From the second we start learning math in school students are taught concentration, perseverance, and the ability to do basic mental arithmetic.
As time passes we start learning more complex topics and preparing for the SATs, A-level classes, and so on until our college years. We are taught any complex mathematical procedure like square root, trigonometry, algebra, and mental calculations. But we have plenty of tips to help with maths.
Keep in mind that some subjects in math are more useful than others. Knowing how to do quick and effective mental arithmetic in our everyday lives is much more useful than log, square root, and others.
With time you will notice that knowing how to quickly do a calculation without the need for a calculator will give you many advantages in life. For now, you can check out these fun math lessons.
You're probably wondering how you can get better at math? Rest assured that there is more than just one method, procedure, or way to improve your math level.
How Could Mental Arithmetic Help You?
Here is a quick list of reasons why doing mental arithmetic and developing the skill to do calculations in your head is positive.
- Free up your mind once calculating becomes second nature. You can save time and money once you learn how to calculate properly.
- Be free of a calculator: we are heavily dependant on technology, learning a trick or two for calculus can save you from countless times where you have to take out your calculator.
- Impress: your friends will be impressed with your addition and multiplication skills.
- You won’t get ripped off when it comes to money.
- You’ll need fewer math tutorials!
Learn How To Calculate Quickly
The first step is to make the mental arithmetic practice regular if you want a fast improvement. With the repetition, your brain will develop a natural and obvious sense of all the calculations.
You need a notebook and perhaps an exercise book to help you practice mental arithmetic. This way you will keep a record of every trick you've used, the mental progress you're making, and how fast you're going.
Having trouble finding a teacher near you? Try an online math tutor.
Here is a list of basic tools to boost your skills:
- Know addition and multiplication tables
- Know complements of the number 10
- Know squares up to 15² (225) as well as the powers of 2
- Multiplying by powers of 10 with negative exponents (moving the decimal place to the left) and positive exponents (moving the decimal place to the right)
- Dividing by a number is the same as multiplying by its reciprocal. For example, divided by 0.25 is the same as multiplying by 4
- Learning any special method: (a+b) ² = a²+2ab+b², (a-b) ² = a²-2ab+b², (a+b) (a-b) = a²-b²
- Learning the rules of factorization
- Know the orders of magnitude for Pi (3.14159), the Golden Ratio (1.618), etc.
Fast Math Tips
Write Down the Problem
It's impossible to become an extraordinary mathematician who can add, subtract, multiply or divide complicated numbers in their head at once. To reach a good level of mental arithmetic you must take it easy!
Write down all of the calculations you need. Some students who are learning math find it easier to solve calculations or problems when they can visualize them on paper.
Become Friends with Approximation
Learning and practicing calculations with an approximation is a good way to improve your mental arithmetic skills. If you need to know what 60 x 120 is, try solving it by multiplying the first number by 100 (a much simpler calculation) and then work from there. With this, you will know approximately how many digits the final number should have.
Numbers Into Shapes Or Objects
Another method is trying not to focus too much on the numbers. Instead of seeing numbers in your head try imagining the single digits as visual blocks or think of the different parts of the calculations as building blocks. Allocating an image in your head to the sets of numbers can change the whole way you approach that group of digits.
These tips and tricks are highly recommended by primary school teachers and tutors. If these tricks aren't enough, then keep reading to find out how you can improve your mental arithmetic.
Look at the last digit
Look at how the number ends.
If it’s 0, 2, 4, 5, 6, or 8 you can divide it by 2, 5, or 10.
For example, 28 ends with an even number so it’s divisible by 2, while 55 ends with a 5 and is divisible by 5.
260 ends with a 0 so it’s, therefore, divisible by 10.
What about 3 or 9? Add up the digits to find out if the number is divisible by 3 or 9.
A number is divisible by 3 if the sum of its digits is equal to a multiple of 3 (e.g.: 18 = 1 + 8 = 9, a multiple of 3).
A number is divisible by 9 if the sum of its digits is equal to a multiple of 9 (e.g.: 936, 9 + 3 + 6 = 18, which is 1 + 8 = 9, which is a multiple of 9).
If the sum of the digits is divisible by 3 and an even number, it’s divisible by 6 too.
Deconstruct the numbers.
For example, 72 + 29 is (70 + 2) + (20 + 9) = (70 + 20) + (2 + 9) = 90 + 11 = 101.
Or even: 13 + 48 is 13 + (50 - 2) = 63 - 2 = 61.
Learn to simplify numbers.
For example, 1958 – 1907. The number 1900 is included in both numbers so just subtract the tens and units, 58 - 7 = 51.
The Japanese Method of Multiplication
You don't feel ready to do complicated multiplication in your head? The visual Japanese multiplication technique allows you to see operations much more clearly. All you have to do is draw lines and the result appears as if by magic.
Learning this method will allow you to carry out calculations in your head easily. Envisioning the lines in your head allows you to visualize the result too.
Fractions can produce headaches! To avoid the step of having a common denominator for adding or subtracting fractions use the butterfly method to do it in your head.
For example: 3/4 + 2/5
First do some cross multiplication: 3 x 5 =15 and 4 x 2 = 8
Then add the two results to get the final numerator, 15 + 8 = 23
To find the denominator, multiply the two denominators: 4 x 5 =20
Therefore: 3/4 + 2/5 = 23/20
You can also use this technique to subtract fractions.
How Do You Multiply by 11?
To work out 32 x 11, all you have to do is multiply 32 x 10, then add 32, so 320 + 32 = 352. Do you know the second technique to do it in your head?
For the same problem, 32 x 11, all you have to do is add the 2 digits from the number being multiplied by 11 and place them between the two numbers.
Therefore, 3 + 2 =5, putting the resulting 5 between the 3 and 2 and we get 352!
If the addition results in a number with two digits like multiplying 56 x 11, the solution is simple. 5 + 6 = 11, we place the second 1 between the 5 and 6 and we add the second 1 to the 5. We, therefore, get 616.
Some Extra Advice
- Wisely group numbers before working anything out.
- Put units that make 10 together to make your additions easier.
- Adding or subtracting by 9, 19, or 29 just add or subtract by 10, 20, or 30, before adding or subtracting 1.
- Dividing by a number is the same as multiplying by its reciprocal,
- To add 2 fractions, make sure they have the same denominator.
Follow these maths tips to the letter!
Online Resources to Improve Your Mental Arithmetic
The internet is an excellent resource to help you improve your math skills. There are plenty of websites that have more than one lesson with quizzes, tests, and exercises.
- BBC Bitesize: The BBC provides resources for students of all ages. Great school-aged children.
- Khan Academy: This website features video lessons as well as practice questions to help you learn.
If you want to get good at math and mental arithmetic you need to learn the basic principles by heart as much as you know the addition and multiplication tables.
Train your brain to remember, everything will become second nature, and your ability in mental arithmetic will increase exponentially.
This, of course, requires time and a personal commitment but the result is worth the cost because you’ll have these reflexes for the rest of your life.
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