Division is the operation people find hardest to do in their heads. The good news is that it is much easier when you stop thinking about “dividing” and treat it as multiplication in reverse, or break it into smaller steps.
Here are six methods you can use, with worked examples and a practice set at the end.
1. Think of Division as Multiplication
To work out 56 ÷ 7, ask “what times 7 equals 56?” The answer is 8, because 7 × 8 = 56.
This is why knowing your times tables matters so much. If you need to brush up, see our times tables chart and the guide to learning multiplication tables fast.
If a few facts keep tripping you up, see the hardest times tables and how to learn them.
2. Halve to Divide by 2, 4 and 8
Dividing by 2 means halving. Dividing by 4 means halving twice, and dividing by 8 means halving three times.
- 84 ÷ 4: half of 84 is 42, half of 42 is 21. The answer is 21.
- 96 ÷ 8: half is 48, then 24, then 12. The answer is 12.
- 150 ÷ 2: half of 150 is 75.
3. Double and Divide by 10 for 5
Dividing by 5 is the same as doubling the number and then dividing by 10.
- 65 ÷ 5: double 65 to get 130, then divide by 10 to get 13.
- 150 ÷ 5: double to get 300, divide by 10 to get 30.
- 85 ÷ 5: double to get 170, divide by 10 to get 17.
4. Chunking: Break the Number Into Easy Parts
Split the number into pieces that divide easily, divide each piece, and add the results.
- 78 ÷ 6: 60 ÷ 6 = 10 and 18 ÷ 6 = 3, so the answer is 13.
- 195 ÷ 15: 150 ÷ 15 = 10 and 45 ÷ 15 = 3, so the answer is 13.
- 112 ÷ 8: 80 ÷ 8 = 10 and 32 ÷ 8 = 4, so the answer is 14.
Chunking works because division spreads over addition. It is the most useful method for numbers that don’t have an obvious shortcut.
5. Use Divisibility Rules
Divisibility rules tell you quickly whether a number divides exactly, without doing the division.
- By 2: the last digit is even.
- By 3: the digits add up to a multiple of 3. 231 has digits 2 + 3 + 1 = 6, so 231 ÷ 3 works exactly (it is 77).
- By 5: the number ends in 0 or 5.
- By 9: the digits add up to a multiple of 9. 459 has digits 4 + 5 + 9 = 18, so 459 ÷ 9 works exactly (it is 51).
- By 10: the number ends in 0.
6. Handle Remainders
When a division doesn’t come out evenly, find the nearest multiple, then see what is left.
- 47 ÷ 5: 5 × 9 = 45, and 47 − 45 = 2. The answer is 9 remainder 2.
- 83 ÷ 9: 9 × 9 = 81, and 83 − 81 = 2. The answer is 9 remainder 2.
If you want a decimal, turn the remainder into a fraction of the divisor. 47 ÷ 5 is 9 and 2/5, which is 9.4.
Check Your Answer by Multiplying
The quickest check is to multiply back. For 168 ÷ 6 = 28, check 28 × 6 = 168. If it matches, you’re right.
Dividing Larger Numbers Step by Step
For bigger numbers, chunking is the most reliable method. Pick a friendly multiple of the divisor, subtract it, and repeat.
432 ÷ 12:
- 12 × 30 = 360, and 432 − 360 = 72.
- 12 × 6 = 72, so nothing is left.
- The answer is 30 + 6 = 36.
245 ÷ 7:
- 7 × 30 = 210, and 245 − 210 = 35.
- 7 × 5 = 35.
- The answer is 30 + 5 = 35.
Dividing by 25
Because 4 × 25 = 100, dividing by 25 is the same as multiplying by 4 and dividing by 100. For 350 ÷ 25, multiply 350 by 4 to get 1,400, then divide by 100 to get 14.
Division in Word Problems
Real questions often use words. Look for phrases such as “shared equally”, “per person” or “how many groups”.
- 84 apples are packed into 7 bags. How many in each bag? 84 ÷ 7 = 12.
- A 150 bill is split among 5 friends. 150 ÷ 5 = 30 each.
- How many 8-minute episodes fit into 96 minutes? 96 ÷ 8 = 12.
Common Mistakes
- Dividing in the wrong order. 12 ÷ 3 is 4, but 3 ÷ 12 is a quarter.
- Forgetting the remainder. If a question asks for a remainder, include it. 47 ÷ 5 is 9 remainder 2.
- Dropping a zero. Be careful with numbers like 1,200 ÷ 4. Divide 12 by 4 to get 3, then restore the two zeros to get 300.
- Chunking errors. Always check that the chunks add up to the original number.
Practice Problems
- 63 ÷ 7
- 132 ÷ 12
- 95 ÷ 5
- 112 ÷ 8
- 168 ÷ 6
- 52 ÷ 4
Answers: 9, 11, 19, 14, 28, 13
Hints: for 95 ÷ 5, double to 190 and divide by 10. For 168 ÷ 6, use chunks: 120 ÷ 6 = 20 and 48 ÷ 6 = 8.
For more drills, see mental math exercises for beginners.
Practice With PureMath
PureMath is a mental math trainer with short exercises in division as well as addition, subtraction and multiplication. You can train one operation at a time or mix them, and difficulty rises as you improve. Progress tracking shows your speed and accuracy over time.
Download PureMath on the App Store or try the mental math practice page.
Frequently Asked Questions
What is the easiest way to divide in your head?
Think of it as multiplication in reverse. For bigger numbers, split them into easy chunks and divide each one.
How do I divide by a two-digit number?
Chunk the number into multiples of the divisor. For 195 ÷ 15, use 150 + 45, which gives 10 + 3 = 13.
Why do I find division hard?
Division depends on fast recall of multiplication facts. Practice the tables first, and division gets much easier.
How do I know if a number divides exactly?
Use the divisibility rules above, such as checking whether the digits add up to a multiple of 3 or 9.
Final Thoughts
Division in your head comes down to a few habits: link it to multiplication, halve or double when the divisor allows it, and chunk everything else. Practice a little every day and it will stop feeling like the hard operation.