Distributive property – simple & visual

Most of the students learn about Distributive Property in Grade 4 or Grade 5 and this is how they usually get introduced to this topic.

a * (b + c) = a * b + a * c

I feel that we can introduce this beautiful & useful mathematical property in a more interesting manner.

I want my students to be amazed by the beauty of Math. I want them to be curious about this subject. My job is not just to ‘teach’, my job is to create the desire for learning .

We teach our children tricks to calculate 42 x 15 mentally. If they can “see” 42 x 15, they won’t need to remember any trick. They can develop their own tricks 😉

Me – You already know that addition is like walking on a line (1 – dimensional activity) How does multiplication look like? Say 2 x 5 ?

Student – Umm….?

Me –  Multiplication ( 2 x 5) is like walking on a 2 – dimensional plane.

If I give you 2 building blocks every day, how many total blocks would you get in 5     days?

Student – Easy! 2 x 5 = 10 blocks

Me –  Won’t it look like this ?


Does it look a 2- dimensional activity now?

Student – Yeah, multiplication looks like area of a rectangle ( 2 x 5 ) now.

Me – Great. That’s exactly the point I wanted to make here. I wanted you to see that multiplication (a x b) is nothing but the area of a rectangle with sides a units and b units.

 Let’s think one step ahead. How will 3 x 4 x 5 look like ? Can you visualise a 3-dimensional cuboid?

 It’s better to have a few interesting questions hanging around in our mind 😉

Let’s get back to 42 x 15.

So, 42 x 15 should look like this rectangle, right?

Me – Now that you know how multiplication looks like, let’s have a look at distribution.

How will ‘distributive property’ look like if we apply it in addition?

Student – Distributive property in addition?

Me – Do you remember the story of Target 10 in Addition ? How will you calculate 8 + 7 ?

Student – Yes! I can do 8 + 2 + 5.

Me – Great! That’s exactly how distributive property should be working in addition. So the idea behind distribution is to break the problem into smaller & simpler ones. Now, let’s implement it to simplify multiplication.

42 can be split into 40 & 2.

Area of big rectangle = Sum of Areas of small rectangles

42 x 15 = 40 x 15 + 2 x 15

42 can be split into 20, 20 & 2 as well.

Area of big rectangle = Sum of Areas of small rectangles.

42 x 15 = 20 x 15 + 20 x 15 + 2 x 15

Yes, it was that simple :). Enjoy the simplicity !

A simple example from real life

We use distributive property while counting money.




If I have to count 13 notes of $20, what is the simplest way to do so?





I believe that it will be simplest to break this counting into 10 &3.

10 notes of $20 = $200

3 notes of $20 = $60

13 notes of $20 = $200 + $60 = $260

And , this is nothing but distributive property.


Distributive property is about breaking down a big problem into smaller & simpler problems.

Breaking down a big problem into smaller ones helps in Maths and in life as well.

Making Maths Simple & Visual @ Maths2Art with Priya Asthana !

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