Properties of Addition
Addition is commutative, associative and has identity 0.
Key idea
Addition is commutative, associative and has identity 0.
In depth
Commutative (a+b=b+a) lets you swap order. Associative ((a+b)+c=a+(b+c)) lets you regroup. Identity (a+0=a) says zero changes nothing. These make mental math possible: reorder and regroup to make friendly numbers.
Worked example
17 + 8 + 3: regroup as 17 + 3 + 8 = 20 + 8 = 28.
Formula
Real-world uses
- Adding numbers in any order when doing mental maths
- Spotting that 7 + 38 + 3 is the same as 7 + 3 + 38
Common mistake
Assuming subtraction has these properties. 5 − 3 ≠ 3 − 5.
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 Properties of Addition?
Addition is commutative, associative and has identity 0. It is a topic at the beginner level in Arithmetic & Number Sense.
What is the formula for Properties of Addition?
The key formula is a+b = b+a; (a+b)+c = a+(b+c); a+0 = a.
Where is Properties of Addition used in real life?
Real-world examples: Adding numbers in any order when doing mental maths; Spotting that 7 + 38 + 3 is the same as 7 + 3 + 38.
What should I learn before Properties of Addition?
Make sure you are comfortable with Subtraction, the previous topic in Arithmetic & Number Sense.
What is a common mistake with Properties of Addition?
Assuming subtraction has these properties. 5 − 3 ≠ 3 − 5.
How can I practise Properties of Addition?
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 Properties of Addition?
Move on to Multiplication as Repeated Addition 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.