Now both factors have two digits. The area model still works: split both numbers by place value, and the rectangle has four parts.
Key idea
For $23 \times 14$, split $23 = 20 + 3$ and $14 = 10 + 4$. Find all four partial products: tens × tens, tens × ones, ones × tens and ones × ones. Then add them.
Why it works
Each part of 23 must be multiplied by each part of 14, because the whole rectangle is $23$ by $14$. Cutting it both ways makes four rectangles. Leave one out and you lose part of the area.
Worked example: Four partial products
Find $23 \times 14$.
- $20 \times 10 = 200$
- $20 \times 4 = 80$
- $3 \times 10 = 30$
- $3 \times 4 = 12$
- Add: $200 + 80 + 30 + 12 = 322$.
Answer: $322$
Worked example: Bigger digits
Find $47 \times 36$.
- $40 \times 30 = 1{,}200$ and $40 \times 6 = 240$.
- $7 \times 30 = 210$ and $7 \times 6 = 42$.
- Add: $1{,}200 + 240 + 210 + 42 = 1{,}692$.
- Estimate: about $50 \times 35 = 1{,}750$. Close, so the answer is reasonable.
Answer: $1{,}692$
Common mistake
Multiplying only tens by tens and ones by ones: $2 \times 1 = 2$ and $3 \times 4 = 12$, written as "212". That skips two of the four parts. Check with an estimate: $23 \times 14$ is about $20 \times 15 = 300$, so 212 is too small.