## To determine whether a quotient will be positive without calculating, you need to understand the rules for dividing positive and negative numbers.

The rule states that dividing two numbers with the same sign (both positive or both negative) will result in a positive quotient. On the other hand, if the two numbers have different signs, the quotient will be negative.

Let's apply this rule to the given options:

A. 1001 ÷ (-143)

Since one number is positive (1001) and the other is negative (-143), the quotient will be negative. Therefore, option A will not be positive.

B. 657 ÷ (-23)

Again, one number is positive (657) and the other is negative (-23), so the quotient will be negative. Therefore, option B will not be positive.

C. -111 ÷ 37

Both numbers in this option are negative, so applying the rule, the quotient will be positive. Therefore, option C can be determined to be positive without calculating.

D. -725 ÷ (-29)

Both numbers in this option are negative, so the quotient will be positive. Therefore, option D can also be determined to be positive without calculating.

So, the quotients that can be determined to be positive without calculating are options C and D (C. -111 ÷ 37 and D. -725 ÷ (-29)).