The answer depends on which properties are being used to prove which rules.
Because it is.
Adding integers, if they have the same sign, add their absolute values and keep the same sign. Subtracting, change the sign of the 2nd number and the add using rules of addition. Multiplying and dividing, Divide the absolute values, if the signs are the same the answer is positive, if the signs are different the answer is negative.
to subtrct integers ,rewrite as adding opposites and use the rules for addtion of integers..
David Missoula's
The set of integers is closed under addition so that if x and y are integers, then x + y is an integer.Addition of integers is commutative, that is x + y = y + xAddition of integers is associative, that is (x + y) + z = x + (y + z) and so, without ambiguity, either can be written as x + y + z.The same three rules apply to addition of rational numbers.
Because it is.
When multiplying integers, multiplying by the same sign will always produce a positive integer. Such as a negative times a negative equals a positive. If the signs are different then the product will be a negative.
The rules are not the same.Multiplication is commutative whereas division is not.Multiplication is associative whereas division is not.
They aren't. The rules are the same as those for adding/subtracting or multiplying integers. Just be careful of the decimal point's location.
Multiplying and dividing integers and rational numbers follow the same fundamental rules. In both cases, the product of two numbers is determined by multiplying their absolute values and applying the appropriate sign rules. Similarly, division involves inverting the divisor and multiplying, maintaining the same sign conventions. Thus, the processes are consistent, with rational numbers simply extending the concept to fractions.
Yes, when multiplying integers, the rules for signs apply consistently. If both integers have the same sign (either both positive or both negative), the product is positive. If the integers have different signs (one positive and one negative), the product is negative. This rule is fundamental in arithmetic involving integers.
Placing a question mark at the end of a phrase does not make it a sensible question. Try to use a whole sentence to describe what it is that you want answered. Your "question" sheds no light on what rules for integers you are interested in: rules for addition, subtraction, and so on; rules for multiplying numbers with integer indices, and so on.
When multiplying two integers, the product follows these basic rules: If both integers have the same sign (either both positive or both negative), the product is positive. If the integers have different signs (one positive and one negative), the product is negative. For example, (3 \times 4 = 12) (positive) and (-3 \times -4 = 12) (positive), while (3 \times -4 = -12) (negative).
Adding integers, if they have the same sign, add their absolute values and keep the same sign. Subtracting, change the sign of the 2nd number and the add using rules of addition. Multiplying and dividing, Divide the absolute values, if the signs are the same the answer is positive, if the signs are different the answer is negative.
In relation to what? In a general sense they are the rules that govern their usage in mathematics and also define their properties. Huurrrmmppfff. I think.
Positive x Positive =Positive Positive x Negative= Negative Negative x Positive= Negative Negative x Negative =Positive
The process of dividing integers is similar to multiplying integers in that both operations involve the concept of groups and repeated actions. Just as multiplication can be thought of as repeated addition, division can be seen as determining how many times one integer fits into another. Additionally, both operations follow the same rules regarding positive and negative signs: multiplying or dividing two integers with the same sign yields a positive result, while differing signs result in a negative outcome. Thus, both processes are foundational arithmetic operations that share similar principles.