Without calculating, which of the following quotients can u determine will be positive?
657 divide (-23)
-111 divide 37
-725 divide (-29)
1,001 divide (-143)
The quotient that can be determined to be positive without calculating is -725 divide (-29).
To determine whether a quotient will be positive or negative, you can follow this rule:
If the divisor and dividend have the same sign (both positive or both negative), the quotient will be positive. If the divisor and dividend have different signs (one positive and one negative), the quotient will be negative.
Now, let's apply this rule to each of the given quotients:
1) 657 ÷ (-23):
In this case, the divisor (-23) is negative, and the dividend (657) is positive. Therefore, the quotient will be negative.
2) -111 ÷ 37:
Here, both the divisor (37) and the dividend (-111) are negative. So, the quotient will be positive.
3) -725 ÷ (-29):
In this scenario, both the divisor (-29) and the dividend (-725) are negative. Hence, the quotient will be positive.
4) 1,001 ÷ (-143):
Lastly, we have a positive dividend (1,001) and a negative divisor (-143). Consequently, the quotient will be negative.
To summarize:
- 657 ÷ (-23) = negative
-111 ÷ 37 = positive
-725 ÷ (-29) = positive
1,001 ÷ (-143) = negative
To determine whether a quotient will be positive or negative without calculating it, you need to consider the signs of the dividend and the divisor.
In division, the sign of the quotient is determined by the signs of the dividend and divisor. There are four possible cases:
1. Positive ÷ Positive = Positive: When both the dividend and divisor are positive, the quotient will be positive.
2. Negative ÷ Positive = Negative: When the dividend is negative and the divisor is positive, the quotient will be negative.
3. Positive ÷ Negative = Negative: When the dividend is positive and the divisor is negative, the quotient will be negative.
4. Negative ÷ Negative = Positive: When both the dividend and divisor are negative, the quotient will be positive.
Using these rules, we can determine which quotients will be positive without calculating them:
1. 657 ÷ (-23): The dividend (657) is positive, and the divisor (-23) is negative. Therefore, the quotient will be negative.
2. -111 ÷ 37: The dividend (-111) is negative, and the divisor (37) is positive. Therefore, the quotient will be negative.
3. -725 ÷ (-29): Both the dividend (-725) and the divisor (-29) are negative. Therefore, the quotient will be positive.
4. 1,001 ÷ (-143): The dividend (1,001) is positive, and the divisor (-143) is negative. Therefore, the quotient will be negative.
From the given options, the only quotient that can be determined to be positive without calculating it is -725 ÷ (-29).