Multiply a single digit number by a four digit number using an area model

Multiplying a single digit number by a $4$4 digit number for area is a tricky task. One strategy we can use is to break it up into $4$4 separate multiplications and then add them all together.

When we multiply area, we multiply one side by another side. We've already looked at how to do this with a three digit number. Now let's look at how to do it with a four digit number.

We can break a four digit number up into $4$4 separate values and multiply it by each. For example, to find the area of the rectangle below, we can break the $4$4 digit number up into $4000+300+50+1$4000+300+50+1 which is the same as $4351$4351, then multiply each value by $2$2.



Then we can add all the answers together.

The video below will show you with an demonstration on how to do just that.

Worked Examples

Question 1