Video: Visualizing the Commutative Property of Addition and Multiplication

The two diagrams show 4 × 3 and 3 × 4 using an area model for multiplication. What can be said about the areas of the rectangles? What does it say about multiplication?

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Video Transcript

The two diagrams show four times three and three times four using an area model for multiplication. What can be said about the areas of the rectangles? What does it say about multiplication?

First, I wanna break up these rectangles into their area pieces. Now, we can see the square units of this four-by-three rectangle. We can do the same thing for the three-by-four rectangle. Remember that area is the number of square units inside this rectangle.

In our four-by-three rectangle, there are 12 square units. Four times three is 12. How many square units are then in our three-by-four rectangle? There are also 12 square units in the three-by-four rectangle. Three times four is also 12.

What can we say about the area of these rectangles? They are equal. What does it say about multiplication? That multiplication is commutative: four times three equals three times four.

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