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Does distributive property of multiplication over addition work for the 12 hour clock system?
Wiki User
∙ 13y ago
No.
Example:
6pm*(7pm+2am) =/= 42pm2+12ampm
Wiki User
∙ 13y ago
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Which of the basic rules of arithmetic are true when you restrict the number system to the positive integers?
Closure with respect to addition and multiplication. Cummutative, Associative properties of addition and of multiplication. Distributive property of multiplication over addition.
Does the distributive property of multiplication over addition hold for the 12-hour clock system?
Yes. It holds for all clock systems.
Solving each system using the substotution method 2x equals 3y x equals 3y-3?
2x=3yx=3y-32(3y-3)=3y substitution6y-6=3y distributive property3y=6 addition property of equalityy=2 multiplication(division) property of equalityx=3(2)-3 substitutionx=6-3x=3
In any base system are addition and multiplication associative and commutative?
Yes
What are the fundamental law of real number system?
The set of real numbers, R, is a mathematical field. For any three real numbers x, y and z and the operations of addition and multiplication, · x + y belongs to R (closure under addition) · (x + y) + z = x + (y + z) (associative property of addition) · There is an element, 0, in R, such that x + 0 = 0 + x = x (existence of additive identity) · There is an element, -x, in R, such that x + (-x) = (-x) + x = 0 (existence of additive inverse) · X + y = y + x (Abelian or commutative property of addition) · x * y belongs to R (closure under multiplication) · (x * y) * z = x * (y * z) (associative property of multiplication) · There is an element, 1, in R, such that x * 1 = 1 * x = x (existence of multiplicative identity) · For every non-zero x, there is an element, 1/x, in R, such that x * 1/x = 1/x * x = 1 (existence of multiplicative inverse) · x * (y + z) = x*y + x * z (distributive property of multiplication over addition)
What did the Chinese use their number system for?
For calculations such as addition, subtraction, multiplication and division .... etc....
How do you find the solution to system of equations?
Parenthesis, exponents, multiplication, division, addition, subtraction. PEMDAS
What is the definition of number system?
The definition of the number system starts with the 5 Peano axioms. These are:Zero is a number.If a is a number, the successor of a is a number.Zero is not the successor of a number.Two numbers of which the successors are equal are themselves equal.If a set S of numbers contains zero and also the successor of every number in S, then every number is in S. (The induction axiom).This defined the set of Natural numbers. The set of real numbers is a mathematical structure known as a field which has the following properties:For any three real numbers x, y and z and the operations of addition and multiplication,x + y belongs to R (closure under addition)(x + y) + z = x + (y + z) (associative property of addition)There is an element, 0, in R, such that x + 0 = 0 + x = x (existence of additive identity)There is an element, -x, in R, such that x + (-x) = (-x) + x = 0 (existence of additive inverse)x + y = y + x (Abelian or commutative property of addition)x * y belongs to R (closure under multiplication)(x * y) * z = x * (y * z) (associative property of multiplication)There is an element, 1, in R, such that x * 1 = 1 * x = x (existence of multiplicative identity)For every non-zero x, there is an element, 1/x, in R, such that x * 1/x = 1/x * x = 1 (existence of multiplicative inverse)x * (y + z) = x * y + x * z (distributive property of multiplication over addition)
What equation is first in a system?
bedmas is what I was taught in school. It stands for brackets, ????, division, multiplication, addition, and subtraction
What are the different properties of real numbers?
Properties of real numbersIn this lesson we look at some properties that apply to all real numbers. If you learn these properties, they will help you solve problems in algebra. Let's look at each property in detail, and apply it to an algebraic expression.#1. Commutative propertiesThe commutative property of addition says that we can add numbers in any order. The commutative property of multiplication is very similar. It says that we can multiply numbers in any order we want without changing the result.addition5a + 4 = 4 + 5amultiplication3 x 8 x 5b = 5b x 3 x 8#2. Associative propertiesBoth addition and multiplication can actually be done with two numbers at a time. So if there are more numbers in the expression, how do we decide which two to "associate" first? The associative property of addition tells us that we can group numbers in a sum in any way we want and still get the same answer. The associative property of multiplication tells us that we can group numbers in a product in any way we want and still get the same answer.addition(4x + 2x) + 7x = 4x + (2x + 7x)multiplication2x2(3y) = 3y(2x2)#3. Distributive propertyThe distributive property comes into play when an expression involves both addition and multiplication. A longer name for it is, "the distributive property of multiplication over addition." It tells us that if a term is multiplied by terms in parenthesis, we need to "distribute" the multiplication over all the terms inside.2x(5 + y) = 10x + 2xyEven though order of operations says that you must add the terms inside the parenthesis first, the distributive property allows you to simplify the expression by multiplying every term inside the parenthesis by the multiplier. This simplifies the expression.#4. Density propertyThe density property tells us that we can always find another real number that lies between any two real numbers. For example, between 5.61 and 5.62, there is 5.611, 5.612, 5.613 and so forth.Between 5.612 and 5.613, there is 5.6121, 5.6122 ... and an endless list of other numbers!#5. Identity propertyThe identity property for addition tells us that zero added to any number is the number itself. Zero is called the "additive identity." The identity property for multiplication tells us that the number 1 multiplied times any number gives the number itself. The number 1 is called the "multiplicative identity."Addition5y + 0 = 5yMultiplication2c × 1 = 2c* * * * *The above is equally true of the set of rational numbers.One of the main differences between the two, which was used by Dedekind in defining real numbers is that a non-empty set of real numbers that is bounded above has a least upper bound. This is not necessarily true of rational numbers.
What is the real number system as a field?
The set of real numbers, R, is a mathematical field. In order for it to be a field, it must satisfy the following.For any three real numbers x, y and z and the operations of addition and multiplication, · x + y belongs to R (closure under addition) · (x + y) + z = x + (y + z) (associative property of addition) · There is an element, 0, in R, such that x + 0 = 0 + x = x (existence of additive identity) · There is an element, -x, in R, such that x + (-x) = (-x) + x = 0 (existence of additive inverse) · x + y = y + x (Abelian or commutative property of addition) · x * y belongs to R (closure under multiplication) · (x * y) * z = x * (y * z) (associative property of multiplication) · There is an element, 1, in R, such that x * 1 = 1 * x = x (existence of multiplicative identity) · For every non-zero x, there is an element, 1/x, in R, such that x * 1/x = 1/x * x = 1 (existence of multiplicative inverse) · x * (y + z) = x*y + x * z (distributive property of multiplication over addition)
What is matrix system?
A matrix is a rectangular array of elements - usually numbers. These, together with rules governing their addition and multiplication make up matrix algebra or system.
