Column multiplication up to 10,000

This is the capstone of the whole topic. We bring together the basic times-tables, work with round numbers, and the column layout you already know from addition and subtraction up to 10,000.

What the layout looks like

Write the multi-digit number on top, place the one-digit multiplier right-aligned below it, and draw a line. Put the result below the line.

1 2 4 8
×     6

Step-by-step approach

Work from right to left, exactly the same way as written addition.

Example: $1, 248 \cdot 6$

Ones: $8 \cdot 6 = 48$ . Write down 8, carry 4.
Tens: $4 \cdot 6 = 24$ , plus the carry $4$ = $28$ . Write 8, carry 2.
Hundreds: $2 \cdot 6 = 12$ , plus the carry $2$ = $14$ . Write 4, carry 1.
Thousands: $1 \cdot 6 = 6$ , plus the carry $1$ = $7$ . Write 7.

Result: 7,488.

The carry rule

When the product in a column is greater than 9, you need to carry:

Write down the last digit of the product.
Carry the remaining digits (the tens) to the next column and add them in after the next multiplication.

For example $9 \cdot 7 = 63$ → write 3, carry 6.

Connection to round numbers

Column multiplication is really just a shorthand for what you learned with round numbers:

1, 248 \cdot 6 = 1, 000 \cdot 6 + 200 \cdot 6 + 40 \cdot 6 + 8 \cdot 6

= 6, 000 + 1, 200 + 240 + 48 = 7, 488

The column algorithm computes this automatically, column by column.

Self-check questions

Where does the one-digit multiplier go? All the way to the right, under the ones of the top number.
How do I know I carried correctly? Check that an estimated answer roughly matches. $1, 248 \cdot 6$ is about $1, 200 \cdot 6 = 7, 200$ , so 7,488 looks right.
What if the answer is larger than 9,999? It won't happen in our exercises — the generator always picks problems with results under 10,000. In school you may run into bigger answers; the method is the same, you just add one more digit on the left.

Watch out for

Alignment. Put the one-digit multiplier under the ones, not under the thousands.
Don't skip the carry. It's easy to forget when you multiply quickly.
Read from right to left. Left-to-right only works for mental addition; not here.

Practice

👉 Exercise: Column multiplication up to 10,000

Guide to multiplication by a one-digit number — topic overview.
Multiplying a round number by the same digit — the easiest building block.
Multiplying a round number — dealing with zeros for any digit.
Addition and subtraction up to 10,000 — the same column-based layout.