Without calculating, which of the following quotients can you determine will be positive?
657 divided by (-23)
-111 divided by 37
1001 divided by (-143)
-725 divided by (-29)
To determine if a quotient will be positive or negative without calculating, we can use the following rules:
- A positive number divided by a positive number will be positive.
- A negative number divided by a negative number will be positive.
- A negative number divided by a positive number will be negative.
- A positive number divided by a negative number will be negative.
Using these rules, we can determine the following quotients will be positive:
- 657 divided by (-23) will be negative, as a positive number divided by a negative number will be negative.
- -111 divided by 37 will be negative, as a negative number divided by a positive number will be negative.
- 1001 divided by (-143) will be negative, as a positive number divided by a negative number will be negative.
- -725 divided by (-29) will be positive, as a negative number divided by a negative number will be positive.
To determine if the quotient will be positive without calculating, we can consider the signs of the dividend (the number being divided) and the divisor (the number dividing the dividend).
For a quotient to be positive:
- If both the dividend and divisor are positive.
- If both the dividend and divisor are negative.
Using this information, we can determine which of the given quotients will be positive:
657 divided by (-23)
This quotient will be negative since the dividend is positive, and the divisor is negative.
-111 divided by 37
This quotient will be negative since the dividend is negative, and the divisor is positive.
1001 divided by (-143)
This quotient will be negative since the dividend is positive, and the divisor is negative.
-725 divided by (-29)
This quotient will be positive since both the dividend and divisor are negative.
Therefore, the only quotient that can be determined to be positive without calculating is -725 divided by -29.