14
Convenient and quick calculation methods
Textbook: Part 1, lesson 14, pp. 58–59
GoalKnow the distributive law of multiplication; use it to multiply conveniently and quickly.
New words
distributive law · taqsimot qonunimultiplying a sum by a number · yig‘indini songa ko‘paytirishmultiplying a difference by a number · ayirmani songa ko‘paytirishconvenient calculation · qulay hisoblash
Explanation
To multiply a sum by a number, multiply each addend by that number and add the products: (a + b) · c = a · c + b · c. To multiply a difference by a number, multiply the minuend and the subtrahend separately and subtract the second product from the first: (a − b) · c = a · c − b · c. These are the distributive laws of multiplication over addition and subtraction. They help us calculate products quickly using round numbers. For example, to multiply a number by 5, multiply it by 10 and divide by 2.
Worked examples
73 × 8 = (70 + 3) × 8 = 70 × 8 + 3 × 8 = 560 + 24 = 584.
99 × 7 = (100 − 1) × 7 = 700 − 7 = 693. Multiplying by 15: 26 × 15 = 26 × 10 + 26 × 5 = 260 + 130 = 390.
Class activity
“Via a round number”: pupils calculate products like 98 × 6, 51 × 7 and 199 × 4 mentally by moving to a round number.
Practice
1
Compute 83 × 6 with the distributive law: (80 + 3) × 6.
498
2
Compute 199 × 4 as (200 − 1) × 4.
796
3
Compute 46 × 15 as 46 × 10 + 46 × 5.
690
4
Why is (a + b) · c = a · c + b · c? Explain with a tile example.
If a floor has c rows with a blue and b white tiles in each, the total can be counted by rows, (a + b) · c, or by colours, a · c + b · c; the result is the same.