Identity Elements Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Identity Elements.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

Special numbers that leave any other number unchanged under a given operation: 0 for addition, 1 for multiplication.

Adding 0 leaves any number unchanged; multiplying by 1 also leaves it unchanged. Both are 'do-nothing' values.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Identity elements act as 'do nothing' values for their operations.

Common stuck point: There's no identity for subtraction or division (as operations).

Sense of Study hint: Ask yourself: which number leaves the other unchanged? Test with 0 for addition and 1 for multiplication.

Worked Examples

Example 1

easy
Show that adding 0 to any number doesn't change it. Verify with \(14 + 0\) and \(0 + 14\).

Solution

  1. 1
    \(14 + 0 = 14\). Adding nothing changes nothing.
  2. 2
    \(0 + 14 = 14\). Same result.
  3. 3
    The identity element for addition is 0: \(a + 0 = 0 + a = a\).

Answer

14 in both cases
Zero is the additive identity. Adding 0 to any number leaves it unchanged. It is like adding an empty set.

Example 2

medium
Show that multiplying any number by 1 doesn't change it. Use \(23 \times 1\) and \(1 \times 23\). Also show what happens with \(23 \times 0\).

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
What is \(387 + 0\)? What property does this demonstrate?

Example 2

medium
Fill in the blank and name the property: \(456 \times \square = 456\) and \(456 \times \square = 0\).
← Back to Identity Elements Formula Explained Practice Mode

Background Knowledge

These ideas may be useful before you work through the harder examples.

additionmultiplication