Multi-Digit Multiplication

Multiplying by One Digit

When you multiply a multi-digit number by a single digit, work from right to left and remember to carry!

Example: $23 \times 4$

$23 \times 4 = 92$

Steps:

1. Multiply ones: $3 \times 4 = 12$ (write 2, carry 1)
2. Multiply tens: $2 \times 4 = 8$, plus carried $1 = 9$
3. Result: $92$

Try it: Cover the answer above and work through each step yourself!

Multiplying by Two Digits

When multiplying by a two-digit number, you create partial products and then add them.

Example: $25 \times 13$

$25 \times 13 = 325$

Steps:

1. Multiply by the ones digit: $25 \times 3 = 75$
2. Multiply by the tens digit: $25 \times 1 = 25$ (shifted one place left → $250$)
3. Add the partial products: $75 + 250 = 325$

Key idea: When you multiply by the tens digit, the result shifts one place to the left (which is the same as multiplying by 10).

The Standard Algorithm

Here's the step-by-step process for any multiplication:

1. Start from the right — always begin with the ones place
2. Carry when needed — if a product is 10 or more, write the ones digit and carry the tens digit
3. Shift for place value — when multiplying by tens, shift one place left; by hundreds, shift two places
4. Add all partial products — sum up all the rows to get your final answer

Another example: $34 \times 26$

| Step | Calculation | Result | |------|------------|--------| | Multiply by 6 (ones) | $34 \times 6$ | $204$ | | Multiply by 2 (tens) | $34 \times 20$ | $680$ | | Add partial products | $204 + 680$ | $884$ |

So $34 \times 26 = 884$.

Tips to Remember

• Line up your numbers carefully — keep digits in the correct columns
• Remember to shift — when multiplying by the tens place, shift one position left
• Check your work — use estimation to see if your answer makes sense (e.g., $34 \times 26 \approx 30 \times 25 = 750$, so $884$ is reasonable)
• Practice carrying — regrouping is essential for accuracy!

Real-World Applications

Multiplication helps us solve everyday problems:

• Shopping: If one toy costs \24$ and you buy 3 toys, how much total?

  • $24 \times 3 = 72$, so \72$

• Area: A rectangle is 18 feet long and 12 feet wide. What's the area?

  • $18 \times 12 = 216$ square feet

• Groups: If each class has 28 students and there are 4 classes, how many students total?

  • $28 \times 4 = 112$ students