36
Dividing positive and negative numbers
Textbook, pp. 168–171
GoalKnow and apply the rule for dividing positive and negative numbers.
New words
quotient · bo‘linmadividend · bo‘linuvchidivisor · bo‘luvchidivision by zero · nolga bo‘lish
Explanation
Division has the same sign rule as multiplication: the quotient of numbers with equal signs is positive and with different signs is negative. The modulus of the quotient is the quotient of the moduli. For example (−36) : 9 = −4 and (−48) : (−6) = 8. If we divide 0 by a nonzero number we get 0: 0 : (−5) = 0. Division by zero is impossible, because no number q satisfies q · 0 = 5. We check division with multiplication.
Worked examples
(−36) : 9: 36 : 9 = 4, signs differ, answer −4. Check: (−4) · 9 = −36.
(−48) : (−6) = 8, because 8 · (−6) = −48.
Class activity
“Reverse check”: pairs solve a division and the partner multiplies the answer back to check. A pupil who finds a mistake explains the rule aloud.
Practice
1
Compute (−56) : 7.
-8
2
Compute (−72) : (−9).
8
3
Compute 0 : (−13).
0
4
Why can 5 : 0 not be calculated?
There is no number q with q · 0 = 5, since any number times 0 is 0.