Without calculating, which of the following quotients can you determine will be positive?
−725 ÷ (−29)
−111 ÷ 37
657 ÷ (−23)
1,001 ÷ (−143)
The quotient −111 ÷ 37 will be positive because the numerator and denominator are both negative numbers.
Which of the following does not have the same value as the others?
3 over −7
−3 over −7
−3 over 7
− 3 over 7
The fraction -3 over 7 does not have the same value as the others.
Using the rules for dividing signed numbers, what is the quotient when you divide 56÷(−4)÷(−2)?
−28
−7
28
7
To divide 56 by -4, we get -14.
To divide -14 by -2, we get 7.
Therefore, the quotient when you divide 56 ÷ (-4) ÷ (-2) is 7.
What is the quotient of −7÷(−3)
3 over 7
-2 and 1 over 3
2 and 1 over 3
- 3 over 7
The quotient of −7 ÷ (−3) is 2 and 1/3.
Which statement is correct?
Division is associative but not commutative.
Division is commutative but not associative.
Division is neither commutative nor associative.
Division is both commutative and associative.
The correct statement is "Division is neither commutative nor associative."
To determine whether a quotient will be positive or negative without calculating, you need to look at the signs of the numbers being divided.
If both numbers have the same sign (either both positive or both negative), the quotient will be positive. If the numbers have different signs (one positive and one negative), the quotient will be negative.
Let's analyze each of the given quotients:
1. −725 ÷ (−29): Both numbers are negative, so the quotient will be positive.
2. −111 ÷ 37: One number is negative and the other is positive, so the quotient will be negative.
3. 657 ÷ (−23): One number is positive and the other is negative, so the quotient will be negative.
4. 1,001 ÷ (−143): One number is positive and the other is negative, so the quotient will be negative.
Therefore, the only quotient you can determine will be positive without calculating is −725 ÷ (−29).