Addition and Subtraction Shortcut Tricks - Basic Math Tricks Part1

Basic Tricks - PART-1

Addition Shortcut Tricks

Addition of Similar Digit Numbers Shortcut tricks

Addition of Similar Digit

5+55+555 = ?
The result of the addition is 5+55+555 = 615.
Shortcut Tricks
Step 1 : Take 5 Common and Replace all 5 with 1. 5(1+11+111).
Step 2 : Count number of digits in each number, i.e, 1=1(digit), 11=2(digit), 111=3(digit) and write down all digits together that is 123.
Step 3 : Multiply 5×123 = 615.
The final result is 615.

Addition of Similar Digit

3+33+333+3333 = ?
The result of the addition is 3+33+333+3333 = 3702.
Shortcut Tricks
Step 1 : Take 3 Common and Replace all 3 with 1. 3(1+11+111).
Step 2 : Count number of digits in each number, i.e, 1=1(digit), 11=2(digit), 111=3(digit),
1111=4(digit), and write down all digits together that is 1234.
Step 3 : Multiply 3×1234 = 3702.
The final result is 3702.

Addition of Similar Digit

7+77+777+7777+77777 = ?
The result of the addition is 7+77+777+7777+77777 = 86415.
Shortcut Tricks
Step 1 : Take 7 Common and Replace all 7 with 1. 7(1+11+111+1111+11111).
Step 2 : Count number of digits in each number, i.e, 1=1(digit), 11=2(digit),111=3(digit),1111=4(digit),11111=5(digit),and write down all digits together that is 12345.
Step 3 : Multiply 7×12345 = 86415.
The final result is 86415.

Addition of Similar Digit

9+99+999+9999+99999+999999 = ?
The result of the addition is 9+99+999+9999+99999+999999 = 1111104.
Shortcut Tricks
Step 1 : Take 9 Common and Replace all 9 with 1. 9(1+11+111+1111+11111+111111).
Step 2 : Count number of digits in each number, i.e, 1=1(digit), 11=2(digit), 111=3(digit),1111=4(digit),11111=5(digit),111111=6(digit) and write down all digits together that is 123456.
Step 3 : Multiply 9×123456 = 1111104.
The final result is 1111104.

Addition of Similar Digit with Decimal Numbers Shortcut tricks

Addition of Decimal Numbers

0.5+0.55+0.555 = ?
The result of the addition is 0.5+0.55+0.555 = 1.605.

Shortcut Tricks

Step 1: Take 5 Common and Replace all 5 with 0.1, 5(0.1 + 0.11 + 0.111).
Step 2: Replace (0.1+0.11+0.111) into 0.321 and Multiply 5(0.321) = 1.605
The final result is 1.605.

Addition of Decimal Numbers

0.6+0.66+0.666 = ?
The result of the addition is 0.6+0.66+0.666 = 1.926.

Shortcut Tricks

Step 1:Take 6 Common and Replace all 6 with 0.1, 6(0.1 + 0.11 + 0.111).
Step 2:Replace (0.1+0.11+0.111) into 0.321 and Multiply 6(0.321) = 1.926.
The final result is 1.926.

Addition of Decimal Numbers

0.7+0.77+0.777+0.7777 = ?
The result of the addition is 0.7+0.77+0.777+0.7777 = 3.0247.

Shortcut Tricks

Step 1:Take 7 Common and Replace all 7 with 0.1, 7(0.1 + 0.11 + 0.111 + 0.1111).
Step 2:Replace (0.1+0.11+0.111+0.1111) into 0.4321 and Multiply 7(0.4321) = 3.0247.
The final result is 3.0247.

Addition of Decimal Numbers

0.9+0.99+0.999+0.9999+0.99999 = ?
The result of the addition is 0.9+0.99+0.999+0.9999+0.99999 = 4.88889.

Shortcut Tricks

Step 1:Take 9 Common and Replace all 9 with 0.1, 9(0.1 + 0.11 + 0.111 + 0.1111+0.11111).
Step 2:Replace (0.1+0.11+0.111+0.1111+0.11111) into 0.54321 and Multiply 9(0.54321) = 4.88889.
The final result is 4.88889.

Addition of common difference in a series of numbers shortcut tricks

Example 1:

49, 55, 61, 67  and 73
here we apply the shortcut tricks which help us to get the result quick
Answer :
Step 1: Add the smallest number to biggest number that is 49 + 73 = 122
Step 2: then multiply the sum 122 x 5 = 610
Step 3: At last divide the number by 2, 610 / 2 = 305
Thus 49 + 55 + 61 + 67 + 73 = 305.

Example 2:

36, 44, 52, 60 and 68
here we apply the shortcut tricks which help us to get the result quick
Answer :
Step 1: Add the smallest number to biggest number that is 36 + 68 = 104
Step 2: then multiply the sum 104 x 5 = 520
Step 3: At last divide the number by 2, 520 / 2 = 260

Example 3:

77, 82, 87, 92 and 97
here we apply the shortcut tricks which help us to get the result quick
Answer :
Step 1: Add the smallest number to biggest number that is 77 + 97 = 174
Step 2: then multiply the sum 174 x 5 = 870
Step 3: At last divide the number by 2, 870 / 2 = 435.

Example  4 :

77, 66, 55, 44 and 33
here we apply the shortcut tricks which help us to get the result quick
Answer :
Step 1: Add the smallest number to biggest number that is 77 + 33 = 110
Step 2: then multiply the sum 110 x 5 = 550
Step 3: At last divide the number by 2, 550 / 2 = 275.

Addition consecutive numbers shortcut tricks

Example 1: Find the addition of consecutive  number from 23 to 29?
Ans:
Step 1: At first we add the smallest number to biggest number in the given group. Result is 23 + 29 =52.
Step 2: Then multiplication the result with amount of numbers in the given group of numbers 52 x 7 = 364.
Step 3: At we last divide the resultant product by 2, 364 / 2 = 182.
So the addition of  all numbers in group from 23 to 29 is 182.
Example 2: Find the addition of consecutive  number from 79 to 89?
Ans:
Step 1: At first we add the smallest number to biggest number in the given group. Result is 79 + 89 =168.
Step 2: Then multiplication the result with amount of numbers in the given group of numbers 168 x 11 = 1848.
Step 3: At we last divide the resultant product by 2, 1848 / 2 = 924.
So the addition of  all numbers in group from 79 to 89 is 924.
Example 3: Find the addition of consecutive  number from 56 to 69?
Ans:
Step 1: At first we add the smallest number to biggest number in the given group. Result is 56 + 69 =125.
Step 2: Then multiplication the result with amount of numbers in the given group of numbers 125 x 14 = 1750.
Step 3: At we last divide the resultant product by 2, 1750 / 2 = 875.
So the addition of  all numbers in group from 56 to 69 is 875.
Example 4: Find the addition of consecutive  number from 33 to 44?
Ans:
Step 1: At first we add the smallest number to biggest number in the given group. Result is 33 + 44 =77.
Step 2: Then multiplication the result with amount of numbers in the given group of numbers 77 x 12 = 924.
Step 3: At we last divide the resultant product by 2, 924 / 2 = 462.
So the addition of  all numbers in group from 33 to 44 is 462.
Example 5: Find the addition of consecutive  number from 82 to 99?
Ans:
Step 1: At first we add the smallest number to biggest number in the given group. Result is 82 + 99 =181.
Step 2: Then multiplication the result with amount of numbers in the given group of numbers 181x 18 = 3258.
Step 3: At we last divide the resultant product by 2, 364 / 2 = 1629.
So the addition of  all numbers in group from 82 to 99 is 1629.

Addition combination of decimal and whole number Tricks

Example 1:

3.3 + 3.33 + 3.333 + 3.3333=?
The result of the addition is 3.3 + 3.33 + 3.333 + 3.3333 = 13.2963.

Shortcut Tricks

Step 1: At First we can calculate the Decimal number 3 ( 0.4321 ) = 1.2963
Step 2: In Step 2 we can calculate the Whole numbers that is maximum number 3 digits is
= 3+3+3+3 So, 3 x 4 = 12
Step 3: Now we can add both result of step 1 and Step 2 = ( 1.2963 + 12 ) = 13.2963.

Example 2:

5.5 + 5.55 + 5.555 + 5.5555 + 5.55555
The result of the addition is 5.5 + 5.55 + 5.555 + 5.5555 + 5.55555 = 27.71605.

Shortcut Tricks

Step 1: At First we can calculate the Decimal number 5 ( 0.54321 ) = 2.71605
Step 2: In Step 2 we can calculate the Whole numbers that is maximum number 5 digits is
= 5+5+5+5+5 So, 5 x 5 = 25
Step 3: Now we can add both result of step 1 and Step 2 = ( 25 + 2.71605 ) = 27.71605.

Example 3:

7.7+7.77+7.777+7.7777+7.77777+7.777777
The result of the addition is 7.7+7.77+7.777+7.7777+7.77777+7.777777 =46.580247.

Shortcut Tricks

Step 1: At First we can calculate the Decimal number 7 (4.580247 ) = 4.580247
Step 2: In Step 2 we can calculate the Whole numbers that is maximum number 7 digits is
= 7+7+7+7+7+7 So, 7 x 6 = 42
Step 3: Now we can add both result of step 1 and Step 2 = ( 42 + 4.580247 ) =46.580247.




Subtraction Shortcut Tricks

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:

“LAST FROM 10, REST FROM 9”

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.