Teaching Notes 1.20: Dividing Integers
Most students have little trouble dividing integers. A trouble spot for some students, however,
is not understanding that dividing by zero is not possible.- Explain to your students that all division problems can be written in two ways. For example,
− 12 ÷3isthesameas
− 12
3
. 3 is the divisor or denominator and−12 is the dividend or
numerator. In each case, the answer, of course, is−4.
2. Explain that division can be checked by multiplication. To check that the answer to a division
problem is correct, students should multiply the quotient by the divisor. The product should
bethesameasthedividend.− 12 ÷ 3 =−4, therefore− 4 × 3 =−12.
3. Offer this example: 0÷− 5 =0. This is correct because 0×(−5)=0.
4. Now offer this example:− 5 ÷0. Some students may say the answer is 0. Emphasize that 0 is
not correct because 0× 0 =−5.
5. Explain that you cannot divide by zero. In division, a quantity is divided into groups. But a
quantity cannot be divided into zero groups. It is impossible. This is why division by zero is
undefined.
6. Review the rules for determining the sign of the quotient and the examples on the worksheet
with your students.
EXTRA HELP:
Use multiplication to double-check your work when you divide two integers.ANSWER KEY:
(1) 10 (2) 5 (3) 0 (4)Undefined (5)− 11 (6)Undefined (7)− 24 (8) 0 (9)− 9 (10) 21
(11) 4 (12)Undefined
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(Challenge)Answers may vary. Following is a possible answer. 0÷ 3 =0but3÷0 is undefined
and has no solution.
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