Speed Up Your Calculations: Mental Maths

Calculations are a prominent reason for students fearing Mathematics. But they are a crucial life skill. It is important to deal with the fear of Mathematics at an early age. Calculations are important for a variety of reasons. They are critical for decision-making; they can also be used to communicate information in a clear and concise way. Calculations can help you develop critical thinking skills by requiring you to analyse problems, identify patterns, and draw conclusions.

This Story also Contains

1. Know Your Basic Maths Facts
2. Rounding Off
3. Estimation
4. Decomposition

Mental Maths can speed up certain types of calculations and help you solve Maths problems quickly and accurately, in the classroom or during tests. It can also be useful in everyday life, such as when you need to make quick calculations in your head while shopping or managing your finances. In addition to being practical, mental Maths and fast calculation skills can also improve your overall problem-solving abilities and boost your confidence in your Maths skills. Developing these skills can also help you perform better on tests and in other academic and professional settings where the ability to solve Maths problems is important.

There are many ways to improve your mental Maths and fast calculation skills, including practising regularly, learning strategies and techniques for solving Maths problems more efficiently, and working with a tutor or teacher to identify and address weaknesses. Some of the techniques of mental Maths to improve your calculation skills are listed – and explained – below.

Know Your Basic Maths Facts

Following are the basic Maths facts which can help you in day-to-day calculations:

1. Multiplication tables:

Knowing your multiplication tables can help you perform calculations quickly and accurately. Make sure you remember tables till at least 20 (the more the better) before starting. Try to not only memorise the tables unidirectionally but also in reverse order as well. For example, we know unidirectionally that 18 X 8 = 144 or 16 X 9 = 144. Try to remember 144 as the product of 18 and 8 or 16 and 9. Now, In this case we can easily comprehend that 8, 9, 16 and 18 are the factors or perfect divisors of 144.

2. Powers of 2, 3 and 5:

Try to remember the powers of 2 up to 10, 3 up to 8 and 5 up to 5. This will directly help you in prime factorization and in turn faster division.

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Rounding Off

Rounding is a mathematical technique that allows us to estimate the value of a number by replacing it with a number that is approximately equal, but simpler to work with. This can be useful when we need to make quick calculations in our head or when we want to simplify more complex calculations.

Rounding numbers to the nearest 10, 100, or 1000 can make calculations easier and faster. For example, if you need to add 345 and 678, you can round 345 to 350 and 678 to 680, which makes the calculation easier: 350 + 680 = 1030. Now if you want the exact answer then you can subtract 7 (5+2) from 1030, i.e., 1023.

Rounding can be a helpful tool for mental Maths, as it allows us to make quick estimates and simplify calculations. However, it is important to remember that rounded numbers are only approximate and if you want to get an exact answer you have to eliminate the round-off margin in the final stage.

Estimation

Estimation can be a useful tool when you need to calculate quickly and don't have a calculator available. For example, if you need to find the product of 35 and 24, you can estimate that it is about 800 (35 x 25 = 875, and 24 is slightly less than 25). This will give you a good idea of the general size of the answer, even if it's not exact. There are several different strategies that can be used for estimation. Here are a few examples:

1. Compatible numbers are pairs of numbers that are easy to work with mentally. By using compatible numbers, you can make quick estimates without having to perform exact calculations. For example, if you wanted to estimate the product of 8 and 9, you could use the compatible numbers 10 and 9, which would give you an estimated answer of 90.

2. Benchmarking involves using a known or familiar value as a reference point for estimating the size of other numbers. For example, if you wanted to estimate the sum of 85 and 107, you could use the benchmark of 100 to estimate that the answer is around 190.

Estimation allows us to get a sense of the size or magnitude of a number or calculation. However, estimates are only approximate and may not be completely accurate.

Decomposition

Decomposition is a mathematical technique that involves breaking down a number or calculation into smaller parts in order to make it easier to solve. It is a useful tool for mental Maths because it allows us to simplify complex calculations making them more manageable.

There are several different strategies that can be used for decomposition. Some of them are given below.

1. Place value decomposition involves breaking a number down into its individual place values (ones, tens, hundreds, etc.) in order to make it easier to work with. For example, if you wanted to add 672 + 394, you could decompose 672 into 600 + 70 + 2 and 394 into 300 + 90 + 4, which would give you an intermediate sum of 900 + 160 + 6.

2. Factorisation involves breaking a number down into its prime factors in order to make it easier to work with. For example, if you wanted to find the prime factorisation of 60, you could decompose it into 2 x 2 x 15, which would give you the prime factorisation of 2 x 2 x 3 x 5.

3. Partial sums decomposition involves breaking a calculation down into smaller, simpler calculations that can be performed mentally. For example, if you wanted to find the sum of 153 + 246 + 367, you could decompose it into (100 + 50 + 3) + (200 + 40 + 6) + (300 + 60 + 7), which would give you an intermediate sum of 600 + 300 + 400.

Mental Maths is a powerful tool that can help you to perform calculations faster without a calculator or other tools. By using techniques like rounding, estimation, and decomposition, you can simplify complex calculations and make them more manageable in your head. With practice, you can develop your mental Maths skills and become more efficient at solving problems. Whether you are a student looking to improve your Maths grades or an adult looking to speed up your everyday calculations, mental Maths can be a valuable skill to have.

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