17
Divisibility rule for 9
Textbook: Part 1, lesson 17, pp. 52–54
GoalKnow and use the divisibility rule for 9.
New words
multiple of 9 · 9 ga karralisum of digits · raqamlar yig‘indisirule (sign) · alomatchecking · tekshirish
Explanation
Divisibility rule for 9: if the sum of the digits is divisible by 9, the number is divisible by 9. Every number divisible by 9 is also divisible by 3, but not the other way round: 12 is divisible by 3 but not by 9. For example, for 7 128 we get 7 + 1 + 2 + 8 = 18, which divides by 9, so 7 128 is divisible by 9.
Worked examples
7 128: 7 + 1 + 2 + 8 = 18 – divisible by 9; 7 128 : 9 = 792.
3 450: 3 + 4 + 5 + 0 = 12 – divisible by 3 but not by 9.
Class activity
“Three or nine”: sort number cards into three groups: divisible only by 3, divisible by both 3 and 9, divisible by neither.
Practice
1
From 513, 624, 7 218, 3 456, 1 001, 8 100 write those divisible by 9.
513, 7 218, 3 456, 8 100
2
Is 9 876 divisible by 3? By 9?
By 3 yes, by 9 no (the digit sum is 30)
3
Which digits can replace the star so that 6*3 is divisible by 9?
0 or 9
4
765 kg of flour was packed into 9 identical sacks. How many kg are in each sack?
85