Hello, a friend’s today we start with Quantitative aptitude which simply means “Basic mathematics” that we are learning from our childhood. Multiplication, Division, square root, cube root, you may think these are too simple to learn and solve, but from the point of view of competitive exams, you need to be a very fast problem solver.

Here our traditional methods do not work as those were time-consuming. Therefore, you need Shortcuts that go with some tricks to solve your puzzles. I am here to give some fair tricks to make your calculation as simpler and easier as it can be. At this moment, you should analyze how proficient you are in solving the basic problems as questions may be asked in a direct or indirect form. Before going to start with shortcuts, there are some

**Basic Definitions** that you must be familiar with:

**Integers**: On the number line all the positive, negative and zero forms a set of integers.

**Even numbers**: Any counting number that exactly divisible by 2 is called an even number. These usually end with 0,2,4,6 or 8.**Odd number**: Any counting number that does not divisible by 2 is called an odd number. These usually end with 1,3,5,7 or 9.**Natural numbers**:: Natural numbers are all the numbers that exist in nature. A set of natural numbers denoted by N= {1,2,3,4,5}**Whole numbers**: All the natural numbers, including “Zero“, forms a set of whole numbers denoting W={0,1,2,3,4,5}.**Rational number**: A number in the form of a/b where a & b are both integers and b never equal to Zero. Types of a rational number are included in**Terminating or finite decimals**: This type gives results infinite decimals, e.g. 21/5=4.2 17/4=4.25**Non-terminating Periodic fractions**:: In this type fractions are periodically repeating over again like 16/3=5.3333**Non-terminating non-periodic fractions**: This type of fraction is non-periodic and non terminating in nature e.g. 5.273545876971

**Irrational numbers**: Non-terminating and non-periodic fractions, both together considered as irrational number e.g2, 3,π**Prime numbers**: A counting number which has exactly two factors that are itself and 1.**Composite numbers**: Natural number which is not prime is called a composite number**Twin primes numbers**: A pair of prime numbers when different by 2 are called twin primes e.g (41,43).**Co-Prime numbers**: if HCF of a pair of two natural numbers is 1 then this pair is called co-prime e.g (2,3), (4,5), (7,9)

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**Introduction to Vedic Mathematics:**

In our classical age of Indian mathematics as of Aryabhata, the popular mathematician-astronomers were efficient in solving mental calculations through some specific techniques. These techniques are booked under 16 Sutras (Principles), on which the whole mathematics concept is based. Multiplication, squaring, cubing, square roots, cube roots become so simple and quick to work out. See how to do it….

**Multiplication (Criss - Cross Method)**

**Multiplication (Criss - Cross Method)**

### Two-Digit Multiplication

**Take an example 87 X 39 =?**

**Step1**: Crisscross the arrows in a manner shown above.**Step2**: First multiply 8 and 3 as first digits multiplication**Step3**: Then crisscross multiplication 8x9, 7x3, and add the result. Write below the last multiplication digit**Step4**: Multiply 7x9 as last digits multiplication and write below the above multiplication result.**Step5**: Lastly add all these to get the final result.

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*Three-Digit Multiplication*

**Take an example 257 x 521 =?**

**Step1**: Crisscross the arrows, take the first block and multiply in the same manner.**Step2**: First multiplies 2x5 as first digit multiplication.**Step3**: Then 2x2, 5x5 and add the result. Write below the last multiplication result.**Step4**: Now multiply extreme digits and middle and add them all.**Step5**: In the second block repeats the criss-cross method and multiplies 5x1 and 7x2 and add.**Step6**: Then multiply 7x1 as 7 is the unit digit number so write in last.**Step7**: Finally, add all these to get the final result.

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*Four-Digit Multiplication*

**Take an example 4531 x 4621=? =?**

**Step1**: Crisscross the arrows, take the first block and multiply in the same manner.**Step2**: First block multiplies 4x4**Step3**: Then 4x6,5x4 and add the result. Write below the last multiplication result**Step4**: Now multiply extreme and middle digits of the first plus second block and add them**Step5**: Repeat the criss-cross method of extreme digits of the first and third block (4x1), (4x1), (5x2), (3x6) and add them**Step6**: Then take the second block, and third apply criss-cross method.**Step7**: Multiply the elements of the Third block (3x1)+(2x1) and add them.**Step8**:Last digit multiplication 1 X 1.**Step9**:Finally, add all these to get the final result.

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**Multiplication With Bases**

### Base 10

When multiplication of a single digit (< 10) is questioned then best to apply base 10 trick mentioned as follows:**Take an example 9 x 8 =?**

**Take another example 7 x 6 =?**

**Step1**:In single digit multiplication take 10 as base.**Step2**:Subtract the number from 10 to get given number as 10-1=9.**Step3**:Repeat the same for next and apply the cross subtraction**Step4**:Final result‘s Unit place comprises of multiplication of variables we subtracted from 10 and Tenth place comprises of cross subtraction.*****Step5**:In case you get two digit numbers on the unit place then as to make it single, take the carry to left side and add to get fully final answer.

### Base 100

When multiplication of a two digit (< 100) is asked then apply base 100 trick mentioned as follows

**Take an example 88 x 98 =?**

**Take another example 75 x 92 =?**

**Step1**:In two digit multiplication take 100 as base..**Step2**:Subtract the number from 100 to get given number as 100-2=98**Step3**:Repeat the same for next and apply the cross subtraction.**Step4**:Final result ‘s Unit and tens place comprises of multiplication of variables we subtracted from 100 and Hundreds place comprises of cross subtraction.*****Step5**:In case you get three digit number on the unit place then as to make it two, take the carry to left side and add to get fully final answer.

### Base 1000

When multiplication of a three digit (< 1000) is asked then apply criteria same as above.

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**Take 998 x 988 and compute it as self assessment**.

*****In Base 1000 remember to take carry to left and add, if right block consist more than three places**