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Q: In any base system are addition and multiplication associative and commutative?

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Closure with respect to addition and multiplication. Cummutative, Associative properties of addition and of multiplication. Distributive property of multiplication over addition.

Closure, an identity element, inverse elements, associative property, commutative property

For calculations such as addition, subtraction, multiplication and division .... etc....

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)

Parenthesis, exponents, multiplication, division, addition, subtraction. PEMDAS

bedmas is what I was taught in school. It stands for brackets, ????, division, multiplication, addition, and subtraction

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, Â· x + y belongs to R (closure under addition) Â· (x + y) + z = x + (y + z) (associative property of addition) Â· There is an element, 0, in R, such that x + 0 = 0 + x = x (existence of additive identity) Â· There is an element, -x, in R, such that x + (-x) = (-x) + x = 0 (existence of additive inverse) Â· x + y = y + x (Abelian or commutative property of addition) Â· x * y belongs to R (closure under multiplication) Â· (x * y) * z = x * (y * z) (associative property of multiplication) Â· There is an element, 1, in R, such that x * 1 = 1 * x = x (existence of multiplicative identity) Â· 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) Â· x * (y + z) = x*y + x * z (distributive property of multiplication over addition)

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.

Yes. It holds for all clock systems.

For addition, subtraction. division and multiplication purposes in the same way that we do maths today but they had their own system of numbers known as the Roman numeral system.

No. Example: 6pm*(7pm+2am) =/= 42pm2+12ampm

You can practice it: Counting Addition Subtraction Multiplication Number Concept Division Fraction Decimals Basic Geometry Metric System Customary System (only U.S.A)

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