6
Adding natural numbers
Textbook: Part 1, lesson 6, pp. 24–27
GoalAdd natural numbers; use the laws of addition and place-value addends; add in a convenient way.
New words
addend · qo‘shiluvchisum · yig‘indicommutative law · o‘rin almashtirish qonuniassociative law · guruhlash qonuni
Explanation
Numbers being added are addends and the result is the sum. Commutative law: if the addends swap places the sum does not change, a + b = b + a. Associative law: the sum of several numbers does not depend on the order in which they are added, (a + b) + c = a + (b + c). Adding zero leaves the number unchanged: a + 0 = a. Every natural number can be written as the sum of its place-value addends; column addition is based on this. To add conveniently, group the numbers that make 10, 100 or 1000.
Worked examples
37 + 68 + 63 + 22 = (37 + 63) + (68 + 22) = 100 + 90 = 190. The associative law made the work easy.
428 + 351 = (400 + 20 + 8) + (300 + 50 + 1) = (400 + 300) + (20 + 50) + (8 + 1) = 700 + 70 + 9 = 779.
Class activity
“Make a hundred”: the teacher calls numbers like 63, 38, 47, 82. Pupils find pairs whose sum is 100 and add them in a convenient way.
Practice
1
Compute 4 785 + 3 216.
8001
2
Compute conveniently: 126 + 78 + 74 + 22.
300
3
A store had 2 345 kg of flour and 1 678 kg more was brought. How many kg of flour are there now?
4023
4
Why do 6 + 3 and 3 + 6 give the same result?
This is the commutative law: swapping addends does not change the sum (a + b = b + a).