Zero and Identity
Zero is the additive identity; one is the multiplicative identity; division by zero is undefined.
Key idea
Zero is the additive identity; one is the multiplicative identity; division by zero is undefined.
In depth
Zero is the additive identity (a + 0 = a), and one is the multiplicative identity (a × 1 = a). Anything times zero is zero. Zero also anchors place value and the number line.
Worked example
57 + 0 = 57, 57 × 1 = 57, 57 × 0 = 0.
Real-world uses
- Understanding why adding nothing changes nothing
- Spotting errors when dividing by zero in spreadsheets
Common mistake
Writing 0 ÷ 5 as undefined. It is 0; it is 5 ÷ 0 that is undefined.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Zero and Identity?
Zero is the additive identity; one is the multiplicative identity; division by zero is undefined. It is a topic at the beginner level in Arithmetic & Number Sense.
Where is Zero and Identity used in real life?
Real-world examples: Understanding why adding nothing changes nothing; Spotting errors when dividing by zero in spreadsheets.
What should I learn before Zero and Identity?
Make sure you are comfortable with Fact Families, the previous topic in Arithmetic & Number Sense.
What is a common mistake with Zero and Identity?
Writing 0 ÷ 5 as undefined. It is 0; it is 5 ÷ 0 that is undefined.
How can I practise Zero and Identity?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Zero and Identity?
Move on to Rounding next.
Related beginner topics in Arithmetic & Number Sense
- Counting & Cardinality – Assigning one number word to each object to find how many there are.
- Place Value – The value of a digit depends on its position: ones, tens, hundreds and so on.
- Number Line – A line where numbers are placed in order at equal spacing to compare and add them.
- Comparing Numbers – Use <, > and = to say which number is smaller, larger or equal.
- Ordering Numbers – Arranging numbers from least to greatest or the reverse.
- Even and Odd Numbers – Even numbers divide by 2 with no remainder; odd numbers leave remainder 1.