Long Division
Master the step-by-step process of dividing large numbers using the long division method.
Definition
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Worked Examples
Calculate
Set up the problem
Write 4 outside and 96 inside the division bracket →
Divide: How many 4s in 9?
(with remainder) → Write 2 above the 9
Multiply:
→ Write 8 below the 9
Subtract:
→ Write 1 below
Bring down the 6
Bring down the 6 next to the 1 → Now we have 16
Divide: How many 4s in 16?
exactly → Write 4 above the 6
Multiply and subtract
, then → Remainder is 0
Answer:
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 ).
Placing digits in the wrong position in the quotient
Why it's wrong: Students write the quotient digits without aligning them properly above the correct digits of the dividend.
Correct: Each digit in the quotient should be written directly above the last digit you brought down.
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.
Interactive Sandbox
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Practice Problems
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Why It Matters
- Sharing equally: Splitting 156 stickers among 12 friends
- Unit pricing: Finding the cost per item when you know the total
- Cooking: Dividing a recipe that serves 24 people into 6 portions
- Time management: Figuring out how many 15-minute segments fit into 2 hours
- 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. pencils per student.
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, and how many are left over?
Step 1: Write the mathematical expression
Divide:
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 dollars.
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:
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 hours.
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:
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 doesn't fit into the first digit, use the first two digits
- 4Continue until all digits have been brought down
- 5The final remainder (if any) is what's left after the last subtraction
Frequently Asked Questions
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