ |-8| = 8, |-14| = 14, |17| = 17, |4| = 4, |2| = 2, |-7| = 7
→ Order: 2, 4, 7, 8, 14, 17
→ So: |2|, |4|, |-7|, |-8|, |-14|, |17|
✔ |2|, |4|, |-7|, |-8|, |-14|, |17|

---

Part 3: Use the number line to compare

From the number line:

- A = -5
- B = -3
- C = -2
- D = 1
- E = 4
- F = 5
- G = 7

Now compare:

15. A ○ D → -5 ○ 1
→ -5 < 1
✔ A < D

16. E ○ B → 4 ○ -3
→ 4 > -3
✔ E > B

17. B ○ C → -3 ○ -2
→ -3 < -2
✔ B < C

18. F ○ E → 5 ○ 4
→ 5 > 4
✔ F > E

19. G ○ A → 7 ○ -5
→ 7 > -5
✔ G > A

---

Part 4: Fill in the blank

> Absolute value is the distance between a number and zero on a number line.

✔ "Absolute value is the distance between a number and zero on a number line."

---

Part 5: Evaluate

Evaluate each absolute value expression.

20. |5| = → 5
21. |-17| = → 17
22. |-9| = → 9
23. |8| = → 8
24. |-1| = → 1
25. -|4| = → -(4) = -4
26. -|7| = → -(7) = -7
27. -|-6| = → -(6) = -6
28. -|-3| = → -(3) = -3
29. -|-5| = → -(5) = -5

✔ Answers:
20. 5
21. 17
22. 9
23. 8
24. 1
25. -4
26. -7
27. -6
28. -3
29. -5

---

✔ Final Answer Summary:

#### Compare:
1. 8 < 10
2. -4 < 6
3. 5 > -9
4. -4 > -6
5. -7 < -5
6. |7| < |-10|
7. |-5| > |-3|
8. |-15| < |-18|
9. |9| = |-9|

#### Order (least to greatest):
10. -9, -5, -3, 0, 8, 10
11. -17, -12, -10, -9, -5, -2
12. -9, -8, -7, -5, -3, 0
13. |0|, |-2|, |-3|, |-6|, |9|, |-15|
14. |2|, |4|, |-7|, |-8|, |-14|, |17|

#### Number Line Comparisons:
15. A < D
16. E > B
17. B < C
18. F > E
19. G > A

#### Fill in the blank:
> Absolute value is the distance between a number and zero on a number line.

#### Evaluate:
20. 5
21. 17
22. 9
23. 8
24. 1
25. -4
26. -7
27. -6
28. -3
29. -5

---

Let me know if you'd like this formatted for printing or as a PDF!