Subtraction facts and strategies

Subtraction is NOT commutative, which means that the order matters. It is important to realise that:

5 - 3 is not the same thing as 3 - 5 .


Methods of *mental* subtraction

Method 1 : Make addition easier by rounding up the right-hand number to a multiple of 10.

The important thing is that when modifying subtractions in this way, you must always take away or add the same number from both numbers - this is different to addition, where you must always do the opposite to each number.

So for example, we can make 26 - 17 easier by adding 3 to the 17 and the 26, with the goal of turning the 17 into 20, a nice round numbers. So the calculation becomes:

29 - 20 which comes to 9, which is a lot easier than the previous version.

You can continue the process to round up to multiples of 100, for larger subtractions. For exmple, 113 - 26

- First adjust it by adding 4 to both sides:

117 - 30 . Now, add 70 to both sides:

187 - 100 - now we can see straight away that this comes to 87.


As a tip, this makes 'column subtraction' with paper and pencil much easier as well. So for example, with 113 - 26, as above, this involves two ugly, error-prone 'borrows' from a more significant digit. But:

187 -
100
---
 87

Is much easier, simply because you are mainly doing a subtraction of zero for most of the digits.


Method 2 : This is the way the 'super mental calculators' do it. Basically, unlike how you were taught at school, you subtract from left to right, not right to left. This better matches the way we say the number aloud, and actually, it's much quicker than all other methods when you get used to it.

It relies on two things:
- A 'carry' is never more than 1
- You need to be able to count down ( by subtracting ) single digits *instantly*.

There are only two scenarios for two digits:
- they subtract without going 'bust' e.g. 6 - 3 = 3
- they subtract and go bust, e.g. 5 - 7 = -2.

In the second case, don't think of this as '-2,' instead, the answer is 8 and a *carry.*
The '8' is the 'complement' of -2 : If we had to count up -10 to -2, it would be eight steps.
This is the skill you have to develop!

Worked example ( easy ):

   1 4 5 +
     7 2
  
Step 1)  1 minus nothing is 1.  But look next door:  4 - 7 goes bust, so subtract the carry ( 1 ) from our current answer : 1 - 1 = 0

Step 2)  4 - 7 = -3  so answer digit is 7.  But!  look next door:  5 + 2 does not go bust, answer digit stays as 7.

Step 3) 5 - 2 = 3.  Answer is 73.


Harder example:

  1 0 0 4 4 - 
    9 2 7 3
    
Step 1)  Look at 0 and 9, this goes bust so ignore the left-most 1 at the top 
         ( bit quicker if you can learn to do this )
         
Step 2)  0 - 9 = -1 so answer digit is 1.  But look next door:  0 - 2 goes bust, so our answer is still 0 as 1 - 1 = 0 

Step 3)  0 - 2 = -2 so answer digit is 8.  But look next door: 4 - 7 goes bust so subtract 1 from answer digit:  7
         Our answer 'so far' is 7

Step 4)  4 - 7 = -3 so answer digit is 7.  But look next door:  4 - 3 does not go bust so answer digit remains at 7.
         Our answer so far is 77.
         
Step 5)  4 - 3 = 1 .   Answer is 771.

   Check:   9273 + 
             771
           10044
                

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Difficulty Levels - typical questions :

1:  19 - 6
2:  61 - 15
3:  315 - 49