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subtraction

Two-digit subtraction mentally

Partition numbers or count up to solve mentally.

Quick answer

You can subtract two-digit numbers mentally by splitting the numbers into tens and ones, or by counting up from the smaller number to the larger one.

Learning outcome

By the end of this page, you will be able to subtract two-digit numbers in your head using partitioning or counting up strategies. Success signs:
  • You can split a two-digit number into tens and ones
  • You can subtract tens from tens and ones from ones
  • You can count up from a smaller number to a larger number
  • You can solve subtraction problems without writing anything down

Why this matters

Mental subtraction helps you solve problems quickly in everyday life. When you're shopping and need to know how much change you'll get, or when you're playing a game and need to work out scores, being able to subtract mentally saves time and builds your confidence with numbers. It also prepares you for more complex maths later on.

How it works

There are two main ways to subtract two-digit numbers mentally:
  1. Partitioning: Split both numbers into tens and ones, then subtract the tens from the tens and the ones from the ones.
  2. Counting up: Start from the smaller number and count up to the larger number. The number of jumps you make is your answer.

Examples you can see

Let's look at some examples using both methods. Example 1: Partitioning Calculate 56 - 23
  • Split 56 into 50 + 6
  • Split 23 into 20 + 3
  • Subtract tens: 50 - 20 = 30
  • Subtract ones: 6 - 3 = 3
  • Add the results: 30 + 3 = 33
Example 2: Counting up Calculate 56 - 23
  • Start at 23
  • Count up to 56
  • 23 to 30 = 7 jumps
  • 30 to 50 = 20 jumps
  • 50 to 56 = 6 jumps
  • Total jumps = 7 + 20 + 6 = 33

Try it as a mini adventure

The Treasure Hunt Challenge You're on a treasure hunt! You have a map showing two locations:
  • Start at 34 steps from the big tree
  • Find the treasure at 78 steps from the big tree
Your mission: How many more steps do you need to walk from the start to find the treasure? Method 1: Partitioning
  • Split 78 into 70 + 8
  • Split 34 into 30 + 4
  • Subtract tens: 70 - 30 = 40
  • Subtract ones: 8 - 4 = 4
  • Answer: 40 + 4 = 44 steps
Method 2: Counting up
  • Start at 34
  • Count up to 78
  • 34 to 40 = 6 jumps
  • 40 to 70 = 30 jumps
  • 70 to 78 = 8 jumps
  • Total jumps = 6 + 30 + 8 = 44 steps

Common mistakes

  • Mistake: Forgetting to borrow when needed
    • Why it happens: Confusing subtraction with addition or not understanding place value
    • Fix: Always check if you need to borrow by comparing the ones digits
  • Mistake: Adding instead of subtracting
    • Why it happens: Not paying attention to the operation sign
    • Fix: Read the problem carefully and look for the minus sign
  • Mistake: Mixing up the order of numbers
    • Why it happens: Rushing or not reading the problem properly
    • Fix: Always identify which number is bigger and which is smaller
  • Mistake: Not partitioning correctly
    • Why it happens: Not knowing how to split numbers into tens and ones
    • Fix: Practice splitting numbers into tens and ones using blocks or drawings

Parent and carer guide

As a parent or carer, you can help your child practice mental subtraction by:
  • Practicing with everyday situations like counting change or comparing scores
  • Using physical objects like counters or blocks to show the partitioning method
  • Encouraging your child to explain their thinking out loud
  • Letting them make mistakes and helping them find the right answer together
  • Practicing both methods so they can choose which one works best for them
What to say:
  • "Can you show me how you solved that problem?"
  • "Which method do you like better, splitting or counting up?"
  • "Let's try a few more examples together"
What not to worry about:
  • Children may make mistakes at first - that's normal
  • They might prefer one method over another - both are correct
  • It takes time to become fluent - practice makes progress

Practice questions

  1. Calculate 65 - 24 using partitioning
  2. Calculate 72 - 38 using counting up
  3. Calculate 87 - 45 using partitioning
  4. Calculate 53 - 19 using counting up
  5. Calculate 91 - 67 using partitioning
Answers:
  1. Partitioning: 65 - 24 = (60 - 20) + (5 - 4) = 40 + 1 = 41
  2. Counting up: Start at 38, count to 72. 38 to 40 = 2, 40 to 70 = 30, 70 to 72 = 2. Total = 34
  3. Partitioning: 87 - 45 = (80 - 40) + (7 - 5) = 40 + 2 = 42
  4. Counting up: Start at 19, count to 53. 19 to 20 = 1, 20 to 50 = 30, 50 to 53 = 3. Total = 34
  5. Partitioning: 91 - 67 = (90 - 60) + (1 - 7) = 30 + (-6) = 24

FAQ

What is mental subtraction?

Mental subtraction is solving subtraction problems in your head without using paper or a calculator.

How can I practice mental subtraction?

You can practice by solving everyday problems like how much change you'll get, or by playing games that involve subtraction.

Which method is better for mental subtraction?

Both methods work well - some children prefer partitioning and others prefer counting up. Try both and see which you like better.

What should I do if I get stuck?

If you get stuck, try using physical objects like counters or drawing pictures to help you understand the problem.

How can I get better at mental subtraction?

Practice regularly with different numbers and problems. The more you practice, the faster and easier it will become.