---
title: "Long multiplication"
description: "Multiply a whole number of up to four digits by a one-digit number, and multiply two two-digit numbers, using formal written methods including long multiplication; illustrate with area models"
canonical: https://lightmysky.com/learn/mathematics/long-multiplication-mt_q9EaJc2FP8
source: https://lightmysky.com/learn/mathematics/long-multiplication-mt_q9EaJc2FP8.md
retrieved: 2026-10-19
---

> **Agent view.** This is the Markdown twin of the page, for tools and assistants.
> When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md
> API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md
> Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt
> Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json
> Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`.

# Long multiplication

Multiply a whole number of up to four digits by a one-digit number, and multiply two two-digit numbers, using formal written methods including long multiplication; illustrate with area models

Subject: Mathematics · Area: Multiplication & Division · Ages 9 to 10
Page: https://lightmysky.com/learn/mathematics/long-multiplication-mt_q9EaJc2FP8

## Ready when they can

- Calculate 2,347 × 6 using formal written layout
- Calculate 34 × 27 using long multiplication
- Draw an area model for 45 × 23 and connect to the written method

## Lesson: Long multiplication

You already know how to multiply and how to split a rectangle into an area model. Now you'll use both ideas to multiply bigger numbers: a four-digit number by a one-digit number, and two two-digit numbers, all set out neatly in columns.

**Example.** Line up 2,347 above 6, ones under ones. Multiply the ones: 6 x 7 = 42. Write 2, carry 4. Multiply the tens: 6 x 4 = 24, plus the carried 4 makes 28. Write 8, carry 2. Multiply the hundreds: 6 x 3 = 18, plus 2 makes 20. Write 0, carry 2. Multiply the thousands: 6 x 2 = 12, plus 2 makes 14. Write 14. Reading the digits together gives 14,082.

**Example.** Now try two two-digit numbers: 34 x 27. First multiply 34 by the ones digit of 27, which is 7: 34 x 7 = 238. Write that row down. Next multiply 34 by the tens digit of 27, which is really 20. Write a placeholder 0, then work out 34 x 2 = 68, giving 680. Add the two rows: 238 + 680 = 918.

*(drawing: This is the same area model idea you already know: rows and columns make rectangles. Long multiplication uses that same splitting idea, just with bigger numbers broken into tens and ones.)*

**Tip.** Keep your digits lined up in neat columns, ones under ones and tens under tens. That placeholder zero is easy to forget, so write it in before you multiply by the tens digit.

**Recap.** Long multiplication multiplies each part of the numbers in careful columns, using placeholder zeros and the same splitting idea as an area model, then adds the parts together.

## Practice

17 questions on this page, each with its working shown.

## Needs first

- [Written Multiplication](https://lightmysky.com/learn/mathematics/written-multiplication-mt_18fK9sQdIz)
- [Area and the distributive property](https://lightmysky.com/learn/mathematics/area-and-the-distributive-property-mt_AQo4u7O4sM)
- [Multiplying by Tens](https://lightmysky.com/learn/mathematics/multiplying-by-tens-mt_isojCL9yy-)

## Opens up

- [Moving between bar models, number lines and equations](https://lightmysky.com/learn/mathematics/moving-between-bar-models-number-lines-and-equations-mt_CUmjcE7W6c)
- [Multi-step word problems with remainders](https://lightmysky.com/learn/mathematics/multi-step-word-problems-with-remainders-mt_p-nbe0w_lf)
- [Long multiplication (age 10+)](https://lightmysky.com/learn/mathematics/long-multiplication-age-10-mt_XLP1IM3Qbb)