Solve larger exact divisions by splitting them into easy parts
Turn one difficult division into two smaller calculations you can solve in your head.
This lesson starts with divisions that have no remainder. Multiply the divisor by an easy number such as 10, 20, or 30. When that result is close to the number you need to divide, subtract it, divide the smaller amount that remains, and combine the two answers.
Get close with an easy multiplication first
For 156 ÷ 12, start with 12 × 10. That reaches 120 and leaves only 36 to solve.
- 1Start with 1012 × 10 = 120
- 2Find what remains156 − 120 = 36
- 3Divide the remainder36 ÷ 12 = 3
- 4Combine the groups10 + 3 = 13
How to choose your starting number
Try 10 groups first. If the number is much larger, try 20 or 30 groups. Choose an easy multiplication that gets close without going past the number you are dividing.
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Multiply by 10, 20, or 30
12 × 10 = 120
For 156 ÷ 12, ten groups of 12 account for 120. You now know the first 10 groups.
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Subtract to find the remainder
156 − 120 = 36
The difference tells you exactly how much is still left to divide.
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Divide the smaller remainder
36 ÷ 12 = 3
The remaining division is small enough to recognize: 12 × 3 = 36. Add those 3 groups to the first 10.
How to solve 84 ÷ 7
Split 84 into 70 and 14 because both numbers are easy to divide by 7.
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Divide the first part
70 ÷ 7 = 10
Seventy contains ten groups of seven.
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Divide the second part
14 ÷ 7 = 2
Fourteen contains two more groups of seven.
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Add the two answers
10 + 2 = 12
There are twelve groups in total, so 84 ÷ 7 = 12.
Pick parts that fit the calculation
There is more than one useful split. Look for a large multiple you know, then divide the smaller remainder.
96 ÷ 8
80 ÷ 8 = 10 and 16 ÷ 8 = 2
10 + 2 = 12132 ÷ 11
110 ÷ 11 = 10 and 22 ÷ 11 = 2
10 + 2 = 12144 ÷ 12
120 ÷ 12 = 10 and 24 ÷ 12 = 2
10 + 2 = 12Now try 91 ÷ 7
91 ÷ 7 = ?
Try splitting 91 into 70 and 21.
Show the answer Hide the answer
70 ÷ 7 = 10 and 21 ÷ 7 = 3. Combine the answers: 10 + 3 = 13.
When splitting is especially useful
Use this strategy when the full division feels too large, but you can see smaller multiples of the divisor inside it.
The answer is larger than your times table
You may not recall 13 × 12 immediately, but you can build it from 10 × 12 and 3 × 12.
You want to calculate without paper
Each small result is easy to remember while you solve the next part.
A different split feels easier
For 96 ÷ 8, both 80 + 16 and 48 + 48 work. Choose the route that is clearest to you.
Build the facts that make splitting fast
Practise a divisor until its familiar multiples are easy to spot. Then use those multiples as building blocks for larger divisions.
Questions about splitting division into parts
How do I choose the first part?
Start with ten groups of the divisor when that fits. For division by 12, ten groups make 120. For division by 7, ten groups make 70. Then look at what remains.
Do I have to split the number in the same way?
No. The useful split is the one that gives you parts you can divide confidently. Different routes can reach the same answer.
What if the number does not divide evenly?
Use friendly chunks to find all the complete groups, then identify what remains. This lesson begins with exact divisions so you can focus on the splitting strategy.