Skill: 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 $0$.