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.

Step-by-step approach

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

Example: $1,248\cdot 6$

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

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:

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

Related articles

• 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.