how to do long multiplication

Here’s a clear, student‑friendly guide on how to do long multiplication , with examples and mini sections to keep it easy to follow.

How to Do Long Multiplication

Long multiplication is a step‑by‑step way to multiply bigger numbers by lining them up in columns and adding the partial results.

Step‑by‑Step: Column Method

We’ll use the classic school method (numbers stacked on top of each other).

1. Set up the problem

Write the larger number on top, the other number under it.
Line up the digits by place value (ones, tens, hundreds, etc.).
Put a multiplication sign to the left and draw a line underneath.

Example: Multiply 64 × 32.

64
× 32
———

2. Multiply by the ones digit

Start with the rightmost digit of the bottom number (the ones digit).
Multiply this digit by each digit of the top number, moving from right to left.
If a product is 10 or more, write the ones digit and carry the tens.

For 64 × 32:

Bottom ones digit is 2.
Compute: 2 × 4 = 8 (write 8 in the first answer row, under the ones column).
Then: 2 × 6 = 12 (write 2, carry 1 to the next column).

First partial product row: 128.

64
× 32
———
128 ← 64 × 2

3. Multiply by the tens digit (add a zero)

Move to the next digit to the left in the bottom number (the tens digit).
Before you write this new row, add one zero at the end as a placeholder, because you’re now multiplying by tens, not ones.
Multiply this tens digit by each digit in the top number again, right to left, carrying when needed.

For 64 × 32:

Tens digit is 3 (which really means 30).
Put a zero at the end of the new row.
3 × 4 = 12 (write 2 above the zero, carry 1).
3 × 6 = 18, plus the carried 1 = 19.

Second partial product row: 1920.

64
× 32
———
128
1920 ← 64 × 30

4. Add the partial products

Draw another line underneath.
Add the partial products column by column, starting from the right.
Carry as you would in normal addition.

For 64 × 32:

128
+1920
———
2048

So 64 × 32 = 2048.

Another Example: 234 × 56

This example shows the same idea with slightly larger numbers.

Write the numbers in columns:

234
× 56
———

Multiply by the ones digit (6):
- 6 × 4 = 24 → write 4, carry 2.
- 6 × 3 = 18, plus 2 = 20 → write 0, carry 2.
- 6 × 2 = 12, plus 2 = 14 → write 14.
  First row: 1404.

Multiply by the tens digit (5, meaning 50):
- Write a zero at the end of the new row.
- 5 × 4 = 20 → write 0 (over that zero), carry 2.
- 5 × 3 = 15, plus 2 = 17 → write 7, carry 1.
- 5 × 2 = 10, plus 1 = 11.
  Second row: 11700.

Add:

1404
11700
———
13104

So 234 × 56 = 13104.

Horizontal / Break‑Apart Method

Some teachers show a “horizontal” style that breaks the second number into parts.

Example: 43 × 65

Write 65 in expanded form: 60 + 5.

Multiply 43 × 60:
- First do 43 × 6 = 258.
- Then add a zero: 2580.

Multiply 43 × 5 = 215.

Add the partial products: 2580 + 215 = 2795.

So 43 × 65 = 2795.

This method is the same idea as the column one: break into tens and ones, multiply each part, then add.

Common Mistakes and How to Avoid Them

Forgetting the zero placeholder when you move to the tens row. (Always add one zero for tens, two for hundreds, etc.)

Misaligning digits when you add the rows; keep everything in neat columns.

Forgetting to carry or to add the carried digit to the next multiplication or addition.

A quick trick: after you finish, roughly estimate the answer (for example, 64 × 32 is close to 60 × 30 = 1800) to see if your result is in the right range.

Mini FAQ View

Do I always start on the right?
Yes, always start with the rightmost digit of the bottom number (ones place).

What if there are more digits (like 3‑digit × 3‑digit)?
You just get more partial rows: one for ones, one for tens, one for hundreds, each shifted one extra place to the left.

Is long multiplication still useful with calculators around?
Yes. It helps you understand place value and check calculator work, and it shows up in exams and schoolwork.

Quick HTML Table of the Key Steps

html

<table>
  <tr>
    <th>Step</th>
    <th>What You Do</th>
    <th>Why It Matters</th>
  </tr>
  <tr>
    <td>1. Line up</td>
    <td>Write numbers in a vertical column, digits aligned by place value.</td>
    <td>Prevents place value mistakes.</td>
  </tr>
  <tr>
    <td>2. Multiply ones</td>
    <td>Multiply top number by bottom ones digit; write first partial product.</td>
    <td>Gives product for the ones part of the multiplier.</td>
  </tr>
  <tr>
    <td>3. Multiply tens</td>
    <td>Add a zero, multiply by tens digit, write the second partial product.</td>
    <td>Accounts for multiplying by tens, hundreds, etc.</td>
  </tr>
  <tr>
    <td>4. Add partials</td>
    <td>Add all rows to get the final answer.</td>
    <td>Combines all parts into one product.</td>
  </tr>
</table>

TL;DR Summary

Stack the numbers in columns.
Multiply by each digit of the bottom number, starting from the right, and write a new row each time.
Shift each new row one place left (add zeros).
Add all rows to get the final product.

Information gathered from public forums or data available on the internet and portrayed here.

how to do long multiplication