126
Properties of multiplication
Textbook: Part 4, lesson 117, pp. 4–5
GoalKnow the commutative and grouping properties of multiplication and use them to calculate easily.
New words
commutative property (swapping) · o‘rin almashtirish xossasigrouping (associative) property · guruhlash xossasifactor · ko‘paytuvchiproduct · ko‘paytma
Explanation
If the factors swap places, the product does not change: a × b = b × a. For example, 3 × 60 = 60 × 3 = 180 (3 times 6 tens = 18 tens). When we multiply three numbers, we may group any two first: (7 × 2) × 5 = 7 × (2 × 5) = 7 × 10 = 70. Choose the handy pair.
Worked examples
6 × 10 = 10 × 6 = 60. Both ways give the same answer.
(4 × 5) × 2 = 4 × (5 × 2) = 4 × 10 = 40.
Class activity
“Rows and columns”: children lay out 3 rows of 6 counting sticks, then turn the picture a quarter turn and see 6 rows of 3. They write both expressions and say the product is the same.
Practice
1
3 × 60 = ?
180
2
70 × 3 = ?
210
3
(6 × 2) × 5 = ?
60
4
One plate holds 4 flatbreads. Each table has 5 plates and there are 2 tables. How many flatbreads in all?
40