Without calculating, which of the following quotients can you determine will be positive?(1 point)
Responses
1,001 ÷ (−143)
1,001divided by Left Parenthesis negative 143 Right Parenthesis
−111 ÷ 37
negative 111 divided by 37
657 ÷ (−23)
657 divided by Left Parenthesis negative 23 Right Parenthesis
−725 ÷ (−29)
−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
−37
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 use the following rule:
"The quotient of two numbers with the same sign is always positive."
Applying this rule to the given quotients, we can determine that:
1) 1,001 ÷ (−143) = Negative ÷ Negative = Positive
2) −111 ÷ 37 = Negative ÷ Positive = Negative
3) 657 ÷ (−23) = Positive ÷ Negative = Negative
4) −725 ÷ (−29) = Negative ÷ Negative = Positive
Therefore, the first and the fourth quotients will be positive.