Skill: Multiply a 2-digit number by a 2-digit number

To multiply two 2-digit numbers, break them into tens and ones. Then multiply each part and add the partial products.

Example: Find $23 \times 14$.

Break apart the numbers:

$$23=20+3 \qquad \text{and} \qquad 14=10+4$$

Multiply each part:

$$\begin{aligned} 23\times14 &=(20+3)(10+4)\\ &=(20\times10)+(20\times4)+(3\times10)+(3\times4)\\ &=200+80+30+12\\ &=322 \end{aligned}$$

So,

$$23\times14=\boxed{322}$$

The standard algorithm shows the same place-value thinking:

   23
×  14
-----
   92   ← 23 × 4
  230   ← 23 × 10
-----
  322

The $3$ in $14$ means $3$ ones, so $23\times3=69$—but in this example, using $14\times23$, the rows shown calculate $23\times4=92$ and $23\times10=230$. Add the two partial products to get the final answer, $322$.