Properties of Multiplication
Multiplication is commutative, associative, has identity 1 and zero property.
Key idea
Multiplication is commutative, associative, has identity 1 and zero property.
In depth
Multiplication is commutative and associative, has identity 1, and distributes over addition: a(b+c) = ab + ac. The distributive property is the engine behind long multiplication and algebra.
Worked example
6 × 14 = 6×10 + 6×4 = 60 + 24 = 84.
Formula
Real-world uses
- Rearranging factors to multiply in your head, such as 4 × 25 × 3 = 100 × 3
- Checking answers
Common mistake
Applying distribution to the wrong operation: a(b×c) is not ab × ac.
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 Multiplication?
Multiplication is commutative, associative, has identity 1 and zero property. It is a topic at the beginner level in Arithmetic & Number Sense.
What is the formula for Properties of Multiplication?
The key formula is a×b = b×a; a×1 = a; a×0 = 0.
Where is Properties of Multiplication used in real life?
Real-world examples: Rearranging factors to multiply in your head, such as 4 × 25 × 3 = 100 × 3; Checking answers.
What should I learn before Properties of Multiplication?
Make sure you are comfortable with Multiplication Tables, the previous topic in Arithmetic & Number Sense.
What is a common mistake with Properties of Multiplication?
Applying distribution to the wrong operation: a(b×c) is not ab × ac.
How can I practise Properties of Multiplication?
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 Multiplication?
Move on to Division 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.