Final answer:
The correct way to label an area model for 21×23 is Option 3, which breaks down the multiplication into partial products of the tens and ones components of the numbers (20×20, 1×20, 3×20, and 3×1) and then adds them together.
Step-by-step explanation:
The correct way to label an area model for 21×23 is by decomposing both numbers into their tens and ones components and then using these to form the parts of the model. The best option is the one that correctly represents this decomposition and the corresponding areas for each part of the model.
Option 3:
20×20 and
1×20+
3×20+
3×1 is the correct way to decompose 21 and 23 into tens and ones and then calculate their product using an area model. This option correctly represents the partial products of 21 (20 + 1) and 23 (20 + 3), which are then added together to find the total area.
Here's how you break it down:
20×20 = 400 (calculating the area for the tens)
20×3 = 60 (calculating the area for the tens of one number and the ones of the other)
1×20 = 20 (calculating the area for the ones of one number and the tens of the other)
1×3 = 3 (calculating the area for the ones)
You would then combine these partial products to get the total:
400
+ 60
+ 20
+ 3
Which gives us the final product of: 21×23 = 483