Arithmetic Progressions – An arithmetic progression is a series in which each term is derived by addition or subtraction of a common numeral to its previous term. The Arithmetic sequence formula is used for determining the nth term of an arithmetic progression.
The nth term formula is as below.
an = a1 + (n – 1) d
an = nth term to be calculated. a1 = the 1st term of the series.
n = number of terms. d = common difference
EXAMPLE
Find the 30th term of the arithmetic progression 0, 2, 4, 6, 8, 10, 12, 14, ……
A fraction is said to be in simplest form when there is no common factor between the numerator and the denominator. The simplest form is also known as representing the fraction in ‘lowest terms’ where the numerator (top of the fraction) and denominator (bottom of the fraction) are whole numbers and cannot be divided further to get a lower number.
Numerator
The upper part of the fraction is called the numerator.
Denominator
The lower part of the fraction is called the denominator.
How to reduce a fraction in the lowest form?
Approach 1: Repetitive Division
To reduce the fraction in its lowest term or simple form, you need to divide them with their common factors. Keep on dividing till the upper and lower number has no common factor except 1.
Approach 2: Prime Factorization
Another way to do this is to break both the numerator and denominator into a product of prime numbers i.e. perform the prime factorization. Cancel out the common terms. The remaining fraction will be termed as the simplest form of the fraction.
Let’s begin
To convert decimal in simplest form, we need to first understand
How to convert a decimal number to a fraction?
Step1: Count the number of digits after the point (.) or decimal. Say it’s ‘X’
Step2: Now your fraction turns out to be:
The numerator will become your decimal number but without the ‘.’ (Decimal)
The denominator will be 1 followed by ‘X’ zeros as calculated in step 1.
Back to the problem, first, we need to convert 0.125 into a fraction.
By following the above steps, we can see that there are three digits after decimal i.e. 1,2,5
So, according to step 1, we have to count the digits after decimal which is 3 in the case of 0.125
Next, it’s time to build our fraction!
Numerator = 125 (remove decimal)
Denominator = 1000 (1 followed by 3 zeros)
Finally, we get our fraction as Numerator/denominator
Now that we have got our fraction as 125 / 1000.
Step1: 0.125 can be represented as 125 / 1000.
Next, we need to convert it into the simplest form by reducing it to the lowest terms.
We need to find common factors of 125 and 1000. It is always good to start with prime numbers. The prime first factor is 5. So, divide both 125 and 1000 by 5.
Step2: – Divide 125 / 1000 by 5
We get,
125 / 1000 = 25 / 200;
5 again is the common factor of the new fraction (25 /200). So, we again divide numerator and denominator by 5
25 / 200 = 5 / 40
Now, 5 again turns out to be the common factor of 5 and 40. So, on dividing 5 and 40 by 5 we get:
5 / 40 = 1 / 8
Now, there is no common factor of 1 and 8. So, we stop our division here.
As we know that 60 is a whole number and a composite number (divisible by more than 2 numbers). Let us find the prime factors of 60 by the following method.
1ststep – Divide 60 with its smallest prime factor, which is 2
Result:- 60/2 = 30
2ndstep – We need to see if 30 is further divided by 2?
Result:- 30/2 = 15
3rdstep – Check if 15 is further divisible by 2
Result:- 15/2 = 7.5
Things to remember – Prime factors cannot be in decimal or fractions. It should be a whole number. So, we proceed to the next prime number i.e., 3
4th step – Divide 15 by 3
Result:- 15/3 = 5
5thstep – Now, we know that prime factor should be in whole number. So, if we divide 5 by 3, it will give us a decimal or fraction. So again, we take the next prime number which is 5
Result:- 5/5 = 1
Now, we just got 1 at last. We cannot divide and calculate prime factors further because multiple of 1 is 1
ANSWER of the Prime Factorisation of 60
Thus, the Prime Factorisation of 60 = 2 × 2 × 3 × 5 or 22 × 3 × 5
Before delving deeper into the topic, it is essential to have a comprehensive idea of what is Vedic Math.
Vedic Maths is a gift to this world from the early scholars of India. The name “Vedic” is borrowed from the Sanskrit word “Veda” which signifies knowledge. Shri Bharat Krishna Tirthaji found it throughout his thorough research on the Vedas.
Vedic Mathematics is a common name provided to a collection of sixteen sutras (mathematical formulae) and thirteen sub sutras (corollaries) that can be utilized for resolving mathematical problems in a very simpler and more natural way.
Vedic Math allows procedures and multiple shortcuts to improve your master factoring calculations in split seconds.
The simplicity of the methods boosts versatility and also encourages learners to get their very own different way. Here occupies the virtue of Vedic Maths. It does not endure restricted to the corresponding rigid approach and enables the student to be imaginative.
Identify The Major Benefits Of Learning Vedic Maths
Due to the simplicity and the efficiency of Vedic math methods, it is obtaining universal fame. It contributes advantages not only to students and kids but to anyone who requires to study math more efficiently. If you are not conscious of the perks that Vedic Math has to offer, then you should have a look at the following list of top benefits of learning Vedic Maths.
Vedic calculations strengthen the efficiency of your math-solving skills.
It supports solving mathematical problems 10 times quicker.
It intensifies the brain, increases mental agility, and aptitude.
Vedic math for kids supports in developing visualization and consistency.
The combined method also gives a collection of independent cross-checking systems.
The element of choice and adaptability helps in the growth of precision of mind and intuition.
Vedic math techniques enhance consciousness and knowledge of mathematics.
It decreases the addition of calculators.
It develops an interest in math and encourages eliminating math phobia.
What is truly inspiring about Vedic Maths is that the concepts are so simple; they can be quickly understood and followed by any pupil. This quality performs the whole discourse of mathematics both simple and fun. Mathematics has three main divisions: Arithmetic, Algebra, and Geometry.
Aspiring Vedic Maths Tricks A Student Must Know:
Arithmetic deals with numbers, Algebra with symbols usually the letters of the alphabet and Geometry deals with shapes and patterns like points, lines, surfaces, and solids. These 3 divisions develop in a structured way and embrace all fields of mathematics in the Vedic system, ‘tough’ problems or substantial sums can oftentimes be resolved instantly by using the Vedic method.
The techniques practiced in Vedic Maths are integral, direct, and simple. With Vedic Maths, you can solve mathematical and numerical calculations in a quicker manner.
By practicing Vedic Maths tricks, one can do calculations 10 times quicker than using common methods that you were trained in school. Vedic Maths gives techniques and alternatives to master numerical calculations in split seconds.
We are existing in the age of a huge amount of competitions and Vedic Mathematics methods come to us as a blessing for all the competitions. Modern maths, a scary thought commands a greater significance of effort in knowledge.
Maths can be studied and learned with the least shots in a very short span of time and can be interpreted into a playful and blissful subject with the help of Vedic Maths.
If you are one who does not expressly enjoy maths, you might just begin understanding maths in a different light. This is the strength of Vedic Maths. It attracts you in with its simple to understand of the idea, performing maths a pleasant drive.
With the level of numeracy patterns running down globally, there is a tremendous requirement for modern alternative approaches that make maths enjoyable and entertaining.
Vedic Mathematics is one such way that strengthens the fundamentals of children and reduces math anxiety.
Vedic Mathematics system to quite an extent also supports students in improving their spiritual part of the personality. It can interject creativity in understanding and smart students while maintaining the slow-learners grasp of the basic ideas of mathematics.
The infinite practice of Vedic math can be fulfilled without any difficulty creating interest in a topic that is generally dreaded by children.
Many Secondary School students consider Vedic Mathematics a very complicated and tricky subject. Some pupils confront difficulty with basic arithmetical operations. Some students consider it challenging to manage numbers and balance equations. In other words, abstract and logical reasoning is their barrier.
Mathematics is one such division that involves thinking and the mind is used at its best. Most of the students studying conventional mathematics can solve problems that are taught to them at school, but they are unable to solve the problems that are new and not taught to them.
The reason for this is – lack of basic concept clarity. Hence, instead of the conventional way, such a method should be received or allowed that provides basic clarity so that overall learning can be improved. But we need not develop any such method because of our rich history and great mathematicians.
Wrapping it up:
If you’re still striving with math practices every day, Vedic Math may improve your viewpoint on how you look at solving complex difficulties in the first place. If you can see the knowledge in combining learning with comfort, there are high possibilities that you will fall in passion with Vedic Math. Give this blog a thorough read to put an end to all your queries on “Advantages Vedic Math.” Understand the definition, history, advantages, and implement these wonderful tricks to fasten your competitive exams like never before.
Mathematics is an unavoidable subject. And for effective learning, one needs dedicated practice to achieve the best results. Set aside a time for your self-study and try to solve your mathematics on your own. With complete focus, determination, time, work, and practice you can attain real strides in maths. However self-studying maths is quite hard.
Basically, it is an industrious journey as much as an intellectual one, so it needs a bit of your determination along with a great sense of understanding. But it is also a fact that many people start this self-studying journey and then easily drop after a few months. It is because they don’t know the right pattern and the right practices of self-studying.
If you are also the one who drops the idea of self-study then this guide is for you. After implementing this, you will surely learn one thing that only you can help yourself in solving that problem and no one can teach you better and faster than yourself.
Steps to Study Mathematics on Your Own
Step 1. Analyse from Where You Want to Start
Obviously, the first and very important part of self-study is to know where you want to start. Analyse the thing and find out from where you want to start practising mathematics.
Let’s talk with the example for this, we all know calculus and its applications are way easier if you have a clear knowledge of Trigonometry and Analytic Geometry.
But Analytics Geometry has some of the elements of Trigonometry. So, you can start your mathematics practice with Trigonometry. So, when you know where you want to start, you need to practice hard to make self-study works well in every manner.
Step 2. Get a Syllabus to Avoid Unnecessary Practice
Whenever we get lost while travelling, we take the help of Google maps to guide us in the right direction. So, what you should do when don’t have a sequence to learn mathematics. Here the syllabus comes into the existence. There is a particular syllabus for every exam and every class.
So, it is good to use an already designed syllabus so you will always go in the right direction with your mathematics practice. Mathematics syllabus can be the roadmap of your self-studying success.
One can easily get a syllabus online, just a single Google search will provide you what you are looking for or you can also look at the resources of the university and check the syllabus for maths subjects.
Step 3. Collect the References, and Required Textbooks
Standard mathematics learning required to go to school, attend classes, do homework, and then wait for it to be checked. This is the way you normally adapt when you are in school. But is this sufficient to learn mathematics? of course not, you need to practice more and more in order to clear your doubts.
There are solved problems or solution manuals type of textbooks available out there, buying them is the smartest thing you can do for self-study. It is good to use these textbooks side-by-side to your problem-solving routine.
Mathematics problems are rather hard, the discussion is succinct and direct to the point, but you will certainly get better problem-solving. Here we are not saying that you need to look at the solution every time when you are solving a maths problem. but it is a good solution whenever you get stuck in a problem as you can easily find out the solution easier and faster.
Step 4. Prioritize Concept-Based Preparation
Mathematics is tricky and concept based you need to be focused and understand it to be with the proper concentration. It is misunderstood by the students that they can memorize how a difficult question can be solved. But it is completely a myth.
You cannot memorize anything until you don’t have a great understanding. Same as, it is also wrong to understand something but don’t practice it, without practice, one cannot get better results.
It is good to do concept base practice for your mathematics self-study. Always remember that mathematics is a sequential subject, so it is essential to have a firm understanding of every key concept that underpins maths topic.
Mathematics is a subject that requires complete focus and more concentration than any other subject. For self-study, one needs to create a distraction-free environment. It could be the determining factor when solving problems or equations in trigonometry, geometry, and algebra.
One can take the help of music for this, a soothing background music will help you to create a relaxing atmosphere and energize the flow of information. Light music in the background can foster the room’s environment for maximum concentration.
Step 6. Manage Your Time for Both Problem Solving and Studying
As told earlier, you have to practice whatever you have learned. The more you practice the better it will fix in your mind. So, you need to manage your time for first learning and then practicing. Don’t just let things go when you learn, practice as much as you can until you’ll get better in this.
Learning happens when you recall information recollect information from your head, not when you try to put things in there. So, it is good to aside from learning time, set aside time for practice also.
Wrapping Up
Mathematics is not difficult but tricky. You just need to clear concepts and pay proper attention to understand the concepts. Apart from this, a little addition of self-study can do wonders with your mathematical performance. The above information is just to let you know how easily and effectively you can learn maths. All you need to do is to adopt a proper pattern of self-study and seriousness of learning.
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