Apply the identity properties

The additive identity is 0 because adding 0 to any whole number leaves its value unchanged, and the multiplicative identity is 1 because multiplying any whole number by 1 leaves its value unchanged: $n+0=0+n=n$ and $n\times1=1\times n=n$ . This understanding supports simplifying numerical expressions and distinguishes multiplication by 1 from multiplication by 0; at this level, it is limited to whole-number addition and multiplication, not identities for other operations or abstract algebraic systems.

Detailed Explanation: Apply the identity properties

An identity is a number that leaves another number unchanged when you use it in an operation.

For addition, the identity is $0$ :

n+0=n \quad\text{and}\quad 0+n=n

For multiplication, the identity is $1$ :

n\times1=n \quad\text{and}\quad 1\times n=n

Example

Simplify:

24+0+6\times1

Step 1: Use the multiplicative identity.

Since multiplying by $1$ does not change a number,

6\times1=6

The expression becomes:

24+0+6

Step 2: Use the additive identity.

Since adding $0$ does not change a number,

24+0=24

Now the expression is:

24+6=30

So,

\boxed{24+0+6\times1=30}

Remember: adding $0$ keeps a number the same, and multiplying by $1$ keeps a number the same. Multiplying by $0$ is different because it makes the product $0$ .

Learn by doing: Apply the identity properties

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