Without calculating, which of the following quotients can you determine will be positive?(1 point)
Responses
657 ÷ (−23)
657 divided by Left Parenthesis negative 23 Right Parenthesis
1,001 ÷ (−143)
1,001divided by Left Parenthesis negative 143 Right Parenthesis
−725 ÷ (−29)
negative 725 divided by Left Parenthesis negative 29 Right Parenthesis
−111 ÷ 37
The quotient −111 ÷ 37 can be determined to be positive.
Which of the following does not have the same value as the others?(1 point)
Responses
−3−7
Start Fraction negative 3 over negative 7 End Fraction
3−7
Start Fraction 3 over negative 7 End Fraction
−37
negative Start Fraction 3 over 7 End Fraction
−37
The expression −37 does not have the same value as the other expressions given.
To determine which of the following quotients will be positive without calculating, we can follow a simple rule:
A quotient will be positive if both the numerator and the denominator have the same sign.
Let's apply this rule to each of the given options:
1) 657 ÷ (−23):
Since the numerator (657) is positive and the denominator (−23) is negative, the quotient will be negative.
2) 1,001 ÷ (−143):
Here, both the numerator (1,001) and the denominator (−143) are positive. Therefore, the quotient will be positive.
3) −725 ÷ (−29):
Both the numerator (−725) and the denominator (−29) are negative, so the quotient will be positive.
4) −111 ÷ 37:
In this case, the numerator (−111) is negative, while the denominator (37) is positive. As a result, the quotient will be negative.
Therefore, out of the given options, the quotients that can be determined to be positive without calculating are:
1,001 ÷ (−143) and −725 ÷ (−29).