Without calculating, which of the following cautions can you determine will be positive?
1,001 divided (-143)
657 divided (-23)
-725 divided (-29)
-111 divided 37
Divide rational numbers quick check
To determine whether the given divisions will be positive or negative, we can look at the signs of the dividend and divisor.
For the first division, 1,001 divided by (-143):
The dividend is positive and the divisor is negative. Therefore, the result will be negative.
For the second division, 657 divided by (-23):
Both the dividend and divisor are negative. Therefore, the result will be positive.
For the third division, -725 divided by (-29):
Both the dividend and divisor are negative. Therefore, the result will be positive.
For the fourth division, -111 divided by 37:
Both the dividend and divisor are negative. Therefore, the result will be positive.
Therefore, two of the given divisions will be positive.
To determine if a division of rational numbers will be positive or negative without calculating, we can use the following rule:
When dividing two numbers with the same sign, the result is positive.
When dividing two numbers with different signs, the result is negative.
Using this rule, we can determine which of the given divisions will result in a positive number:
1,001 divided (-143): Different signs, the result is negative.
657 divided (-23): Different signs, the result is negative.
-725 divided (-29): Same signs, the result is positive.
-111 divided 37: Different signs, the result is negative.
Therefore, -725 divided (-29) will be positive without calculating.