Without calculating, which of the following quotients can you determine will be positive?(1 point)
Responses
−111 ÷ 37
negative 111 divided by 37
1,001 ÷ (−143)
1,001divided by Left Parenthesis negative 143 Right Parenthesis
−725 ÷ (−29)
negative 725 divided by Left Parenthesis negative 29 Right Parenthesis
657 ÷ (−23)
657 divided by Left Parenthesis negative 23 Right Parenthesis
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 3 over negative 7 End Fraction
−3−7
Start Fraction negative 3 over negative 7 End Fraction
−37
−3−7
Using the rules for dividing signed numbers, what is the quotient when you divide 56÷(−4)÷(−2)?(1 point)
Responses
7
7
−7
negative 7
−28
negative 28
28
28
−7
What is the quotient of −7÷(−3)?(1 point)
Responses
−213
negative 2 Start Fraction 1 over 3 End Fraction
−37
negative Start Fraction 3 over 7 End Fraction
37
Start Fraction 3 over 7 End Fraction
213
2 Start Fraction 1 over 3 End Fraction
2 1/3
Which statement is correct?(1 point)
Responses
Division is neither commutative nor associative.
Division is neither commutative nor associative.
Division is associative but not commutative.
Division is associative but not commutative.
Division is both commutative and associative.
Division is both commutative and associative.
Division is commutative but not associative.
Division is commutative but not associative.
Division is neither commutative nor associative.
To determine whether a quotient will be positive or negative without actually calculating it, you need to consider the signs of the dividend (the number being divided) and the divisor (the number by which it is being divided).
In general, a quotient will be positive if the signs of both the dividend and the divisor are the same (both positive or both negative). Conversely, a quotient will be negative if the signs of the dividend and the divisor are different (one positive and one negative).
Let's analyze each of the given quotients:
1. −111 ÷ 37:
The dividend is negative and the divisor is positive. Since the signs are different, the quotient will be negative.
2. 1,001 ÷ (−143):
The dividend is positive and the divisor is negative. Since the signs are different, the quotient will be negative.
3. −725 ÷ (−29):
Both the dividend and the divisor are negative. Since the signs are the same, the quotient will be positive.
4. 657 ÷ (−23):
The dividend is positive and the divisor is negative. Thus, the signs are different, and the quotient will be negative.
In summary, out of the given options, only the quotient −725 ÷ (−29) will be positive.