Showing posts with label GeneralAptitude. Show all posts
Showing posts with label GeneralAptitude. Show all posts

30 Multiplication Tricks to Speed Up your Calculations - You Must Know

Multiplication is important and difficult while doing simplifications. I have provided 30 multiplication tricks. Multiplication tricks are helpful for easy calculations and to save time. I recommend you to learn multiplication table up to 20. If it is not possible, you should learn up to the 9th table.

To speed up your calculations play multiplication games. Many Android applications are providing games for calculation practice. Try android apps like elevate. If you play games on the elevate app, multiplication practice is also done. I have provided multiplication chats below that you need to remember.

1. Multiplication of Single Digit Numbers:

I know no need to explain about single digit number multiplication. You all well-known method is single digit multiplication. Just I want to tell you simple trick for fast calculations.

I would like give you an example with explanation. Let’s see,

4×6 takes some time that is more than 6×4. So try to do multiplication with large numbers. If you know multiplication well, you can do any format. This trick is only for fast calculations and beginners.

No need to explain anything about single-digit multiplication. I have given three examples to understand.

E.g. 6×4=24
E.g. 7×2=14
E.g. 9×7=63

2. Multiplication of Two-Digit Numbers:

Multiplication of two-digit number is a really good trick for time-saving. Most of the time two digit multiplication is required, so you should learn. Two digit multiplications are basic for three and four digit multiplication.

The normal method we do is three lines. Here you can do with the single line. Let’s see,

E.g.
26×32
=26×32
∴832

Steps to Solve Two Digit Multiplication:

Step1: Multiply unit digits of two numbers, i.e.6×2=12. 1 forward carries. [2]

Step2: Multiply cross of two digits and add, i.e. 2×2+6×3=22. Then add carry to 22 (from step1, i.e. 23. 2 is a carry of 23 number (from step 2). [32]

Step3: Multiply ten digit of the numbers, i.e. 2×3=6. Then add carry from previous step i.e. 6+2=8. The final value of this multiplication is [832].

3. Multiplication of Three Digit Numbers:

Multiplication of three digit number is some advanced method compared to two digit multiplication. It is a similar method of two digit multiplication. The only difference is, we are adding only one more step extra compared to two digit multiplication.

Normal three digit multiplication is usually taking more time. So you should learn multiplication of three-digit method to speed up your calculations. Let’s see example and steps to do.

E.g.
242×364
∴88088

4. Multiplication of Four-Digit Numbers:

Multiplication of four digit number is an advanced method. It is not so easy. This method requires some practice for accurate values. The little bit of concentration is required to do four-digit multiplication. You can do four-digit multiplications in 7 simple steps.

So please practice as much as possible and remember steps. Practice is required, by seeing you will not get accurate values for some time. You will confuse without practice. Let’s see,

E.g.
3214×1298
∴4171772

5. Distribution Method:

The distribution method is an advanced time-saving method. If you want to go blindly, you can do two-step multiplication trick. I recommend you to learn this trick and practice. Pen and paper not required for distribution method calculations. It sounds good right. Practice is required for faster calculations.

E.g.
12×17
=(12×10)+ (12×7)
=120+84
∴204

6. Giving and Taking Method:

Giving and taking method is also advanced time-saving method. If you don’t want to learn so many tricks, simply do two-digit multiplication of above trick.

I agree sometimes too many tricks makes you confuse without enough practice. If you are able to practice, learn all tricks of this post. All tricks are recommended.

This trick works when the value is nearer to 10, 20, 30, 40, 50 etc. that means unit digit is must be zero. If it is less than 50, take negative of that value. If it is more than 50, take positive of that value.

E.g.
12×47
=12×(50-3)
=12×50-12×3
=600-36
∴564

E.g.
56×99
=56×(100-1)
=5600-56
∴5544

7. Multiplication of the Same Number:

Multiplication of the same number is square of a number. This trick not required to learn. Now I am telling you for understanding purpose only. Sometimes it is also time-saving method.

Learn every method and trick, but I suggest you, practice well. If don’t want to do practice, simply go with usual methods. You don’t know where to use tricks without practice.

It looks usual method.

E.g.
362=0936+0360
∴1296

8. Multiplication of any Number between 12 and 19:

Multiplication of any number is between 12 and 19 method. You can also call (include 12) teen method for multiplication. This method of multiplication is applicable to numbers between 12 and 19.

Apply this trick, when your calculation of numbers between 12 and 19.

E.g.
14×17
Step1: Multiply unit digit of two numbers. 4×7=28 (2 carry). [8]
Step2: Add 14 and another number unit number i.e. 14+7=21. then add 21 and previous step carry i.e 21+2=23. [238]

9. Multiplication of 11:

Multiplication of 11 with any number is easy. It is an easy and time-saving method. It is basic for three and four digit method. You should learn this to understand three and four digit 11 multiplication.

E.g.
11×345
∴3795

Step1: First digit is take as it is 5. [5]
Step2: It is two digit 1's. So add two digits every time. Add 4+5=9.{95]
Step3: Add next two digits 3+4=7. [795]
Step4: Take last digit as it is 3. [3795]

10. Multiplication of 111:

Multiplication of 111 is the advanced method. It is similar to 11 multiplication i.e. previous method.

E.g.
111×873
∴96903

11. Multiplication of 1111:

Multiplication of 1111 is an advanced method for larger numbers. It is also similar to above two methods.

E.g.
1111×5365
∴5960515

12. Multiplication of 5:

Multiplication of 5 method is easy. It is helpful to larger numbers. This method is basic for next level of methods. Multiplication for larger numbers takes more time. This method is helpful to save your time.

You can answer within 2 seconds for any number that may be larger number.

E.g.
428×5
=428/2×10
∴2140

13. Multiplication of 50:

It is similar to the above method. Just we are adding as a unit digit zero to 5. Multiplication of 50 means it is a larger number compared to 5 right.

E.g.
18×50
=18/2×100
∴900

14. Multiplication of 500:

It is similar to above two methods. I have increased one more zero for understanding purpose. 500 means it is larger number compared to above two methods. That above two methods I have explained for this method.

E.g.
21×500
=21/2×1000
∴10500

15. Ending with 5 and Difference 10:

Ending with 5 and difference is 10. This method is tricky. You need to check before applying this method, conditions of the method are satisfied or not.

E.g.
45×35
=(4+1)×3=15
∴1575

16. Ending with 5 and Same Number:

Ending with 5 and the same number is similar to above method but not 100%. The similarity is ending unit digit number is 5. This method is also somewhat tricky. Check all the conditions are satisfied or not before applying this method.

E.g.
25×25
=(2+1)×2=6
∴625

17. Multiplication Near Value 50:

Multiplication of number i.e. near the value of 50. It is a completely different method of above I mentioned. It is simple mathematics.

47 is near the value of 50, if you can add 3 to 47, then it is 50. So subtract 3 from 47 and add it to 47. Then your multiplication looks like 44×50. Now multiplication is easy right.

E.g.
(47)2
=47×47
=44×50
=2200
// 32=9
∴2200+9=2209

18. Multiplication of the Same Number Near the Value of 100, 200, 300,400….

Multiplication of the same number, that is near value of 100, 200, 300 etc. It is a similar method of above but little complicated. If you can practice it is also easy.

Let’s see one example, I am taking 86 square. It is near the value of 100. 86 value is 14 less compared to 100. Then take 14 value as minus sign and multiply (14×14). I will tell you with simplified steps.

E.g.
86
86 | -14
86 | -14
72 | 196 (1 is carry)
7396

19. Multiplication of 37 with 3 Tables:

Multiplication of 37 with 3 tables is an advance time-saving method. This means 37 and any number multiplied by 3, multiplication method. This method works only product of 3. It is very easy.

E.g.
37×3
=7×3=21 {Multiply unit digits] ∴Take last digit i.e. 111

E.g.
37×9
=7×9=63 [Multiply unit digits]
∴Take last digit i.e. 333

E.g.
37×21
=7×21 [Multiply unit digits]
=147
∴Take last digit 777

20. Common Digit Number is Greater than the Normal Number:

Common digit number is greater than the normal number method saves time a lot. It works only one number is same digits and that is larger than other. See below example number

It looks big but you can answer within 2 seconds.

Don't you believe? Let’s see,

E.g.
5732×9999
=5732<9999
∴57314268

21. Checksum Method for Verification:

Checksum method is useful for all multiplications. Learn how to do and how does it works. Above I did multiplication for the larger number. That may right or wrong. Checksum method is used for verification of multiplication. We got 5732×9999=57314268 (previous method).

Add every digits of numbers each side that separating multiplication symbol. If no multiplication symbol, you can add all digits.

E.g.
5732×9999
=17×36
=8×9
=72
=7+2
∴9 Satisfied

22. Increasing 3’s Multiplication Method:

Increasing 3’s multiplication method is easy and no need to do any calculation. You have to remember this numbers with some logic that I will tell you.

Square of first (3) value is 09. Just analyze how it is increasing.

E.g.
3=09
33=1089
333=110889
3333=11108889

23. Increasing 6’s Multiplication Method:

Increasing 6’s multiplication method is similar to above. You have to remember values with some logic. No need to do any calculations for this method.

E.g.
6=36
66=4356
666=443556
6666=44435556

24. Increasing 9’s Multiplication Method:

Increasing 9’s multiplication method is also similar to above two methods. Just remember values of below what I mentioned. Please understand and follow the logic for larger numbers.

E.g.
9=81
99=9801
999=998001
9999=99980001
999999999×999999999=999999980000001

25. Sequential Inputs of Numbers with 9 (1’S):

Sequential inputs of numbers with 9. Here increasing numerical digits of units, tens and adding numbers also increasing. Finally, you will get result output is same for all that is 1’s. You need to remember no need any calculations.

E.g.
1×9+2=11
12×9+3=111
123×9+4=1111
1234×9+5=11111
12345×9+6=111111
123456×9+7=1111111
1234567×9+8=11111111
12345678×9+9=111111111
123456789+10=1111111111

26. Sequential Inputs of Numbers with 9 (8’S):

Sequential inputs of numbers with 9. It is similar to the above method. Above method, sequential inputs are ascending order (1234). Here sequential inputs are descending order (987).

No need to do any calculation, you have to remember.

E.g.
9×9+7=88
98×9+6=888
987×9+5=8888
9876×9+4=88888
98765×9+3=888888
987654×9+2=8888888
9876543×9+1=88888888
98765432×9+0=888888888

27. Multiplication Series of Numbers Without 8:

Multiplication series of numbers without 8. Here we are taking without 8 number series and multiplying by 9th table numbers. Finally, you will get values of 1’s, 2’s, 3’s, 4’s …etc

E.g.
12345679×9=111111111
12345679×18=222222222
12345679×27=333333333
12345679×36=444444444
12345679×45=555555555
12345679×54=666666666
12345679×63=777777777
12345679×72=888888888
12345679×81=999999999

28. Numerical Palindrome with 1’s:

Numerical palindrome with 1’s method is easy that i motioned above multiplication method of 1's. I am hoping you know about palindrome. Here I am not explaining anything about palindrome.

See values, it looks like a palindrome. No need any calculation simply remember.

E.g.
1×1=1
11×11=121
111×111=12321
1111×1111=1234321
11111×11111=123454321
111111×111111=12345654321
1111111×1111111=1234567654321
11111111×11111111=123456787654321
111111111×111111111=12345678987654321

29. Multiply two digits numbers ending in 1

Multiplication of two digit numbers i.e. ending unit digit number is 1. Two numbers unit digit should be one. Then you can apply this method. This method is new to me also. Let’s see

E.g.
51×31=1581
Step 1: Unit digit keep as it is 1. [1]
Step 2: Add the left digits 5+3=8. [81]
Step 3: Multiply the left digits i.e. 5×3=15. [1581]

30. Common Sense Method for Multiplication:

Common sense method is for multiplication in aptitude numerical simplification. I gave this method name for understanding purpose only. Please use common sense and choose what method is required.

I know difficult to solve without practice. If you practice well, It is very easy. It is ultimate method for multiplication. You should know all methods of multiplication to apply this method.

I will give an example, think how you can solve? You should apply more than one method to solve this example. Let’s see,

E.g.
33×333×3333
3×11×333×3333
11×333×9999
3663×9999
36626337

RajashekarKankanala
Tuts Raja
NTR Colony
9110760272
http://www.tutsraja.com/

Simplification Rules for Numerical Calculations

If you know simplification rules, simplification is an easy topic. Many bank exams focusing on simplification. It is a compulsory question, tricky and easy to make mistakes. All simplification questions are based on BODMAS rule. Simplification is done by addition, subtraction multiplication and division, while doing numerical calculations, simplification rules are necessary to follow. Simplification rule is VBODMAS, a complete form of VBODMAS is vinculum bracket of division multiplication addition subtraction.

Operators for Simplification with Example:

Operators for Simplification

NameSymbolExmple
Subtraction-a - b
Multiplication×a × b
Division / a / b
Percentage % a%
Of×a of b
Vinculum abc a + b + c

Operator Sign Table

Sign Table

OperandOperatorOperandEqual toResult
-×-=+
-×+=-
+×-=-
+×+=+

The Formula for Simplification (VBODMAS):

VBODMAS is a short form for remembering simplification rules. Here I will tell one by one in depth priority.
Let's see,

1. V (Vinculum):

V is nothing but vinculum. It is a horizontal line, drawn over a group of digits. We can also call bar. It is the first priority in simplification.

Example: 32 - [5 - 8 * 5 + 6 - 3]

```=32 - [5 - 8 *  5 + 6  - 3] [∴ Simplify 5 and 6]
=32 - [5 - 8 * 11 - 3]      [∴ Simplify 8 and 11]
=32 - [5 - 88 - 3]          [∴ Add equal signs]
=32 - [5 - 91]              [∴ Perform subtraction]
=32 - [- 86]                [∴- × - = +]
=32 + 86                    [∴ perform addition]
=118```

2. B (Bracket):

B is nothing but bracket. Here three brackets are there (), {} and []. We have a priority among those brackets. First priority is open bracket (). The second priority is flower bracket {}. Finally, third priority is a closed bracket.

Example: 8 - [3 + {7 - (9 - 5)}] +5^2

```8 - [3 + {7 - (9 - 5)}] +5^2       [∴Simplify open bracket 9, 5 ]
=8 - [3 + {7 – 4}] + 25            [∴Simplify flower bracket]
=8 - [3 + 3] +25                   [∴Simplify closed bracket]
=8 – [6] +21                       [∴add same signs]
=29 - [6]                          [∴Perform subtraction]
=23```

Note: remember bracket priority with small trick. Someone gave you a gift. What will you do, “just open gift, see gift (flowers) and close the gift.

3. O (of):

O is nothing but OF. We write Multiplication *, Instead of OF. Here first priority is OF after brackets even though multiplication.

Example: 49 ÷ 7 × 4 ÷ 2 + 5 of 63 ÷ 3

```49 ÷ 7 × 4 ÷ 2 + 5 of 63 ÷ 3      [∴Perform OF 5, 63]
=49 ÷ 7 × 4 ÷ 2 + 315 ÷3          [∴Perform division]
=7 × 2 + 105                      [∴Perform multiplication]
=119```

4. D (Division):

D is nothing but division. Here division and multiplication is the equal priority. You can do both simultaneously.

Example: 36 ÷ 6 × 25% × 4 + ½ of 100 ÷ 5

```36 ÷ 6 × 25% × 4 + ½ of 100 ÷ 5       [∴Perform OF ½, 100]
=36 ÷ 6 × 25 / 100 × 4 + 50 ÷5        [∴Perform division]
=6 × 1 / 4 × 4 + 10                   [∴Perform division]
=16  ```

5. M (Multiplication):

M is nothing but multiplication. Here division and multiplication is the equal priority after OF.

Example: 5 × [-12 × (121 ×11) - (-4) × {3 – 1 - 3}]

```5 × [-12 × (121 × 11) - (-4) × {3 – 1 - 3}]        [∴Simplify open bracket]
=5[-12 × 1331 + 4 × {3 - 1 -3}]                    [∴Simplify flower bracket]
=5[-12 × 1331 + 4 × {-1}]                          [∴Perform multiplication]
=5[-15972 - 4]                                     [∴Add values of equal signs]
=5[-15976]                                         [∴Perform multiplication]
=79880  ```

A is nothing but an addition. Here addition and subtraction is the equal priority. You can add same signs of values simultaneously.

Example: 3 - [22 + (46 + 77) - {3 - 11}]

```3 - [22 + (46 + 77) - {3 - 11}]            [∴Simplify open bracket]
=3 - [22 + 123 - {3 - 11}]                 [∴Simplify flower bracket]
=3 - [22 + 123 - {-8}]                     [∴Add values of equal signs]
=3 - [145 + 8]                             [∴Perform addition]
=3 - [153]                                 [∴Perform Subtraction]
=-153  ```

7. S (Subtraction):

S is nothing but Subtraction. Here Subtraction and addition is the equal priority. It is last priority in calculation of numbers.

Example: 3 - 45 + 19 + 77 - 17 – 11

```3 - 45 + 19 + 77 - 17 – 11        [∴Add values of equal signs]
=99 - 73                          [∴Perform subtraction]
=26  ```

Remember: VBODMAS = Vinculum Bracket Of Division Multiplication Addition Subtraction

Remember Key points:

Finally, simplification priority list for all numerical calculations.

1. First priority is vinculum.
2. Second priority is brackets (), {} and [].
3. Third priority is OF.
4. Forth priority is division and multiplication.
5. Fifth priority is addition and subtraction.
RajashekarKankanala
Tuts Raja
NTR Colony
9110760272
http://www.tutsraja.com/

Classification of Numbers for Numerical Aptitude

An arithmetical number can express by a word, symbol, or figure. Those are representing a particular quantity and used in counting, measuring and making calculations. We covered almost all number classifications for Competitive exam point of view. These number classifications are necessary to learn for numerical aptitude.

Decimal Number:

Decimal number contains decimal point. Decimal point is .

Example: 27.45

Digit:

Classification of number system 0, 1, 2,3,4,5,6,7,8 and 9 symbols are called digits.

Example:0,1,2,3,4,5,6,7,8,9.

Number:

Group of digits is called as a number.

Example: 21, 456, 1244, 25734 etc

Face Value:

Face value is nothing but actual value of the digit.

Example: 458
Face value of 4 is 4
Face value of 5 is 5
Face value of 8 is 8

Place Value:

When the value contains digits that is number, such digits counting is units, tens, hundreds, thousands…etc

Example: 342
The place of 2 is units. Place value of 2 * 1 = 2
The place of 4 is tens. Place value of 4 * 10 = 40
The place of 3 is Hundreds. Place value of 3 * 100 = 300

Natural Numbers (N):

Counting numbers without zero is called natural numbers. Natural numbers does not contain zero. Natural numbers denoted by N

Formula: n > 0

Example: 1,2,3,4,5,6,7,8,9,10,11,12…

Whole Numbers (W):

Counting numbers with zero is called as whole numbers. Whole numbers denoted by W.

Formula: n ≥ 0
Whole numbers = Natural numbers + zero

Example: 0,1,2,3...

Integers(Z):

Counting Numbers with zero and –ve numbers is called as integers. All integers are fractions. Not all fractions are integers. Integers denoted by Z

• Positive Integers: n > 0; [1, 2, 3...]
• Negative Integers: n < 0; [-1,-2,-3...]
• Non-Positive Integers: n ≤ 0; [0,-1,-2,-3...]
• Non-Negative Integers: n ≥ 0; [0, 1, 2, 3...]

Formula: n ≥ 0 or n ≤ 0
Integers = Whole numbers + the negative of the whole numbers.

Example: ….3,-2,-1, 0,1,2,3...

Rational Numbers (Q):

Rational numbers nothing but fraction of real number. Rational numbers denoted by Q. Fractions can be written as a terminating decimal or a repeating decimal

Example: 22/7, 45/6…

Formula: m/n remainder is not zero
Rational numbers = Integers + fractions

Irrational Numbers (P):

irrational number is a number that perfectly divisible by itself. Irrational Numbers is denoted by P.Irrational numbers are numbers that cannot be written as a fraction Another way to see them is that they are neither repeating decimals nor terminating decimals

Example: 22/2, 45/5…

Formula: m/n remainder is zero

Real Numbers(R):

Collection of rational and irrational numbers called as real numbers. Real number is denoted by R.

Example: 22/2, 45/5, 22/2, 45/5…

Formula: m/n
Real numbers = rational numbers + irrational numbers

Even Numbers:

A number perfectly divisible by 2 is called as even number. Alternative numbers from zero is also called as even numbers.

Example: 0, 2, 4,6,8,10,12…

Formula:n / 2 = 0

Odd Numbers:

A number not perfectly divisible by 2 is called as odd number.

Example: 1, 3,5,7,9…

Formula: n / 2 ≠ 0

Prime Numbers:

Numbers which is divisible by itself and 1 is called as prime numbers. 1 is not a prime number.

Example: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 71, 73, 79, 83, 89, 97

1Q: How to check 157 is prime number or not?
Solution:
Step 1 : 13 > √157
Step 2 : Prime numbers less than 13. So less than 13 prime numbers are 2, 3, 5, 7 and 11.
Step 3 : 157 is not divisible by any prime numbers (below 13).
Result : Finally 157 is a prime number.

Formula: n/n, n/1

Composite Numbers:

non prime numbers are called composite prime numbers. 1 is neither a prime number nor a composite number. 2 is the only even prime number.

Example: 4, 6, 8, 9….

Formula: Natural numbers- prime numbers

Co-Primes Numbers:

Two natural numbers are co-primes if their H.C.F. is 1. For example, (2, 3), (4, 5) are co-primes.

Example: (2,3), (4,5),(4,9), (21,44)..

Formula: 2 number H.C.F is 1

Twin prime numbers:

A pair of prime numbers difference is two are called twin prime number.

Example: The twin prime numbers between 1 and 100.
(3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43), (59, 61), (71, 73).

Formula: n2-n1=2

Consecutive numbers:

If the difference between two numbers is 1, it is called as consecutive number

Formula: x, x+1, x+2

Example: 16,17,18,19

Consecutive even numbers:

if the difference between two numbers is 2, it is called as consecutive even numbers.

Formula: x, x+2, x+4

Example: 16, 18, 20

Consecutive odd numbers:

if the difference between two numbers is 2, it is called as consecutive even numbers.

Formula: x, x+2, x+4

Example: 17, 19, 21

Complex Number:

A Complex Number is a combination of Real Number and Imaginary Number. Complex number is denoted by Im(z).

Formula: a + bi
a, b real numbers
I imaginary number.

Example: √(-7), √(1-8), √(-25) = 5i, etc...

RajashekarKankanala
Tuts Raja
NTR Colony
9110760272
http://www.tutsraja.com/

Speed Addition Tricks for Competitive Exams

Let’s see,

Trick 1:

Here is a trick that is for near value of 10, 100, 1000, 10000 etc. Just do mind calculation for near value of numbers. It is easy, instead of a regular method. It is also for the time-saving trick.

Example: 136+89

```136+89       ∴ 89 is near value of 90
136+90-1     ∴ add 90 and 136
226-1        ∴ subtract
225```

Trick 2:

This trick is useful for long length calculations. It is simple when you add a decimal and natural numbers separately.

Example: 15.5+8.25

```15.5+8.25      ∴ Separate natural and decimal numbers
23.75```

Trick 3:

When you see same number and increasing series, follow this trick. It is for all same and increasing order numbers. Just take a common number and multiply. This type of addition tricks available in Vedic maths. This type addition tricks for large numbers.

Example: 6+66+666+6666+66666

```6+66+666+6666+66666        ∴ take 6 common
6(1+11+111+1111+11111)     ∴ Add increasing 1’s, see below result
6(12345)                   ∴ multiply number with 6
74070```

Trick 4:

It is similar to trick 3. The only difference is numbers series is reverse when you add. Just add and multiply with a common number.

Example: 0.8+0.88+0.888+0.8888

```0.8+0.88+0.888+0.8888       ∴ Take 8 common
8(0.1+0.11+0.111+0.1111)    ∴ Add increasing decimal 1’s
8(0.4321)                   ∴ multiply 8 with that decimal
3.4568```

Trick 5:

This trick makes calculations simpler. First, add unit’s digit then add the total. These are speed addition tricks.

Example: 17 + 6.

```17 + 6.      ∴ Separate tens and units.
23```

Trick 6:

The addition operation perform between separated suitable digits. Separation of digits done for suitable other numbers.

Example: 74+8

```74+8      ∴ Separate unit’s digit suitable for other numbers
82```

Trick 7:

Separation makes calculation simpler. So separate possible numbers then add.

Example: 662+579

```662+579        ∴ Separate hundreds and tens
1241```

Trick 8:

If you found suitable units digit numbers, add those numbers first then other numbers.

Example: 7 + 8 + 3 + 2 + 5

```7 + 8 + 3 + 2 + 5      ∴ Add suitable numbers
25```

Trick 9:

If you don’t know additions what will you do? Counting numbers, am I right? So add numbers 7+2 instead of 2+7. It is also useful for counting numbers.

Example: 2 + 7

```2 + 7      ∴ Add number 7+2