12
Dividing natural numbers
Textbook: Part 1, lesson 12, pp. 48–53
GoalKnow the meaning of division; check division and multiplication by each other; find an unknown factor, dividend or divisor.
New words
dividend · bo‘linuvchidivisor · bo‘luvchiquotient · bo‘linmaunknown factor · noma’lum ko‘paytuvchi
Explanation
In a : b = c, a is the dividend, b the divisor and c the quotient. By the meaning of division, if a : b = c then c · b = a. So we check division by multiplication and multiplication by division. Division by zero is impossible; a : 1 = a, a : a = 1 (a ≠ 0) and 0 : a = 0. Unknown factor: if a · x = b then x = b : a. Unknown dividend: if x : a = b then x = b · a. Unknown divisor: if a : x = b then x = a : b.
Worked examples
If 9x = 108 then x = 108 : 9 = 12. If x : 15 = 6 then x = 6 × 15 = 90. If 144 : x = 18 then x = 144 : 18 = 8.
1 092 : 28 = 39 is correct because 28 × 39 = 1 092. To check multiplication: 1 092 : 39 must give 28.
Class activity
“Hidden number”: the teacher says things like “x divided by 6 gives 9”; pupils find x and show the check.
Practice
1
Compute 1 092 : 28.
39
2
Solve 12x = 156.
13
3
Solve 144 : x = 18.
8
4
Why can a non-zero number not be divided by zero?
Multiplying by zero always gives 0, so no quotient multiplied by 0 can give a non-zero dividend.