The distributive property of multiplication might be a long expression, but the meaning of it is really useful for us. Before we can use it though, we need to know what it means, but more importantly, trust that it works.

It's a good idea to refresh our memories of arrays for multiplication, as this helps us imagine what we are working out. Then, we can discover the distributive property of multiplication, and use it to solve multiplication number problems. In Video 1, we prove that the distributive property of multiplication works, so have a look at how we do this.

Some trickier problems

Once we trust that we can split our number problems into smaller problems, we can use this to solve other problems. Let's work through some examples in Video 2, including how you can use the distributive property of multiplication to solve some trickier multiplication problems.

Remember!

We can write an equation such as $5\times12$5×12 as $5\times10+5\times2$5×10+5×2. So that it works for any number, we could write this as:

$a\times bc=a\times b+a\times c$a×bc=a×b+a×c

Worked Examples

Question 1

We want to use the distributive property to rewrite $2\times19$2×19 as easier multiplications.

This diagram shows how $2$2 groups of $19$19 objects can be split up.

Use the diagram to fill in the blank to make the statement true.