Which statements are true about the rules of division? Check all that apply.
A. The quotient of two negative integers is positive.
B. The quotient of two integers with different signs is positive.
C. The quotient of two integers with the same sign is positive.
D. The quotient of a positive integer and a negative integer is positive.
E. The quotient of a negative integer and a positive integer is positive.
A. The quotient of two negative integers is positive. - True
B. The quotient of two integers with different signs is positive. - False
C. The quotient of two integers with the same sign is positive. - True
D. The quotient of a positive integer and a negative integer is positive. - False
E. The quotient of a negative integer and a positive integer is positive. - False
The correct statements about the rules of division are:
B. The quotient of two integers with different signs is positive.
C. The quotient of two integers with the same sign is positive.
D. The quotient of a positive integer and a negative integer is positive.
E. The quotient of a negative integer and a positive integer is positive.
To determine which statements are true about the rules of division, let's analyze the options one by one:
A. The quotient of two negative integers is positive.
To verify this statement, you can pick two negative numbers and divide them. For example, consider -6 divided by -3. When you perform the division, you will see that the quotient is positive 2. Therefore, statement A is TRUE.
B. The quotient of two integers with different signs is positive.
To test this statement, choose two integers with different signs and divide them. For instance, consider -8 divided by 4. After performing the division, you will find that the result is negative -2. Thus, statement B is FALSE.
C. The quotient of two integers with the same sign is positive.
To prove or disprove this statement, choose two integers with the same sign and divide them. For example, consider 12 divided by 3. The result of this division is 4, which is positive. Hence, statement C is TRUE.
D. The quotient of a positive integer and a negative integer is positive.
To verify this statement, divide a positive integer by a negative integer. For instance, perform the division 10 divided by -2. The result will be -5, which is negative. As a result, statement D is FALSE.
E. The quotient of a negative integer and a positive integer is positive.
To test this statement, divide a negative integer by a positive integer. For instance, divide -16 by 4. The result of this division is -4, which is negative. Therefore, statement E is FALSE.
In conclusion, the statements that are true about the rules of division are A and C.