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Mental Maths: Overview, Techniques, Benefits, Tips to Improve

Mental Maths involves performing calculations in your head, improving speed, problem-solving, memory, and confidence in numerical tasks. Check this article to know everything about mental math.

Neha Tanna1 Oct, 2024

Mental Maths: Mental maths is the process of doing mathematical operations alone using the human brain, devoid of the need for calculators or other aids. When calculators are unavailable or the computation time is significantly less than the computation time, people resort to mental maths.

Mental maths can be used to do arithmetic operations quickly for calculations. Primary school students in grades 1 through 5 can practise mental maths by employing shortcuts and time-saving techniques. Specific strategies created for different types of math problems are included in mental math techniques. Since their capacity for mental computation is the greatest, very few people are called mental calculators. The majority of the methods depend on the decimal system of numbers. Which methods to utilise is determined by the choice of radix.

What is Mental Maths?

As the name suggests, mental math refers to a combination of skills that allows people to complete arithmetical calculations “in their head” without the assistance of calculators or other resources. Mental maths is helpful in daily life to provide answers to a variety of questions, such as:

What is a certain item's final selling price?
What is the appropriate quantity of change I should get from the cashier?
When should I leave so that I may go to a certain location on time?

Related Links -

Mental Maths	Mental Maths Worksheet for Class 2
Mental Maths for Class 2	Mental Maths Worksheets for Class 3
Mental Maths for Class 3	Mental Maths Questions With Solutions
Mental Maths for Class 4	Mental Maths Worksheets for Class 4
Mental Maths for Class 5	Mental Maths for Class 7

Mental Maths Techniques

Mental math techniques help in performing calculations quickly in your head without the need for paper or a calculator. Here are some common and useful mental math strategies:

Estimation

When performing mental calculations, one must think in terms of scaling. For example, the estimating approach provides the expected number of digits for the final response when the product of the integers 1 531 and 19 625 is obtained. Here's one method to go about doing this. 1 531 is rounded to the nearest thousands = 1500 and 19 625 rounded to the nearest thousands = 20000 So, the result of 1500 × 20000 = 30 000 000 The actual result is 1531 × 19 625 = 30 045 875.

Factors

Factors are numbers that divide evenly into another number. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12. Every number has at least two factors: 1 and itself. Prime numbers have only two factors, while composite numbers have more. Factoring is crucial in simplifying fractions, solving equations, and analyzing number properties. For instance, 14 × 15 = 201 is not reasonable. 15 is a multiple of the number 5, 14 is a multiple of the number 2. Hence the product must be an even number. A number that is a multiple of 5 and 2 is a multiple of the number 10. The right answer is 210.

Finding differences

i) Direct computation

Consider two numbers a and b. The calculation is performed digit by digit when the second number's digits are smaller than the first number's digits. For example, find the difference of 872 – 41. Subtract 1 from 2 in the one’s place and 4 from 7 in the 10’s place. The final answer is 831.

ii) Indirect computation

Indirect computation refers to solving problems by using alternate methods or intermediary steps rather than direct calculation. It often involves breaking a complex problem into simpler parts or using properties of numbers to find the solution. For example, instead of multiplying two large numbers directly, you can decompose one number into smaller components or use approximation methods to get a quicker answer.

iii) Borrow method

The borrow method, commonly used in subtraction, helps when the top digit in a column is smaller than the bottom digit. To perform this, you "borrow" 1 from the next higher place value (e.g., the tens column), adding 10 to the smaller digit to allow subtraction. This is typically used in multi-digit subtraction to avoid negative results in individual columns. Subtract the numbers from left to right. For example:

iv] Using square numbers

Using square numbers is a mental math technique that leverages the fact that squaring a number (multiplying it by itself) provides useful reference points for quick calculations. For example:

1 ²	1	11 ²	121	21 ²	441
2 ²	4	12 ²	144	22 ²	484
3 ²	9	13 ²	169	23 ²	529
4 ²	16	14 ²	196	24 ²	576
5 ²	25	15 ²	225	25 ²	625
6 ²	36	16 ²	256	26 ²	676
7 ²	49	17 ²	289	27 ²	729
8 ²	64	18 ²	324	28 ²	784
9 ²	81	19 ²	361	29 ²	841
10 ²	100	20 ²	400	30 ²	900

v) Finding roots

Finding roots, particularly square roots or cube roots, involves determining which number, when multiplied by itself (or cubed), gives the original number.

vi) Approximation of common logarithms

Approximating common logarithms (logarithms with base 10) involves estimating the value of a logarithm for numbers that are not exact powers of 10.

One must know the following logarithm rules.

log(a × b) = log a + log b
log (a/b) = log a – log b
log m ⁿ = n log m
log 1 = 0
log 0 = undefined

How to Improve Mental Maths?

Improving mental maths skills requires consistent practice and the use of specific strategies. Here are some effective ways to enhance mental maths abilities:

1. Practice Regularly :

The more you practice, the better you get. Set aside time daily to solve basic arithmetic problems without using a calculator.

2. Learn Number Tricks :

Familiarize yourself with number patterns, shortcuts, and tricks like multiplying by 11, squaring numbers, or adding/subtracting multiples of 10 to improve speed.

3. Break Down Complex Problems :

Divide larger problems into smaller, simpler steps. For example, break up numbers when adding or multiplying to make calculations easier.

4. Use Estimation :

Estimating the answer first can help in arriving at the correct solution faster by narrowing down possibilities.

5. Memorize Key Facts :

Memorize multiplication tables, square numbers, and basic arithmetic rules to reduce the need for lengthy calculations.

6. Play Mental Maths Games :

Engage in puzzles, brainteasers, or apps designed to improve calculation speed and accuracy in a fun, interactive way.

Benefits of Mental Maths

Mental math offers several key benefits:

Improves Numerical Fluency : Enhances your ability to perform calculations quickly and accurately without external tools.
Boosts Problem-Solving Skills : Encourages thinking creatively to find shortcuts and strategies for solving problems efficiently.
Enhances Memory : Strengthens working memory by requiring you to hold numbers and steps in your head while calculating.
Increases Confidence : With practice, you gain confidence in handling numbers in real-life scenarios like shopping or budgeting.
Saves Time : Makes everyday tasks faster by reducing reliance on calculators or paper.

About CuriousJr Mental Maths Classes

We at Physicswallah helps you to master the art of problem-solving with over 50 mental math strategies designed to boost your speed and accuracy. Enhance your logical reasoning and thinking skills to tackle complex problems with ease. Our CuriousJr Classes not only improves your ability to solve challenging tasks but also strengthens your overall cognitive abilities, empowering you to achieve more in less time.

Mental Maths FAQs

What are mental math questions?

Mental math is a group of skills that allow people to do math “in their head” without using pencil and paper or a calculator. One of these skills is remembering math facts, like 8 × 5 = 40. Other skills include rounding numbers and estimating calculations.

What is another name for mental math?

Mental math is the ability to perform mathematical calculations in your mind. It is also known as mental arithmetic, mental calculation, quick math, fast math, or doing math in your head. In German, it is known as Kopfrechnen, which translates into English as “head calculation”.

What is the fastest mental math system?

Vedic mathematics

Does mental math improve memory?

Mental arithmetic is a great tool for training the memory and concentration.

Why do we need mental math?

Mental arithmetic enables children to visualize numbers and make calculations mentally.

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