Two integers are divided and their quotient is a positive number. What must be true about the two integers?
they have the same sign
If two integers are divided and their quotient is a positive number, then one of the following three scenarios must be true:
1. The two integers have the same sign (both positive or both negative).
2. One of the integers is zero.
3. One of the integers is positive and the other is negative.
In any of these scenarios, when the two integers are divided, the quotient will be a positive number.
To determine what must be true about the two integers when their quotient is a positive number, we need to understand the properties of division and positive numbers.
1. Dividing two integers:
When dividing two integers, the possible outcomes are a positive number, a negative number, or zero.
- If both integers have the same sign (either both positive or both negative) and are non-zero, their quotient will be a positive number.
- If the integers have different signs (one positive and one negative), their quotient will be a negative number.
- If one or both integers are zero, the quotient will be zero.
2. Quotient is a positive number:
Since the question states that the quotient is positive, we can conclude that the two integers must have the same sign (either both positive or both negative). This means they cannot have opposite signs or include zero.
In conclusion, when the quotient of two integers is a positive number, the two integers must have the same sign (either both positive or both negative) and should not include zero.