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multiplication

Multiplying three numbers

Choose the easiest order using commutativity and associativity.

Quick answer

You can multiply three numbers in any order and still get the same answer, because of the commutative and associative properties of multiplication.

Learning outcome

By the end of this page, you will know how to multiply three numbers together by choosing the easiest order to calculate. Success signs:
  • You can rearrange three numbers in any order to multiply them
  • You can use the associative property to group numbers in different ways
  • You can solve real-life problems using three-number multiplication
  • You can explain why multiplication works the same way no matter how you group or order the numbers

Why this matters

Multiplying three numbers is useful in many everyday situations. For example, when you are planning a party, you might need to work out how many snacks to buy. If you have 3 tables, each with 4 people, and each person gets 2 cookies, you multiply 3 × 4 × 2 to find out how many cookies you need. This is also helpful in games, cooking, shopping, and even in building with LEGO blocks. Understanding how to multiply three numbers helps you solve problems faster and more easily.

How it works

Multiplying three numbers is just like multiplying two numbers, but with one extra step. The key is that you can change the order of the numbers or group them in different ways, and you'll still get the same result. This is because of two important maths rules: Commutative property: The order of the numbers doesn’t matter. For example: 2 × 3 × 4 = 4 × 3 × 2 Associative property: The way you group the numbers doesn’t matter. For example: (2 × 3) × 4 = 2 × (3 × 4) This means you can multiply three numbers by: 1. Choosing the easiest order to calculate 2. Grouping numbers that are easy to multiply first 3. Working step-by-step to get your final answer

Examples you can see

Let’s look at some examples to understand how to multiply three numbers. Example 1: 2 × 3 × 4 You can multiply in any order: - 2 × 3 × 4 = 6 × 4 = 24 - 4 × 3 × 2 = 12 × 2 = 24 - 3 × 2 × 4 = 6 × 4 = 24 All give the same answer: 24. Example 2: 5 × 2 × 6 You might find it easier to do: - 5 × 2 = 10 - Then 10 × 6 = 60 Or you might choose: - 2 × 6 = 12 - Then 12 × 5 = 60 Again, the answer is 60. Example 3: 10 × 3 × 2 This is a good one to think about: - 10 × 3 = 30 - Then 30 × 2 = 60 You might also do: - 3 × 2 = 6 - Then 6 × 10 = 60 Still 60!

Try it as a mini adventure

Adventure: The Great Cookie Challenge You are planning a party for your friends. You have 3 tables, and each table has 4 friends sitting around it. Each friend will get 2 cookies. How many cookies do you need in total? Let’s solve this step-by-step: 1st time: 3 tables 2nd time: 4 friends at each table 3rd time: 2 cookies per friend 4th time: Multiply 3 × 4 × 2 You can do this in different ways: - 3 × 4 = 12, then 12 × 2 = 24 cookies - 4 × 2 = 8, then 8 × 3 = 24 cookies - 2 × 3 = 6, then 6 × 4 = 24 cookies You need 24 cookies for the party!

Common mistakes

  • Mistake: Thinking that 3 × 4 × 5 is harder than 5 × 4 × 3 Why it happens: Confusion about order Fix: Remember that the order doesn’t matter. Choose the easiest way to multiply!
  • Mistake: Forgetting to multiply all three numbers together Why it happens: Getting distracted or rushing Fix: Count your steps: multiply two numbers, then multiply by the third
  • Mistake: Using the wrong operation Why it happens: Mixing up multiplication with addition Fix: Remember that multiplication is repeated addition. 3 × 4 means 3 groups of 4

Parent and carer guide

Parents and carers can help by:
  • Encouraging children to try different orders of numbers to multiply
  • Using real-life examples like party snacks, LEGO blocks, or toy collections
  • Practising with simple multiplication problems together
  • Helping children understand that the answer stays the same no matter the order
  • Reinforcing that multiplication is repeated addition (e.g., 3 × 4 = 4 + 4 + 4)
Remember: Don’t worry if a child makes a mistake. It’s part of learning. Keep the atmosphere fun and supportive!

Practice questions

  1. What is 2 × 3 × 4? Answer: 24
  2. Calculate 5 × 2 × 6 Answer: 60
  3. Find the result of 4 × 3 × 5 Answer: 60
  4. Solve 10 × 2 × 3 Answer: 60
  5. What is 6 × 1 × 7? Answer: 42

FAQ

Why can I multiply three numbers in any order?

Because of the commutative property of multiplication, which says that changing the order of numbers does not change the result.

What does "associative" mean in multiplication?

It means that how you group the numbers when multiplying doesn’t change the answer. For example, (2 × 3) × 4 = 2 × (3 × 4).

Is it better to multiply 2 × 3 × 4 or 4 × 3 × 2?

No, both give the same answer. You can choose whichever order feels easier for you.

How can I practice multiplying three numbers?

You can use everyday situations like counting how many eggs are in 3 cartons with 6 eggs each, or how many toys are in 4 boxes with 5 toys each.

Can I use multiplication to solve word problems with three numbers?

Yes! Word problems often involve three numbers, and you can multiply them in any order to find the answer.