Without calculating, which of the following quotients can you determine will be positive?(1 point)
Responses
−725 ÷ (−29)
negative 725 divided by Left Parenthesis negative 29 Right Parenthesis
657 ÷ (−23)
657 divided by Left Parenthesis negative 23 Right Parenthesis
−111 ÷ 37
negative 111 divided by 37
1,001 ÷ (−143)
−725 ÷ (−29)
Which of the following does not have the same value as the others?(1 point)
Responses
−37
Start Fraction negative 3 over 7 End Fraction
−3 −/7
Start Fraction negative 3 over negative 7 End Fraction
−3/7
negative Start Fraction 3 over 7 End Fraction
3−/7
3−/7
To determine which of the given quotients will be positive without calculating, we can look at the signs of the numbers involved.
A quotient will be positive if both the dividend and divisor have the same sign (either both positive or both negative).
So, without calculating, we can determine that the following quotient will be positive:
-725 ÷ (-29)
To determine whether a quotient will be positive or negative without calculating, you can use the rule that states:
- If the signs of the dividend and divisor are the same (both positive or both negative), the quotient will be positive.
- If the signs of the dividend and divisor are different (one positive and one negative), the quotient will be negative.
Now, let's apply this rule to the given quotients:
1. −725 ÷ (−29): Both the dividend (−725) and divisor (−29) have negative signs. So, the quotient will be positive.
2. 657 ÷ (−23): The dividend (657) is positive, but the divisor (−23) is negative. Therefore, the quotient will be negative.
3. −111 ÷ 37: The dividend (−111) is negative, and the divisor (37) is positive. Hence, the quotient will be negative.
4. 1,001 ÷ (−143): The dividend (1,001) is positive, and the divisor (−143) is negative. Consequently, the quotient will be negative.
Based on the rule mentioned above, we can determine that the only quotient in the given options that will be positive is: −725 ÷ (−29).