Explanation:
We will use some simple examples.
Addition:
Positive: When two positive numbers are adding, the sum stays positive.
Mixed: When two numbers, positive and negative numbers are adding, ex: 1 + (-2), it's subtracting 2 from 1. Think of the problem as 1 - 2.
Negative: When two Negative numbers are adding, the sum stays negative. Ex: (-4) + (-4) = -8.
Subtraction:
Positive: When two positive numbers are subtracting, the difference stays positive, or in the case that if the 2nd number is greater than the 1st, a negative difference.
Mixed: When two numbers, positive and negative are subtracting, the negative number changes to a positive. Ex: 4 - (-9), -9 changes to a positive because you can't subtract a negative number. But, if the problem was (-9) - 4, the problem will still be the same.
Negative: Same rule applies with mixed numbers. Ex: -4 - (-9), -9 changes to a positive 9, leaving the problem as -4 + 9. If the terms were flipped, the problem will be the same, change -4 to a positive number.
Multiplication:
Positive: A number times a number = a positive product. Ex: 7 x 7 = 49
Mixed: A number times a negative number = a negative product. Ex: 7 x (-7) = -49
Negative: A negative number times a negative number = a positive product. Ex: (-7) x (-7) = 49.
Division:
Positive: A number divided by a number = a positive quotient. Ex: 30 / 3 = 10.
Mixed: A number divided by a negative number = a negative quotient. Ex: 30 / -3 = -10.
Negative: A negative number divided by a negative number = a positive quotient. Ex: -30 / -3 = 10