We used the relationship between multiplication and division to make conjectures about the signs of quotients of integers.
The division of two integers with opposite signs is negative. The division of two integers with the same sign is positive.
We can use multiplication to understand why division by zero is not possible.
Think about the division problem below and its related multiplication problem.
5 ÷ 0 = ? 0 × ? = 5
The multiplication sentence says that there is some number times 0 that equals 5. We already know that 0 times any number equals 0. This means division by 0 is not possible, so we say that division by 0 is undefined.
Example 1 :
Divide: 24 ÷ (-3)
Solution :
Step 1 :
Determine the sign of the quotient.
24 is positive and -3 is negative. Since the numbers have opposite signs, the quotient will be negative.
Step 2 :
Divide.
24 ÷ (-3) = -8
Example 2 :
Divide: -6 ÷ (-2)
Solution :
Step 1 :
Determine the sign of the quotient.
-6 is negative and -2 is negative. Since the numbers have the same sign, the quotient will be positive.
Step 2 :
Divide.
-6 ÷ (-2) = 3
Example 3 :
Divide: 0 ÷ (-2)
Solution :
Step 1 :
Determine the sign of the quotient.
The dividend is 0 and the divisor is not 0. So, the quotient is 0.
Step 2 :
Divide.
0 ÷ (-2) = 0
Example 4 :
Divide: 3 ÷ 0
Solution :
The dividend is 3 and the divisor is 0.
Dividing any number by 0 is not possible, so we say that division by 0 is undefined.
Hence,
3 ÷ 0 = Undefined
Example 5 :
Divide: 8 ÷ 4
Solution :
Step 1 :
Determine the sign of the quotient.
8 is positive and 4 is positive. Since the numbers have the same sign, the quotient will be positive.
Step 2 :
Divide.
8 ÷ 4 = 2
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