Concept 6 of 10
Long Division: When Short Division Runs Out
Today's big idea
Long division writes down the subtraction that short division kept in your head.
23 into 87 goes 3 times, leaving 18. Bring the 4 down and 23 into 184 goes 8.
How it works
👀 What's going on?
Short division works because you can hold 'how many 6s in 43' in your head. Ask how many 23s are in 179 and the head-work stops. Long division is the same method with the subtractions written down instead of remembered.
💡 Here's the trick
Look at the worked sum above. You are sharing 874 into groups of 23. Start with 87 tens. Three 23s make 69, which fits, and four would make 92, which is too big. So the 3 goes above the 7, and you write 69 under 87 and subtract to leave 18. Bring down the 4 to make 184. Now 23 times 8 is exactly 184, so the 8 goes on top and nothing is left. The answer is 38. Every step is a small multiplication you can check, and the subtraction on the page is what short division was doing invisibly.
🪄 How to do it
- 1.Ask how many times the divisor fits into the front digits, as the sum above does with 23 into 87.
- 2.Write that digit on top, multiply it by the divisor, and subtract.
- 3.Bring the next digit down and repeat until none are left.
✍️ Try it
Work out 552 divided by 24. Start by asking how many 24s fit into 55.
Two 24s make 48, and three would make 72, which is too big. So write 2, subtract 48 from 55 and 7 is left. Bring down the 2 to make 72, and 24 times 3 is exactly 72. The answer is 23.
⚠️ Watch out
You might be thinking you should pick the biggest digit that looks close. Try 4 for 23 into 87 and you get 92, which is larger than 87, so there is nothing to subtract. If your subtraction would go negative, the digit on top is one too big.
🌟 Why this matters
Splitting a 874 rupee bill between 23 people needs exactly this. So does working out how many full boxes of 24 a delivery of 552 fills. Writing the steps down means you can find your slip instead of starting again.
Exam tip: Multiply your answer back by the divisor and you have checked the whole thing in one move.
See it in action
⚡ Time to play!
THE PROBLEM
874 ÷ 23
?answer
23 ) 874
How many 23s fit inside the first two digits, 87?
Quick check
✅ VERIFICATION
Dividing 966 by 23, how many 23s fit into the first two digits, 96?
⚡ Finish the activity above first to answer.
Keep going!
Up next: The Leftover Rule
What do you do with the leftovers?