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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

−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

1 answer

To determine the signs of the quotients without calculating, we can use the rule that states:

  • A positive divided by a negative results in a negative quotient.
  • A negative divided by a positive results in a negative quotient.
  • A negative divided by a negative results in a positive quotient.
  • A positive divided by a positive results in a positive quotient.

Now, let's analyze each quotient:

  1. 657 ÷ (−23): A positive number (657) divided by a negative number (−23) will be negative.
    Result: Negative

  2. −111 ÷ 37: A negative number (−111) divided by a positive number (37) will be negative.
    Result: Negative

  3. 1,001 ÷ (−143): A positive number (1,001) divided by a negative number (−143) will be negative.
    Result: Negative

  4. −725 ÷ (−29): A negative number (−725) divided by a negative number (−29) will be positive.
    Result: Positive

Therefore, the only quotient that can be determined to be positive is:

−725 ÷ (−29).