Looking at the worksheet, I need to solve problems 1-24. Let me work through them systematically.
Problems 1-8: Classify each number
1. -16: This is a negative whole number, so it's an integer (Z) and rational (Q)
2. 5/2: This is a fraction, so it's rational (Q)
3. 16.17: This is a terminating decimal, so it's rational (Q)
4. 4√2: √2 is irrational, so 4√2 is irrational (I)
5. 1/3: This is a repeating decimal (0.333...), so it's rational (Q)
6. 4.63: This is a terminating decimal, so it's rational (Q)
7. 0.11: This is a terminating decimal, so it's rational (Q)
8. 1/3: Same as #5, rational (Q)
Wait, let me check #8 again - it shows "1/3" but looking at the pattern, this might be different from #5. Actually, both are 1/3, so both are rational.
Problems 9-16: State the property illustrated
9. 3(2x + 4) = 6x + 12: Distributive property
10. 6 + 3 = 3 + 6: Commutative property of addition
11. -7 + 0 = -7: Identity property of addition
12. 5 · 10 = 10 · 5: Commutative property of multiplication
13. 20 + 0 = 20: Identity property of addition
14. If 8 + 3 = 11, then 11 = 8 + 3: Symmetric property of equality
15. (a + b) + c: Associative property of addition
16. 4(3) = 3(4): Commutative property of multiplication
Problems 17-24: Fill in the blank
17. If 2 + 3 = 5, and 5 = 4 + 1, then 2 + 3 = 4 + 1: Transitive property
18. (2 + 4) + (4 + 4) = 2 + (4 + 4) + 4: Associative property
19. 13 + 6 = 6 + 13: Commutative property
20. 5 · (4 · 3) = (5 · 4) · 3: Associative property
21. 21 · 0 = 0: Zero property of multiplication
22. If 5x = 15, then x = 15/5: Division property of equality
23. 4(3) = 3(4): Commutative property
24. If 5x = 25, then x = 25/5: Division property of equality
Final Answer:
1. Z, Q
2. Q
3. Q
4. I
5. Q
6. Q
7. Q
8. Q
9. Distributive
10. Commutative (addition)
11. Identity (addition)
12. Commutative (multiplication)
13. Identity (addition)
14. Symmetric
15. Associative (addition)
16. Commutative (multiplication)
17. Transitive
18. Associative
19. Commutative
20. Associative
21. Zero
22. Division
23. Commutative
24. Division
Parent Tip: Review the logic above to help your child master the concept of real numbers worksheet.
