11
Multiplying natural numbers
Textbook: Part 1, lesson 11, pp. 44–47
GoalKnow the meaning and properties of multiplication; use the grouping property to calculate.
New words
product · ko‘paytmafactor · ko‘paytuvchicommutative property · o‘rin almashtirish xossasiassociative property · guruhlash xossasi
Explanation
Multiplying a by b means finding the sum of b addends each equal to a: a · b = a + a + ... + a. The numbers a and b are factors and a · b is the product. If the factors swap places, the product does not change: a · b = b · a. Grouping property: a · (b · c) = (a · b) · c. For every m, 1 · m = m and 0 · m = 0. The product of a number and a letter is written without a sign: 8a instead of 8 · a, and 2(a + b) instead of 2 · (a + b). Without brackets, multiplication is done step by step from left to right.
Worked examples
125 + 125 + 125 + 125 = 4 × 125 = 500: four equal addends were written as a product.
25 × 17 × 4 = (25 × 4) × 17 = 100 × 17 = 1 700. The grouping property helped us form a convenient pair.
Class activity
“Rows and columns”: pupils count desks by rows and by columns, then compute rows × columns and columns × rows and see they are equal.
Practice
1
Write 38 + 38 + 38 + 38 + 38 as a product and compute it.
190
2
Use the grouping property to compute 4 × 37 × 25.
3700
3
1 kg of apples costs 7 400 so‘m. How much do 6 kg cost?
44400
4
Why is 0 × 1 234 = 0?
It is the sum of 1 234 zeros: 0 + 0 + ... + 0 = 0.