Area Models for Decimal Multiplication | CK-12 Foundation - Free Printable

Looking at the image, we see a grid divided into sections with different colors. The labels on the left and top indicate:

- Left side: “2.8 or 280 hundredths” — this is the height of the green and blue sections combined.
- Top: “3.5 or 350 hundredths” — this is the width of the orange and yellow sections combined.

The entire colored rectangle (orange + yellow + green + blue) represents a multiplication of these two numbers: 2.8 × 3.5.

Let’s break it down using the grid:

Each big square in the grid is 1 unit by 1 unit, and each small square inside is 0.01 (one hundredth).

The orange section covers 3 full columns (each 1 unit wide) and 2 full rows (each 1 unit tall), so that’s 3 × 2 = 6 square units → 600 hundredths.

But wait — actually, looking more carefully:

The orange area spans 3 full vertical blocks (each 1 unit wide) and 2 full horizontal blocks (each 1 unit tall) — but also includes part of the third row? No — let’s reorient.

Actually, the grid is set up as a multiplication model:

- The horizontal axis goes from 0 to 3.5 (so 3 full units plus 0.5)
- The vertical axis goes from 0 to 2.8 (so 2 full units plus 0.8)

So the total area represented is 3.5 × 2.8.

We can compute this directly:

3.5 × 2.8

Break it down:

3.5 × 2 = 7.0
3.5 × 0.8 = 2.8
Add them: 7.0 + 2.8 = 9.8

Alternatively, convert to hundredths:

3.5 = 350 hundredths
2.8 = 280 hundredths
Multiply: 350 × 280 = ?

350 × 280 = 350 × (200 + 80) = 350×200 + 350×80 = 70,000 + 28,000 = 98,000 hundredths

Now convert back: 98,000 hundredths = 98,000 ÷ 100 = 980? Wait — no!

Wait — mistake here.

If you multiply two numbers in hundredths, you get ten-thousandths.

Because: (a/100) × (b/100) = (a×b)/10,000

So 350 hundredths × 280 hundredths = (350 × 280) / 10,000

350 × 280:

350 × 200 = 70,000
350 × 80 = 28,000
Total = 98,000

Then divide by 10,000: 98,000 ÷ 10,000 = 9.8

Yes — so the product is 9.8.

Looking at the grid, the total colored area should represent 9.8 square units.

We can verify by adding the parts:

- Orange: 3 units wide × 2 units high = 6.0
- Yellow: 0.5 units wide × 2 units high = 1.0
- Green: 3 units wide × 0.8 units high = 2.4
- Blue: 0.5 units wide × 0.8 units high = 0.4

Add them: 6.0 + 1.0 + 2.4 + 0.4 = 9.8

Perfect.

So the value represented by the entire colored region is 9.8.

Final Answer:
9.8