About Subtraction
While solving the subtraction problems, people often make the mistakes, especially when the numbers needs to be subtracted from 1000, 10000, 100000 and so on.
Main errors happens when the numbers are borrowing from the neighbouring digit during the calculation in our normal school method.
The method I will share with you is actually originated from an ancient Indian Vedic Maths system.
To solve such kinds of subtraction sums, just remember this small vedic maths formula:
Let’s start with an example
1000 ⇐Forgot these numbers
-289 ⇐Apply the formula here from right to left
———-
10-9 =1 [Last from 10, i.e. the last number (at unit place) should be subtracted from 10]
9- 8 = 1 [Rest from 9, i.e. rest all numbers (at subsequent places) should be subtracted from 10]
9-2 = 7
So the Answer is = 7 1 1——————– [Caution: Remember the sequence while writing the numbers]
Let’s try another
100000
-456
———–
Here in this example, there are 5 zero in the 100000 and below there are only three digits (456), so to match digits equal to 5 zero, just add 2 zero before 456 to make it 00456, and apply the formula
“LAST FROM 10, REST FROM 9”
10-6=4 ——–[Last number subtracted from 10]
9-5= 4
9-4= 5
9-0= 9
9-0= 9 —— [Rest all numbers subtracted from 9]
Answer: 99544
Tip: Total number in the lower row is equal to the total umbers of zero in the above row. If not, make it equal by putting the zero before the numbers.
One more example
10000
-1420
———–
Now in this example, number in the lower row is ending with zero.
In this case, keep the zero as it is and start your formula from non-zero number. i.e. start your formula from 2, in this case.
0 [Keep the zero as it is]
10-2= 8 [Last number subtracted from 10]
9-4=5
9-1=8 [Rest all numbers subtracted from 9]
Answer is: 8580
Group in to twos (starting from the right)
Same idea applies to subtraction, what’s easier to think about, 15528-1210 or:
| 1 | 55 | 28 | |||
| – | 12 | 10 | |||
| 1 | 43 | 18 |
It’s easier to think “28-10=18” and “55-12=43”
Carries still apply as normal:
4812 – 1598
| 48 | 12 | |||
| – | 15 | 98 | ||
| 32 | 14 | A bit like school, 12 – 98, make it 112 – 98 = 14 carry one | ||
| 1 |
Do 48-15 then subtract one, 48-15=33, 33 – 1 = 32
Slide up or down and make them easier
You may remember from school, that subtraction was sometimes referred to as the difference between two numbers so when calculating numbers in my head, I sometimes slide BOTH numbers up or down in my head (which keeps the difference between them the same):
| 52 | |
| – | 19 |
I think, if I slide the 19 up one to 20, then slide the 52 up one to 53, it becomes:
| 53 | |
| – | 20 |
| 33 |
This is easier to do in your head (no carries to think about)
Another example 84 – 68:
| 84 | |
| – | 68 |
I think, if I slide the 84 up two to 86, then slide the 68 up two to 70, it becomes:
| 86 | |
| – | 70 |
| 16 |
Again, no carries to think about. Prove this to yourself by calculating 84 – 68 = 16
Choose a nice middle number
When subtracting two numbers in my head that are fairly near to each other, I like to choose a nice looking number that comes between the numbers e.g. 100, 200, 5000 etc.
If you know someone was born in 1979 and you want to find out how old they are, you have:
2008 – 1979
Well, a nice number between these is the number 2000.
First of all, work out the differences between 2000 and 2008, and 1979 and 2000, and then add the differences up
The difference between 2000 and 1979 is 21
The difference between 2000 and 2008 is 8
Add the differences: 21 + 8 = 29
Align the decimal point and do the same
If you have 12.58 – 6.2, just align the decimal point, and do the same maths (add trailing zeros to make it look easier):
| 12 | • | 58 | |
| – | 6 | • | 20 |
| 6 | • | 38 |
Subtract in bits at a time
There’s no need to subtract things all at once in your head. If you have to subtract 150 from something, you have 100 and 50 to subtract separately.
1100 – 150 → First of all, subtract the 100 to make it easier:
1100 – 150 = 1000
now all you have to do is subtract the remaining 50:
1000 – 50 = 950
Another example:
1450 – 125
I can either subtract the 100, the 20 and the 5 separately, but looking at it, I have decided to subtract the 100 and the 25 instead:
1450 – 100 = 1350
13 50 – 25 = 13 25 (I split them up in to pairs so I can think about them more easily, as explained above.
Just to explain last bit, I thought in my head:
| 13 | 50 | |
| – | 25 | |
| 25 |
This method is like the ‘sliding rule’ above, only thought about in a different way.
Negative numbers
There are numerous ways to understand these. You can think of a ruler:
| -4 | -3 | -2 | -1 | 0 | 1 | 2 | 3 | 4 | 5 |
So for the number 2 – 5, you would start at 2, and then count down 5 until you get to -3. To add, count to the right -3 + 4 → -3, -2, -1, 0, 1
So -3 + 4 = 1.
Another way to think of them is a positive number is like being in credit and negative is like being in debt.
Let’s look at 2 – 5 again. If you had £2 in a bank and you withdrew £5, you will be £3 in debt or 2 – 5 = -3. If you have £3 of debt and you put in a cheque for £4 then you will have £1 in the bank so -3 + 4 = 1.