Multiplication Using The Standard Algorithm

The final result when you multiply.

4 thousands, 7 hundreds, 8 tens, and 2 ones.

90 × 30 = 2,700.

I can draw a model with four sections. On the top, I put 80 and 7. On the left, I put 30 and 1. The four sections represent the four partial products.
80 × 30 = 2,400, 7 × 30 = 210, 80 × 1 = 80, 7 × 1 = 7. 2,400 + 210 + 80 + 7 = 2,697.

Yes, my estimate was very close. It is important because it lets us know approximately what number to expect, and if we make a mistake in our calculations, we know that we need to go back and fix it.

Both help us in different ways. The area model helps us to understand what we are multiplying and to visualize the result. The algorithm is faster and can help us multiply large numbers more quickly, but we should only use it if we understand what it represents.

Sometimes when we use the multiplication algorithm, we end up with two or more partial products. These are part of the answer, and need to be added together to get the final product.

Multiplying 7 × 2 is 7 × 2 ones, multiplying 7 × 5 is 7 × 5 tens, multiplying 7 × 3 is 7 × 3 hundreds.

The 5 goes under the ones place and the 6 is written above the tens place, to be added to the product after multiplying by 8 × 1.

He forgot to write a 0 on the ones place of the second partial product. We need to put 0 in the ones place because there are 0 ones in the partial product. He also forgot to add the partial products together to get the final product.