Final answer:
The consequence of mathematical operations involving addition, subtraction, multiplication, or division is determined by the signs of the numbers involved. Positive numbers result in positive outcomes, negative numbers in negative outcomes, and mixed signs result in a result that adopts the sign of the larger absolute value for addition and subtraction, or a negative outcome for multiplication or division.
Step-by-step explanation:
When we look at mathematical operations, the consequence of an operation is essentially its result. If two positive numbers are added together, like in the example 3+2 = 5, the result is positive. Similarly, when two negative numbers are added, such as -4 + (-2) = -6, the consequence is also negative.
Moving on to operations involving numbers with opposite signs, the rule is to subtract the smaller number from the larger number, and the result takes on the sign of the larger number. For instance, -5 +3 = -2 demonstrates this, with the result being negative since the larger absolute value is negative. In subtraction, we effectively change the sign of the number being subtracted and follow the rules of addition. For example, 5 - (+3) = 2 shows that changing the sign of the number being subtracted (making it -3) results in a positive consequence when it's added to 5.
Multiplication and division follow similar rules regarding signs. Two positive numbers or two negative numbers multiplied will yield a positive result, for instance, 2x3 = 6 or (-4) x (-3) = 12. If numbers with opposite signs multiply, the result is negative, like (-3) x 2 = -6. The same rules apply for division, affirming that the consequence of an operation depends greatly on the signs of the numbers involved.