Distributive property for children

Quick answer

The distributive property means you can break one of the numbers in a multiplication into smaller parts, then multiply each part separately and add the results together. For example, 7 × 8 = (5 × 8) + (2 × 8).

Learning outcome

By the end of this page, you will understand how to use the distributive property to solve multiplication problems by splitting one of the numbers into smaller parts.

• You can split a number into two parts to make multiplication easier.
• You can multiply each part separately and add the results.
• You can solve multiplication problems using the distributive property.
• You can explain how the distributive property works with examples.

Why this matters

Knowing the distributive property helps you solve bigger multiplication problems more easily. It’s a useful trick that makes maths feel less scary and more like a game. You can use it when you’re doing maths in your head or when you're working with bigger numbers in class.

It also helps you understand how multiplication works, which is important for learning more advanced maths later on. You’ll use it when you learn about algebra, where it helps you simplify expressions.

How it works

Let’s imagine you’re trying to find the answer to 7 × 8. Instead of just doing 7 × 8 straight away, you can split the 7 into two smaller numbers, like 5 and 2. Then you multiply each part by 8 and add the answers together.

1. Split one of the numbers into two parts. For example, 7 = 5 + 2.
2. Multiply each part by the other number. So 5 × 8 and 2 × 8.
3. Add the two answers together. 40 + 16 = 56.
4. So, 7 × 8 = 56.

Examples you can see

Let’s look at a few examples to see how this works in real life.

Example 1: 6 × 9

1. Split 6 into 5 + 1.
2. Do 5 × 9 = 45.
3. Do 1 × 9 = 9.
4. Add 45 + 9 = 54.
5. So, 6 × 9 = 54.

Example 2: 3 × 7

1. Split 3 into 2 + 1.
2. Do 2 × 7 = 14.
3. Do 1 × 7 = 7.
4. Add 14 + 7 = 21.
5. So, 3 × 7 = 21.

Example 3: 9 × 5

1. Split 9 into 5 + 4.
2. Do 5 × 5 = 25.
3. Do 4 × 5 = 20.
4. Add 25 + 20 = 45.
5. So, 9 × 5 = 45.

Try it as a mini adventure

Imagine you are a chef in a big restaurant kitchen. You need to make 8 trays of cupcakes, and each tray holds 7 cupcakes. But you’re not sure how many cupcakes you need in total. You can use the distributive property to figure it out!

1. You know 8 × 7 = ?
2. Split 8 into 5 + 3.
3. Do 5 × 7 = 35.
4. Do 3 × 7 = 21.
5. Add 35 + 21 = 56.
6. You need 56 cupcakes!

Now, you can also try it with 6 × 8:

1. Split 6 into 4 + 2.
2. Do 4 × 8 = 32.
3. Do 2 × 8 = 16.
4. Add 32 + 16 = 48.
5. So, 6 × 8 = 48.

Common mistakes

• Mistake: Forgetting to multiply both parts by the same number.
• Why it happens: Kids might only multiply one part and forget the other.
• Fix: Always double-check that both parts are multiplied by the same number.

• Mistake: Adding the parts before multiplying.
• Why it happens: Kids might add 5 + 2 = 7 and then multiply 7 × 8.
• Fix: Multiply each part by the other number first, then add.

• Mistake: Thinking that 3 × 4 = 12 and 3 × 6 = 18, so 3 × 10 = 30.
• Why it happens: Kids might think that because 4 + 6 = 10, then 3 × 10 = 30.
• Fix: Remember that 3 × 10 = 30 is correct, but you must split one number, not add the second number.

Parent and carer guide

Parents and carers can help children understand the distributive property by:

1. Using visual aids like blocks or counters to show how splitting numbers works.
2. Practising with simple examples like 4 × 6 = (2 × 6) + (2 × 6).
3. Encouraging children to explain their thinking aloud.
4. Using real-life examples like sharing snacks or grouping toys.
5. Reinforcing that the final answer must be the same whether you do it one way or the other.

Remember, it’s okay if your child doesn’t get it right away. Practice makes progress!

Practice questions

1. What is 5 × 7 using the distributive property?
2. What is 8 × 6 using the distributive property?
3. What is 9 × 4 using the distributive property?
4. What is 3 × 8 using the distributive property?
5. What is 6 × 5 using the distributive property?

Answers:

1. 5 × 7 = (3 × 7) + (2 × 7) = 21 + 14 = 35
2. 8 × 6 = (5 × 6) + (3 × 6) = 30 + 18 = 48
3. 9 × 4 = (5 × 4) + (4 × 4) = 20 + 16 = 36
4. 3 × 8 = (2 × 8) + (1 × 8) = 16 + 8 = 24
5. 6 × 5 = (4 × 5) + (2 × 5) = 20 + 10 = 30

FAQ

What is the distributive property?

The distributive property means you can split one number in a multiplication into two parts, multiply each part by the other number, and then add the results together.

Why is it called the distributive property?

Because you are "distributing" one number across the parts of another number.

Can I use it with any numbers?

Yes! You can use it with any multiplication problem, but it’s especially helpful when one number is a bit tricky to multiply.

Is it the same as repeated addition?

Repeated addition is when you add the same number many times, like 3 + 3 + 3 = 9. The distributive property is about splitting one number to make multiplication easier.

How can I practice it at home?

You can split numbers and multiply each part, then add the answers. Try it with your child’s times tables or with everyday situations like sharing food or counting toys.