Long division, step by step
Divide 4-digit numbers by a 2-digit number with the four steps and a clever estimate. Read one step, play with it, then tap “I understand this”.
The parts of a long division sum
Long division is a neat way to share a big number into equal groups, one digit at a time.
We read it as “744 divided by 3 is 248”, and we can also write it as 744 ÷ 3 = 248.
The four steps
Every round of long division uses the same four steps, in the same order. Then you start again with the next digit.
Remember the order with Dad, Mom, Sister, Brother: Divide, Multiply, Subtract, Bring down.
After you subtract, the number left must be smaller than the divisor. If it is not, your top number was too small.
Think of R744 shared by 3 children. First you hand out the R100 notes, then the R10 notes, then the R1 coins. If a R100 note is left, you swap it for ten R10 notes and share again. That is exactly what “bring down” does.
Watch a sum being worked out
Show me how
Pick a sum and tap “Next step”. Each step is written on the board and explained.
Your turn
The board asks one step at a time. Type with the number buttons, or tap the digit you bring down.
Long division practice
Choose a level. You get a new sum every time.
Sums finished: 0
Remainders and checking your answer
Sometimes the number does not share out exactly. The bit left over at the end is the remainder. We write it with an r: 593 ÷ 4 = 148 r 1.
The remainder must always be smaller than the divisor. When you divide by 4, the remainder can only be 0, 1, 2 or 3.
Check by multiplying back
Division and multiplication are opposites. Multiply the answer by the divisor, then add the remainder. You must get the number you started with.
148 × 4 = 592, and 592 + 1 = 593. Correct!
The checking machine
Change the sum with the buttons. The machine divides, then multiplies back to check.
If you divide by 4 and there are still 4 or more left, every group can get one more. Then you have not finished sharing. Only what is too little for a whole round stays as the remainder.
Two traps to watch for
In 618 ÷ 3, after the 6 you bring down the 1. 3 does not fit into 1, so you write 0 on top. Never skip it, or 206 becomes 26. Watch it happen: pick 618 ÷ 3 in “Show me how”.
In 256 ÷ 7, 7 does not fit into 2. Use the first two digits, 25, and write your first answer digit above the 5.
Always check back: multiply your answer by the divisor and add the remainder. If you get the dividend, you are right.
The 0 says: there were no tens to share out. It holds the tens place open, just like in place value. Without the 0 the digits slide over and 206 becomes 26.
Dividing by a 2-digit number: estimate first
How many times does 24 fit into 86? Round the divisor to the nearest 10: 24 is about 20, and 20 fits 4 times into 86. Try 4: 4 × 24 = 96, too much. Try 3: 3 × 24 = 72. Right!
Estimate with the rounded divisor, then check by multiplying. Too much? One less. More than the divisor left over? One more.
Write the first few multiples of the divisor first (24, 48, 72, 96 …). Then you can just look it up. The “Show the times table” button on the practice board does this for you.
Check yourself
- Divide, Multiply, Subtract, Bring down: the same every round.
- Start on the left with the biggest place, like handing out the R100 notes first.
- The remainder is always smaller than the divisor.
- Doesn’t fit? Write 0 on top and bring down the next digit.
- Check: answer × divisor + remainder = dividend.
Write these points in your maths book. Read them again the night before the test.
Quick questions
Tap an answer. If you get one wrong, read why and go back to that step. You get new questions every time.
You ticked all 7 steps! Now you are ready for the quiz.- Practice sheet for this classQuestions + memo · 3 A4 pagesPractice sheet
- Numbers16 pages · PDFPaperMemo
Ready for more? The Grade 6 division quiz gives you new sums every time.
- One step a day is enough. Ten calm minutes work better than an hour the night before the test.
- Long division stands on times tables. Let your child write out the divisor’s times table first; the “Show the times table” button does the same.
- Let them multiply every answer back. It teaches that division and multiplication belong together, and they catch their own mistakes.
- Ask your child to tell you the rule in their own words. If they can explain it, they understand it.
- The ticks (“I understand this”) are saved on this device only. We never ask for names or emails.
Follows CAPS for Grade 6 Maths. Always check your teacher’s notes and textbook too.