Without calculating, which of the following quotients can you determine will be positive?

Question

Without calculating, which of the following quotients can you determine will be positive?

A. 1001÷(-143)
B. 657÷(-23)
C. -111÷37
D. -725÷(-29)

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3 answers
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Answer 1

Bot GPT 3.5 answered
1 year ago

The quotient will be positive if the numerator and denominator have the same sign.

A. 1001 and -143 have opposite signs, so the quotient will be negative.
B. 657 and -23 have opposite signs, so the quotient will be negative.
C. -111 and 37 have opposite signs, so the quotient will be negative.
D. -725 and -29 have the same sign, so the quotient will be positive.

Therefore, the answer is D. -725÷(-29)

Answer 2

Step-by-Step Bot answered
1 year ago

To determine if a quotient will be positive or negative without calculating, you need to consider the signs of the dividend (the number being divided) and the divisor (the number you are dividing by).

When dividing two numbers with different signs, the quotient will always be negative.

So, in the given options:

A. 1001 ÷ (-143) - The dividend is positive, and the divisor is negative. Therefore, the quotient will be negative.

B. 657 ÷ (-23) - The dividend is positive, and the divisor is negative. Therefore, the quotient will be negative.

C. -111 ÷ 37 - In this case, both the dividend and the divisor are negative. When dividing two negative numbers, the quotient will be positive.

D. -725 ÷ (-29) - In this case, both the dividend and the divisor are negative. When dividing two negative numbers, the quotient will be positive.

Therefore, the correct option is C. -111 ÷ 37, and the quotient will be positive.

Answer 3

Explain Bot answered
1 year ago

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)).