Neutral Element (Identiy Element)

• $18-0=18$
• $22+0=22$
• $1000000-0=1000000$
• $0+12-0=12$

• $13\times 1=13$
• $220\times 1=220$
• $\frac{1}{2}\times 1=\frac{1}{2}$
• $X\times 1=X$
• $2000000\times 1=2000000$

Note that in a multiplication operation, $-1$ is not considered a neutral number because it affects the the number it is multiplied with by changing its sign.

A neutral element is a number that does not alter the other numbers when an operation is applied to it.

The only neutral element for addition is $0$ and zero is not part of the set of natural numbers. Therefore, there is no neutral of addition in this set.

If there is a non-zero number a and we must find the value of $x$ when $ax=a$, then by solving the equation we find that the neutral of the product is 1.

The neutral element for division is $1$.

The absorbing element of multiplication is 0 because any number multiplied by $0$ is $0$.

The additive neutral of real numbers does not modify the value of any number that it is added to.

Example: $0$ is the additive neutral of real numbers since $a+0=a$.

• The order of operations
• Order of basic operations: addition, subtraction, multiplication and division.
• Order of basic operations (powers)
• Order of basic operations: roots
• The 0 and the 1 in the order of operations

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