How to Do Long Division: Complete Step-by-Step Guide

Long division is a foundational arithmetic technique that allows you to break down complex division problems involving multi-digit numbers. While the process may appear intimidating at first, it follows a logical five-step sequence that, once understood, makes dividing large numbers straightforward.

This guide walks through the complete method used in UK classrooms, covering everything from basic two-digit divisors to decimal answers you might encounter in Year 6. The approach taught here aligns with Key Stage 2 and Key Stage 3 curriculum expectations, giving learners a consistent technique they can rely on throughout their mathematical education.

Whether you are a parent supporting a child with homework, a student revisiting the method, or a teacher seeking a clear reference, the following sections provide worked examples and practical tips to build confidence with long division.

How to Do Long Division with 2 Digits

When a divisor has two digits, mental estimation often falls short. Long division provides a systematic way to find the quotient by processing the dividend in stages. The method works equally well whether you are dividing a three-digit number by a two-digit divisor or handling much larger numbers.

The Five-Step Process

The standard method in UK primary schools follows a memorable sequence often taught using the initial letters DMSBR:

• The DMSBR sequence repeats until every digit of the dividend has been processed
• A remainder occurs when the final subtraction does not reach zero
• Writing the multiplication table of your divisor in the margin helps maintain accuracy
• Always check your answer by multiplying the quotient by the divisor and adding any remainder
• When the first digit of the dividend is smaller than the divisor, include an additional digit to get started
• Practice with smaller two-digit by one-digit problems before progressing to two-digit by two-digit
• Remainders can be expressed as fractions or decimals depending on the question requirements

Worked Example: 7397 ÷ 13

This example demonstrates each stage of the process clearly. Setting out the calculation with the divisor outside the division bracket and the dividend underneath helps keep columns aligned.

The answer reads from top to bottom: 569. You can verify this result by calculating 569 × 13, which equals 7397 exactly.

Additional Practice Problems

How to Do Long Division for Kids

Children typically encounter long division during Key Stage 2, usually in Years 5 and 6 when they are aged between 9 and 11. At this stage, learners have already mastered basic times tables and short division, making the written method a natural next step for more challenging calculations.

Building from Short Division

Short division works well when dividing by a single-digit number, but the process needs adaptation for larger divisors. The key difference lies in chunk size: instead of processing one digit at a time, long division allows you to take bigger chunks when the divisor exceeds nine.

According to guidance from Third Space Learning, the written method becomes necessary when the divisor has two or more digits, as most children cannot perform these calculations entirely in their heads.

Keeping Children Engaged

The repetitive nature of DMSBR can feel tedious, so educators often use games and timed challenges to maintain motivation. Writing the divisor’s multiplication table in the margin before starting gives children a reference point that reduces cognitive load and helps them work more independently.

Parents supporting at home can start with problems where the divisor fits neatly into the first chunk, avoiding remainders in early attempts. Once the pattern becomes familiar, introducing problems with remainders adds the next layer of complexity.

UK Curriculum Expectations

The national curriculum for England specifies that by the end of Key Stage 2, pupils should use written division methods in cases where the answer has up to two decimal places. This means the technique taught in primary school directly prepares learners for Key Stage 3 mathematics and beyond.

BBC Bitesize provides practice resources aligned with this curriculum, making it straightforward to find age-appropriate exercises.

How to Do Long Division with Decimals

Extending long division to handle decimal answers follows the same DMSBR sequence, with one important addition: when you reach the decimal point in the dividend, you place a decimal point in the quotient at exactly the same position.

Adding Decimal Places

If the dividend does not divide exactly, you can continue the process by adding zeros after the decimal point. Each zero brought down effectively extends the accuracy of your answer by one decimal place.

For example, when dividing 10.4 by 13, you would first establish 10.4 as your dividend, then continue bringing down zeros beyond the decimal point until you reach a satisfactory level of precision or the remainder becomes zero.

Two Decimal Places Standard

The UK curriculum expectation at Year 6 level is that pupils should handle answers up to two decimal places. This means most classroom exercises and assessments will require either an exact decimal answer or rounding to the nearest hundredth.

Resources from Twinkl include worksheets specifically designed for this skill, with problems gradually increasing in difficulty.

Checking Decimal Answers

The verification process for decimal division works identically to whole number division: multiply the quotient by the divisor. If the result matches your original dividend, your answer is correct. Any small discrepancy usually indicates a rounding choice or minor calculation error that can be identified and corrected.

What the Long Division Method Covers and What It Does Not

While the DMSBR method remains consistent across these variations, the standard school curriculum focuses primarily on numerical examples rather than algebraic expressions. Parents and teachers seeking to introduce algebraic long division would need to move into secondary-level mathematics resources.

When Long Division Fits Into the Maths Curriculum

Long division typically appears in the UK mathematics curriculum during Key Stage 2, building on earlier work with multiplication and division facts. The progression usually follows a clear path from concrete manipulatives to mental methods, then on to short division, and finally written long division.

At primary level, the technique prepares pupils for the quantitative reasoning required in secondary mathematics, science, and everyday problem-solving. The same written method continues to serve students through GCSE preparation, where questions involving division frequently appear in examination papers.

For those reviewing past examination questions, resources such as Edexcel Maths Past Papers: GCSE IGCSE Foundation PDF provide practice opportunities that include division problems within broader mathematical contexts.

What Educators Say About Teaching Long Division

Long division often causes anxiety among learners because it involves multiple simultaneous considerations. Breaking the process into discrete steps that can be mastered independently helps reduce this cognitive burden and builds genuine understanding rather than rote memorisation.

— Third Space Learning educational guidance

The key insight for teachers is that the method itself is not the end goal. We want pupils to recognise when written division is appropriate, to execute it accurately, and to verify their results independently. Each of these skills develops through deliberate practice with varied examples.

— MathsIsFun educational approach

Educational platforms consistently emphasise that the DMSBR mnemonic serves as a memory aid rather than a substitute for understanding. When children grasp why each step exists—why we subtract to find remainders, why we bring down digits to build new numbers—the method becomes meaningful rather than arbitrary.

Getting Started with Long Division Practice

Mastering long division requires consistent practice with problems of increasing difficulty. Begin with straightforward examples where the divisor fits neatly into the first chunk, then progress to problems involving remainders, and finally tackle decimal answers once the basic sequence feels automatic.

The investment in learning this method pays dividends throughout a student’s mathematical education, from handling everyday calculations to succeeding in formal examinations.

For additional context on measurement standards referenced in UK education, What Size is A4 in cm? Dimensions in mm, Inches & Comparisons provides useful background information on standard paper sizes that frequently appear in school resources.

Frequently Asked Questions