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Teacher Guide: Long Division

Master the step-by-step process of dividing large numbers using the long division method.

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All practice problems on paper, with a separate answer key.

Worksheet Answer key

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10 questions on Basic Operations. Students join with a name, you see everyone's score.

For Teachers

Learning Objectives
  • Execute the long division algorithm with single-digit divisors
  • Apply long division with two-digit divisors
  • Interpret remainders in division problems
  • Check division answers using multiplication
Prerequisites
  • • Mastery of multiplication facts through 12
  • • Understanding of basic division concepts
  • • Ability to subtract multi-digit numbers
Discussion Starters
  • 1. Why do we call it 'long' division? What's different about it?
  • 2. What real-life situations require you to divide large numbers?
  • 3. How can you check if your long division answer is correct?
  • 4. When might you need to round a remainder up versus down?
Common Misconceptions

The remainder must always be written as a separate number

Remediation: Show that remainders can be expressed different ways: R3, as a fraction 3divisor\frac{3}{\text{divisor}}, or as a decimal. The context determines which is best.

You always start with the first digit only

Remediation: Demonstrate problems where the divisor is larger than the first digit, requiring students to consider the first two digits together.

Differentiation Ideas

For Struggling Students:

  • • Use division mats with clear sections for each step
  • • Start with single-digit divisors and two-digit dividends
  • • Provide multiplication tables as a reference
  • • Use graph paper to keep digits aligned

For On-Level Students:

  • • Practice with two-digit divisors
  • • Solve word problems requiring interpretation of remainders
  • • Check answers using multiplication

For Advanced Students:

  • • Extend division to decimals
  • • Explore why the algorithm works mathematically
  • • Solve multi-step problems requiring division
Standards Alignment
  • 4.NBT.B.6 (CCSS.MATH.CONTENT.4.NBT.B.6)

    Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors

  • 5.NBT.B.6 (CCSS.MATH.CONTENT.5.NBT.B.6)

    Find whole-number quotients with up to four-digit dividends and two-digit divisors

Lesson Resources
  • visualLong Division Steps Chart

    Visual flowchart showing Divide, Multiply, Subtract, Bring Down

  • activityDivision Mat Practice

    Hands-on activity with step-by-step division sections

  • worksheetProgressive Division Practice

    Problems from 2-digit to 4-digit dividends

Lesson Content

Everything students see: definition, examples, common mistakes, applications. Tap to open.

Definition

Long division is a method for dividing large numbers step by step. It breaks a difficult division problem into a series of easier steps.
The four steps of long division are:
  1. 1.Divide - How many times does the divisor go into the current number?
  2. 2.Multiply - Multiply the divisor by your answer
  3. 3.Subtract - Subtract to find what remains
  4. 4.Bring down - Bring down the next digit
We write it like this:
quotientdivisor)dividend‾\begin{array}{r} \text{quotient} \\ \text{divisor}\overline{\smash{)}\text{dividend}} \end{array}
For example, 156÷12156 \div 12 means: "How many groups of 12 are in 156?"

Worked Examples

Calculate 96÷496 \div 4
1

Set up the problem

Write 4 outside and 96 inside the division bracket → 4)96‾4\overline{\smash{)}96}
2

Divide: How many 4s in 9?

9÷4=29 \div 4 = 2 (with remainder) → Write 2 above the 9
3

Multiply: 2×42 \times 4

2×4=82 \times 4 = 8 → Write 8 below the 9
4

Subtract: 9−89 - 8

9−8=19 - 8 = 1 → Write 1 below
5

Bring down the 6

Bring down the 6 next to the 1 → Now we have 16
6

Divide: How many 4s in 16?

16÷4=416 \div 4 = 4 exactly → Write 4 above the 6
7

Multiply and subtract

4×4=164 \times 4 = 16, then 16−16=016 - 16 = 0 → Remainder is 0

Common Mistakes

Forgetting to bring down the next digit

Why it's wrong: After subtracting, students sometimes try to divide the small remainder instead of bringing down the next digit.

Correct: Always bring down the next digit after subtracting. If you have 3 remaining and the next digit is 7, you now work with 37.

Using a quotient that's too large

Why it's wrong: Students guess a number that, when multiplied by the divisor, gives a result larger than what they're dividing into.

Correct: If your multiplication result is bigger than the number you're working with, try a smaller quotient. For example, if dividing 32 by 7, try 4 (not 5, because 7×5=35>327 \times 5 = 35 > 32).

Forgetting a 0 in the quotient

Why it's wrong: When the divisor does not fit into the number after bringing down a digit, students skip that place and go straight to the next digit.

Correct: If the divisor does not fit, write 0 in the quotient, then bring down the next digit. Example: 618÷6=103618 \div 6 = 103, not 1313, because 6 does not fit into 1.

Stopping too early with a remainder

Why it's wrong: Students get a non-zero remainder and think they're done, even though there are more digits to bring down.

Correct: Keep going until you've brought down every digit. Only then is the remaining number your final remainder.

Why It Matters

Long division is essential for:
  • Sharing equally: Splitting 156 stickers among 12 friends
  • Unit pricing: Finding the cost per item when you know the total
  • Cooking: Finding how many 250 g portions you can make from 3,000 g of pasta
  • Time management: Figuring out how many 15-minute segments fit into 2 hours
Even with calculators available, understanding long division helps you:
  • Estimate answers quickly
  • Check if calculator results make sense
  • Build mental math skills

Real World Applications

Splitting Items Equally

When you need to divide items among a group of people fairly.

Example:

A teacher has 156 pencils to distribute equally among 12 students. 156÷12=13156 \div 12 = 13 pencils per student.

1Try It Yourself

A scout troop collected 234 cans for recycling. They want to split them equally among 9 patrol groups.

How many cans does each patrol get?

Step 1: Write the mathematical expression

Divide: 234÷9234 \div 9

Calculating Unit Price

Finding how much one item costs when you know the total cost of multiple items.

Example:

A pack of 8 notebooks costs 24 dollars. Each notebook costs 24÷8=324 \div 8 = 3 dollars.

2Try It Yourself

A family bought a bulk pack of 15 juice boxes for 45 dollars total.

How much does each juice box cost?

Step 1: Write the mathematical expression

Divide the total by the number of items: 45÷1545 \div 15

Planning and Scheduling

Figuring out how to organize time or resources into equal parts.

Example:

A road trip is 420 kilometers. If you drive 60 kilometers per hour, the trip takes 420÷60=7420 \div 60 = 7 hours.

3Try It Yourself

A factory produces 1,296 items in an 8-hour shift.

How many items are produced per hour?

Step 1: Write the mathematical expression

Divide total items by hours: 1296÷81296 \div 8

Key Takeaways

  • 1Long division uses four repeating steps: Divide, Multiply, Subtract, Bring down
  • 2Always start with the leftmost digits of the dividend
  • 3If the divisor is bigger than the first digit, use the first two digits (or three, if needed)
  • 4Continue until every digit has been brought down; if the divisor does not fit, write 0 in the quotient
  • 5The final remainder (if any) is what's left after the last subtraction

Frequently Asked Questions

How do I know which number to try first?

Estimate! Ask yourself: 'How many times does the divisor fit into this number without going over?' If 12×3=3612 \times 3 = 36 and 12×4=4812 \times 4 = 48, and you're dividing into 46, use 3.

What if the divisor is bigger than the first digit?

Use more digits! If dividing 468 by 12, you can't fit 12 into 4, so look at 46 instead.

What do I do with the remainder?

It depends on the context. Sometimes you write it as 'R3', sometimes as a fraction (like 37\frac{3}{7}), and sometimes you round up or down based on the situation.

Glossary

Dividend
The number being divided (inside the division bracket)
Divisor
The number you divide by (outside the division bracket)
Quotient
The answer to a division problem (written above the bracket)
Remainder
The amount left over when division doesn't come out evenly

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