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Properties of operations
Textbook Part 4, pp. 48–49
GoalWrite the commutative and associative properties with letters and use them for easy calculation.
New words
commutative property · o‘rin almashtirish xossasiassociative property · guruhlash xossasihealthy lifestyle · sog‘lom turmush tarzi
Explanation
Commutative property: a + b = b + a. Associative property: (a + b) + c = a + (b + c). These rules work for any numbers, which is why we write them with letters.
Worked examples
a = 6, b = 7: 6 + 7 = 13 and 7 + 6 = 13 ✓.
a = 38, b = 8, c = 12: (38 + 8) + 12 = 46 + 12 = 58; 38 + (8 + 12) = 38 + 20 = 58 ✓ — the second way is easier!
Class activity
“Pack the box”: children fit pieces into a box in different orders — the result (a full box) is the same. Then they write the properties in their notebooks.
Practice
1
8 + x = x + ?
8
2
The easy way: 38 + 8 + 12
58
3
The easy way: 27 + 15 + 5
47
4
Check: (5 + 3) + 2 = 5 + (3 + 2)?
Yes, both are 10