Skill: Multiply two 2-digit numbers using partial products

To multiply two 2-digit numbers using partial products, break each number into tens and ones. Then multiply every part of the first number by every part of the second number.

Example: Find $23 \times 45$.

Write each number in expanded form:

$$23=20+3 \qquad 45=40+5$$

Now multiply each pair of parts:

1. Tens times tens:

$$20 \times 40=800$$

2. Tens times ones:

$$20 \times 5=100$$

3. Ones times tens:

$$3 \times 40=120$$

4. Ones times ones:

$$3 \times 5=15$$

Add the four partial products:

$$800+100+120+15=1{,}035$$

Therefore,

$$\boxed{23 \times 45=1{,}035}$$

The four products show the contribution from each place-value part of the numbers. For example, $20 \times 40=800$ because $2$ tens times $4$ tens equals $8$ hundreds.