5 Tips to Easily Solve Math Problems

Mathematics is a fundamental part of life, be it in buying groceries at the market to finding the mass of a gluon in particle physics, mathematics is involved. Hence, it is quite evident that everyone should have a requisite understanding of mathematics. But we know that mathematics is not everyone’s cup of tea. From calculus to geometry, everyone has difficulty with some topic. Here I am to give you a few tips and tricks which will help you to improve your efficiency in maths helping you to perform better in your exams and certain life scenarios.

  • Easy percentage calculation: We know how percentage implies to a portion of a 100. To calculate percentages first multiply the percentage to the number and then shift decimal point two places to the left. It is as simple as that but for our better understanding let us use an example.
    Consider the case in a restaurant where you have to tip the waiter 20% of a bill of 1500. The tip can be calculated as => 1500 x 20 = 30000
    Shifting the decimal point two places to the left => 300
  • Divisibility: Checking if a number, usually a large number, is divisible by 2, 3, 4, 5, 6, 9 is something that happens now and then in daily life, like in the case of splitting a bill and so on. Let us see a few tips which tell us if a number is properly divisible.
    i. Divisibility by 2: 1’s place digit will be divisible by 2.
    ii. Divisibility by 3: If sum of the digits is divisible by 3. (eg: 501= 5 + 0 + 1 = 6 = 3 x 2)
    iii. Divisibility by 5: If the last digit is 5 or 0.
    iv. Divisibility by 6: If the condition for divisibility of 2 and 3 are satisfied.
    v. Divisibility by 9: If sum of the digits is divisible by 9. (6930 = 6 + 9 + 3 + 0 = 18 = 9 x 2)
    vi. Divisibility by 12: If the criteria of divisibility of 3 and 4 are satisfied.
  • Temperature Conversion: To convert temperatures between Celsius and Fahrenheit, we have certain shortcuts which help us save both time and effort.
    i. C->F
    F = (C x 1.8) + 32
    ii. F->C
    C=(F-32)÷1.8
  • An easy way to remember the value of Pi: Consider the sentence “May I have a large container of coffee”. Counting the number of letters in each word is 31415926 and after adding a decimal place after 3 we get 3.1415926 which is the actual value of Pi correct to 7 decimal places.
  • Multiplication by 11: Let me explain this with an example, consider the problem 45 x 11; Write down the number in the 100’s place as 4 and the 1’s place as 5. Then the number in the 10’s place is the sum of the digits; 4+5 = 9. Thus, 45 x 11 = 495. If the sum of the digits exceeds 9, then just carry over the digit to the 100’s place.
    For example, 89 x 11;
    100’s place = 8
    10’s place = 9
    Sum of the digits = 17
    Product =        17
    8  _  9
    =      979

Thus, here we have stated a few genius tricks which will help you through scenarios which require you to have quick thought processing when it comes to mathematics. For a better understanding of topics of mathematics like algebra, Quadratic Equation, geometry and more tricks check out our YouTube channel.

 

Calculate Square Root Quickly Without Calculator

In this post, we will learn how to find the square root of numbers which are not perfect squares. The answer we get using this quick calculation technique gives us an approximate answer. However, approximation becomes a necessity when we are attempting questions in a competitive exam, where time is short and options are given. Most of the time we’re not required to get exact answer.

Prerequisite to Use this Method

The prerequisite of using this method is you should remember the squares of as many numbers as possible. I would recommend that one should memorize square of numbers from 1 to 50. Later this can be extended t0 100.

It will be a wonderful idea to first learn the short cut method of finding the square of any number. Other awesome short cut method which you should consider knowing before moving forward is Herons method of finding roots.

Square Root of any number which is not a Perfect Square

Square Root = Sq. Root of Nearest Perfect Square + {difference of the given number from the nearest perfect square / 2 x (Sq. Root of Nearest Perfect Square)}

For example,

Short cut to find the Square Root of 47.
Square Root of 47
= 7 + (47-49) / 2 x 7 (since the perfect square closest to 47 is 49; we will take square root of 49 i.e. 7 for calculations)
= 7 – 2/2×7
=7 – 1/7
= 6.86 (approx).
The exact answer is 6.85565

Short cut to find the Square Root of 174
Square Root of 174
= 13 + (174-169) / 2 x 13 (since the perfect square closest to 174 is 169; we will take square root of 169 i.e. 13 for calculations)
= 13 + 5 / 26
= 13.19 (approx).
The exact answer is 13.1909

Short cut to find the Square Root of 650
Square Root of 650
= 25 + (650-625) / 2 x 25 (since the perfect square closest to 650 is 625; we will take square root of 625 i.e. 25 for calculations)
= 25 + 25/50
= 25.50 (approx).
The exact answer is 25.4950

This method has got a limitation. You can use it only till the point you remember the square
If you’ve questions related to the above shortcut method or anything else related to mathematics, please post on QM’s Q & A platform. For anything else you can comment below.

Vedic Mathematics and Its Relevance in Modern Times

Land of millions, India has contributed greatly in the field of science and mathematics. From Trigonometry to Zero and many others; Vedic Mathematics is one such concept that has been introduced by Indian mathematicians. The following post takes a quick look at Vedic Mathematics. Read on to know more.

Introduction

The Indian subcontinent is highly regarded for its contribution to the field of mathematics. From the classical period till the eighteenth century, contributions have been exceptionally, great. Leading scholars like Aryabhtta, Bhaskarcharya, Brahmaguptas and many others have made exceptional contributions. Right from the concept of zero to the decimal system that we use today has been expounded by these stalwarts.

Among all the contributions, Vedic Mathematics have been one of the most intriguing that continues to draw attention and has been subject of interest for thousands across the globe.

What is Vedic Mathematics?

Vedic Mathematics is the name given to the system that has its origins in the Vedas – the sacred Hindu scriptures. It is a unique technique of calculations that is based on simple principles and rules, applying which, any kind of mathematical problems can be solved –orally!

To put in simple words, Vedic Mathematics is a compilation of a few ‘tricks’ that help in solving mathematical calculations quite easily. Originating from the Atharva Veda, Vedic Mathematics deals with the concepts of core mathematics, engineering, medicine, sculpture and other related fields.

While the concept existed since 1200 BC, it was reintroduced by the noted mathematician Sri Bharati Krishna Tirthaji in 1911. After an extensive research he concluded that, the ‘tricks’ of Vedic Mathematics lie in the sixteen sutras. For example, vertically or crosswise is one of the main sutras.

Features of Vedic Mathematics

It is believed that coherence is one of the main features of Vedic Mathematics. Some relevant features of Vedic Mathematics are explained below:

Coherence: Coherence is often rated as one of the most important features of Vedic Mathematics. The entire system is highly inter-related to one another and unified together.

Flexibility: Another feature that sets apart Vedic Mathematics is its, flexibility. The Vedic System of Mathematics follows general methods and needless to say that they always work wonders. The system follows several special methods in solving an array of calculations. You can end up representing numbers in more than one way and we can work two or more figures at one time. It is this aspect of flexibility that adds to the fun element in practicing. This in turn leads to the development and creativity among students.

While mathematics comprises all deep ideas including numbers and computation, and an entire gamut of number theories and much more—the Vedic Mathematics is a handful of tricks that usually involves elementary arithmetic.

Vedic Mathematics in Modern Times

Vedic Mathematics is one of the most natural ways of working and can be learnt with very little efforts and that also within a very short span. Vedic Mathematics is also supported by a set of checking procedures for independent crosschecking that we do. As mentioned earlier, it is the element of flexibility that continues to add to the very essence of Vedic Mathematics. The calculation techniques provided are highly creative as well as effective. The core idea focused on Vedic Mathematics is that mathematical calculations can be carried out easily and of course mentally.

Even now, in the twenty-first century, Vedic Mathematics continues to be the centre of attention and researches spanning across the globe. Researches are being carried out in multiple areas that include the effect of use of Vedic Mathematics in modern times. Easy applications of the sutra are being propounded by theorists that can help students solve problems related to Calculus and Geometry.

In modern times, many students are resorting to the use of Vedic Maths; especially the ones who sought to appear for competitive exams. The sutras help in solving a lot of complicated problems easily. Vedic mathematics offer students the extra edge that general mathematics might not be able to provide them with. Such is the versatility of Vedic Mathematics is that; even scientists from NASA have applied certain principles of Vedic Mathematics in the realm of artificial intelligence.

These days, Vedic Mathematics is being taught at school level and special attention is being provided to students those who want to learn more about the subject.

Author Bio: Sampurna Majumder is a professional writer who enjoys creativity and challenges. Barely a year into new media, she has written several posts, articles and blogs for prominent websites like Shiksha.com that covers all about the world of education. The above post explores the concept of Vedic Mathematics and its relevance.

How to Quickly Calculate Square of Three Digit Numbers?

Learn to Quickly Calculate Square of Any Three Digit Number

The method of squaring any 3 digit number is an extension of my last post on finding square of any two digit number. To understand and appreciate squaring of 3 digit numbers you should be well versed with shortcut of squaring any 2 digit number. Let us start learning this with the help of an example.

What is the square of 384?

Step 1: To begin with ignore the 3 of 384. You are left with only 84, a two digit number. Using the method of squaring 2 digit numbers, find the square of 84. We get the answer as

Square of 8  |   twice of 8 X 4   |  square of 4

64            64           16

7056 (consolidating the result obtained above)

Step 2: This step is new and different from what we’ve learned in the previous post for squaring 2 digit numbers. Watch carefully.

We have to multiply the first and last digits of our original number and double it. Essentially, that is multiplying together 3 and 4 and then doubling it. Hence we get 24.

Add this number directly to the two left hand digits of our number obtained from the first step.

7056

Add 24 to 70. 70+24=94. So 7056 gets converted to 9456.

Step 3: In the first step we left out the first digit of our number and squared the last two digits. Now we will forget about the unit’s digit 4 and square the first two digits i.e. 38 as before just omitting to square the last digit 8.

Square 38 as a regular 2 digit number, except that you omit the 8 squared.

Square of 3 | twice of 3 X 8

9       |   48

Step 4: Consolidating this with the result obtained in step 2,

9   |  48   |  9456

14        7       456

Hence the answer is 147456.

I’ve shared this method of squaring 3 digit numbers as an extension to the shortcut of squaring 2 digit numbers. Initially you might feel that the traditional method is quicker than having to memorize and execute these steps. However, this method can prove to be quicker than the useful one only if you master this technique with lot of practice.

Do you think this method will help you in reducing the time to calculate square of 3 digit numbers?

How to Quickly Calculate Square of Any Two Digit Number?

In this post I’ve tried to improvise on the method of squaring presented in one of the earlier posts on Quickermaths.com itself. This trick of squaring any two digit number with ease is inspired by squaring techniques from the book – The Trachtenberg Speed System of Basic Mathematics

I would like to explain this method of squaring any 2 digits number with the help of an illustration.

What is the square of 32?

Step 1. In finding the last two digits of the answer, we shall find the square of the last digit of the number. Square the right-digit digit, which is 2 in this case. Hence we get 04

_ _04

Step 2. We shall now need to use the cross product. This is what we get when we multiply the two digits of the given number together. Multiply the two digits of the number together and double it: 3 times 2 is 6, doubled is 12: We write 12 as 2 and carry over 1 to the next step.

_ 24

Step 3: In finding the first two digits of the answer we shall still need to square the first digit of the number. That means we square the left hand figure of the number. Here square of 3 will be 9. Add 1 which is carried over from last step. Hence we get 9 + 1 =10

1024

That’s the answer.

This method can also be compared with another shortcut to find the square of any number posted by me on Quickermaths.com in the past.

Let’s try another example by squaring 64.

Square of 64 =     Square of 6 | double of cross product of both given digits 4 & 6| square of 4

Square of 64 =      36 |2x6x4 | 16

=      36 | 48 | 16

Collapsing the numbers

=      36 | 48 + 1 | 6

=      36 + 4 | 9 | 6

=      40 | 9 | 6

Hence the answer is 4096.

Have you come across any other squaring method like this?

Multiplication Trick for Multiples of 11

If you know how to quickly multiply any number by 11 (click on the link to read further), the short cut multiplication method for 22, 33, etc. becomes easy to grasp. It’s an extension to the earlier method and you’ve seen earlier that there is no need to remember multiplication tables.

Multiplication by 11 is easy. Start from the right, add the two adjacent digits and keep on moving left. Since you can write only one digit in each step, if there is a carryover add it to the number obtained in the next step. So let’s begin to learn multiplication by multiples of 11.

Multiplication Trick for 22

For multiplication with 22, the rule is (number +next number)*2

Let us look at it step by step –
Step 1: For sake of simplicity, assume that there are two invisible 0 (zeroes) on both ends of the given number.
Say if the number is 786, assume it to be 0 7 8 6 0

Step 2:Start from the right, add the two adjacent digits and multiply by 2. Keep on moving left.
07860
Add the last zero to the digit in the ones column (6), and multiply by 2. Write the answer below the ones column.
Then add this 6 with digit on the left i.e. 8 and multiply by 2.
Next add 8 with 7 and multiply with 2.
Next add 7 with 0 and multiply by 2.
(0+7)*2     |    (7+8)*2  |    (8+6)*2   |   (6+0)*2
=   14   |   30   |  28   |  12

Step 3: Start from right most digit. Keep only the unit’s digit. Carryover and add the ten’s digit to the next number to the left. Doing this we get the answer as 17292.
Yes, job done. Quite simple, isn’t it?

Multiplication with Other Multiples Of 11

For multiplication with 33, the rule is (number +next number)*3
For multiplication with 44, the rule is (number +next number)*4
and so on….till
For multiplication with 99, the rule is (number +next number)*9. However, their is a simpler way of multiplication trick for 99

Multiplication Examples:
56789*22 = 0567890*22= (0+5)*2  |   (5+6)*2  |   (6+7)*2  |   (7+8)*2  |   (8+9)*2  |   (9+0)*2=1249358
123678*88 = 01236780*88 = (0+1)*8  |   (1+2)*8  |   (2+3)*8  |   (3+6)*8  |   (6+7)*8  |   (7+8)*8  |   (8+0)*8=10883664

Try it yourself. Share your experience with all by posting a comment below.

Shortcut to Find Square of 2-Digit Numbers with Unit Digit as 1

Special shortcut methods of squaring 2 digit numbers

In previous articles we’ve discussed special shortcut Vedic Math Techniques to find the square of any number ending in 5 and square of 2 digit numbers ending in 9.  In this article we will discuss –

Square of 2-digit numbers whose unit digit is 1

Let us take a 2 digit number in its generic form. Any two digit number whose unit digit is 1, say a1 can be expressed as 10a+1, where a is the digit in ten’s place

Square of a1= a2 | 2xa | 1

Here, ‘|’ is used as separator.

That means for the left most part of the answer, a is squared, hence first part will be a2. The middle part will be twice of a and the last or the right most part will always be 1.

Let us see a few examples.

(21)2= 2 squared | 2 . 2 |1 = 441
(31)2= 3 squared | 2 . 3 |1 = 961
(41)2= 4 squared | 2 . 4 |1 = 1681
(51)2= 5 squared | 2 . 5 |1 = 2601 (Here the square of 5 is 25 but since the product of 2.5 is 10 we write down 0 and add 1 to 25). Similarly,
(91)2= 9 squared | 2 . 9 |1 = 8281

Square of 3-digit numbers ending in 1

Now let us try to extend the above shortcut method to 3 digit numbers as well. Let us straight away start with an example 131.

Like earlier separate the given number in 2 halves, left hand side will have digits other than 1 and right hand side will have 1 as usual.

Hence, the answer is

(131)2= 13 squared | 2 . 13 | 1 =

= 169 | 26 | 1

= 17161

Let’s take another example of squaring a three digit number ending in 1.

261 = 26 squared | 2×26 | 1

= 676 | 52 | 1

= 68121

From the above illustrations you must have noticed that higher the initial number to be squared higher is the square in first part. Hence to extend this method to large 3 digit numbers one should be proficient in squaring any 2 digit number.

Try it yourself

21, 71, 91, 161, 231 and 321

Answers: 441, 5041, 8281, 25921, 53361 and 103041

This article is based on a suggestion given by a Quickermaths.com reader Vishal Mishra. If you also have some suggestions you can email it to me or post it here as comment. 

Vedic Maths Tricks for Multiplication

Both the videos given below cover Vedic Maths Multiplication Trick i.e. The Criss-Cross Method or Urdhva Tiryak Sutra.

Each video is made using different tools and aids. I would request you to share your opinion on which format of the recording did you like more. Please share your views by posting a comment below. I intend to make more such videos after getting your feedback.

 Vedic Maths Multiplication Tutorial: Video 1

 

Vedic Maths Multiplication Tutorial: Video 2

The videos are posted without any sort of editing. Kindly ignore all kind of disturbances and aberrations. Your feedback will help me in improving the quality of future video tutorials, which will be posted for free on Quickermaths.com.  

Best Tips for Modern Students for Vedic Mathematics

Vedic Mathematics is the name given to the ancient mathematics system. The “Bharati Krsna Tirthaji” from the Vedas rediscovered it and according to him, all the mathematics is based on the 16 sutras. These are also known as word formulas. Below are mentioned some of the tips for the students to learn easily and become a master of Vedic math.

It is all about the numbers

Whether numerical or word formulas both of them certainly employ the use of the numbers. Make yourself master of the numbers. Learn the general multiples of all the numbers and make a habit to spend your free time with numbers only. Practice as much as you can and you will be on the right track. You can also figure out something so that you come across these numbers repeatedly. You can paste wallpaper in your room, make some numerical figure as your desktop and subscribe to numerical magazines.

Try to Grip from the Fundamentals and then move forward

Have an approach, which will make youthe basics and fundamentals strong. Once you have a grip over the basics it means half of the work is done. Try to learn what it is all about the “Sutras” and the “Sub sutras” from the starting to the end. What does it all mean? Just solving the examples will not be sufficient but you have to make sure that you have the thorough knowledge of every aspect.

Practice as much as you can

Figures always need practice and you have to make them as your part and parcel. Try to practice every exercise you get your hand on and just solving the problems will not work check the answers also. If you get wrong answers, make sure you look for the right solution and method for a specific problem. There is no end to practice try as many problems as you can since Vedic math is meant to shorten your normal problem solving time pay special attention to any shortcuts you come across and learn them by heart.

Try to Get some Good References

It is always recommended to follow some trusted books. It is always true that right teaching and guidance can do wonders and you have to search both of these for you to get into the right direction. You can follow some good reference books and take some guidance in the form of internet, magazines, friends and family members. Here is a list of some popular vedic math and other quicker maths books

Some Mind and Brain Exercise can do wonders

Since Vedic math is all about the mind, you can learn a few exercises so that your brain is fresh while you start studying the Vedic math. Our brain needs regular exercise. In addition, you can learn how to refresh your mind after several intervals. Here are 7 resources available for exercising your brain

Keeping in mind the above tips will certainly give you an edge over the others in learning Vedic math and you can solve lengthy and complicated calculations beating the calculator after learning this math.

Author Bio
Claudia is a talented writer who has performed her duties well. She had taken up various assignments about IT Jobs training. She loves to share her knowledge and expertise with other people through her articles, follow me @ITdominus1.

Quick Multiplication by 5

Tricks for fast calculation by 5

It is a simple trick which is very intuitive and easy to understand. Many QuickerMaths.com followers might find it very simple. However, there are many who will enjoy this simple yet readily usable trick to multiply any number by five.

1. Multiplying 5 times an even number: halve the number you are multiplying by and place a zero after the number.

Example:

i. 5 * 136, half of 136 is 68, add a zero for an answer of 680.

ii. 5 * 874, half of 874 is 437; add a zero for an answer of 4370. Read More