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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**!

Does school Math bring financial literacy? Find out!

## 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.

### For Addition

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.

### For Subtraction

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.

### Butterfly Fractions

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.

Check for online Math tutor here on Superprof.

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