Why it works: the distributive law

Hello, and welcome to Myriora Maths! Seven times thirteen. You might not know it by heart. But there's a rule that makes it easy, and it's secretly behind almost every multiplication trick!

Here are seven rows of thirteen dots. Draw a line after the tenth dot in every row. Now there are two blocks: seven rows of ten, and seven rows of three.

Seven times ten is seventy. Seven times three is twenty-one. Seventy plus twenty-one is ninety-one. So seven times thirteen is ninety-one.

This is called the distributive law. When you multiply a number made of parts, multiply every part, then add. Seven times ten plus three, is seven times ten, plus seven times three.

It works with take away too. Seven times nineteen is seven times twenty, take away seven times one. A hundred and forty take away seven is a hundred and thirty-three.

You've already been using this law! The grid method multiplies every part by every part. Long multiplication does one row for each part. And the times eleven trick is times ten, plus times one.

Let's try one together. What is eight times fifteen? Split fifteen into ten and five. Say it out loud!

Eight times ten is eighty. Eight times five is forty. Eighty plus forty is a hundred and twenty!

Here's a question that catches lots of people. What is seven times ten plus three? Some people only multiply the first part: seventy plus three is seventy-three. But all seven rows have three more dots, not just one row! Multiply every part: seventy plus twenty-one is ninety-one.

Your turn! What is six times seventeen? Pick the right card. You've got fifteen seconds, or pause the video. Go!

Time's up! Seventeen is ten plus seven. Six times ten is sixty, and six times seven is forty-two. So add them. Sixty plus forty-two is a hundred and two!

Quick review. To multiply a number made of parts, multiply every part, then add. It works with take away too. And it's the reason the grid method, long multiplication and lots of tricks work. See you next time!