without calculating which of the following quotients cn you determine will be positive a. -111 divided by 37 b. 657 divided by (-23) c. 1001 divded by (-143) d. -725 divided by (-29)

Answer 1

To determine which of the given quotients will be positive without calculating them, we can use the rule that states:

• The quotient of two numbers is positive if both numbers have the same sign (both positive or both negative).
• The quotient is negative if one number is positive and the other is negative.

Now, let's analyze each option:

a. \(-111\) divided by \(37\): Here, \(-111\) is negative and \(37\) is positive. Since the signs are different, the quotient will be negative.

b. \(657\) divided by \(-23\): Here, \(657\) is positive and \(-23\) is negative. Since the signs are different, the quotient will be negative.

c. \(1001\) divided by \(-143\): Here, \(1001\) is positive and \(-143\) is negative. Since the signs are different, the quotient will be negative.

d. \(-725\) divided by \(-29\): Here, both \(-725\) and \(-29\) are negative. Since the signs are the same, the quotient will be positive.

From this analysis, the only quotient that we can determine will be positive is d. \(-725\) divided by \(-29\).