# The Science of Mental Math: How It Works and Why It Matters

## Mental Math: What Is It and Why Is It Important?

Mental math is a skill that many people use every day, but may not realize how much it helps them in various aspects of life. Mental math is not only useful for solving math problems, but also for developing logical thinking, enhancing memory, and boosting confidence. In this article, we will explore what mental math is, why it is important, and how to improve it with some strategies, techniques, and resources.

## What is mental math?

Mental math is a group of skills that allow people to do math in their head without using pencil and paper or a calculator. According to the Manitoba Association of Mathematics Teachers, mental math is:

## mental math

A combination of cognitive strategies that enhances flexible thinking and number sense. It is calculating mentally without the use of external memory aids. It improves computational fluency by developing efficiency, accuracy, and flexibility.

Some examples of mental math are:

Adding or subtracting two-digit numbers by breaking them into tens and ones.

Multiplying or dividing by powers of ten by moving the decimal point.

Estimating the answer to a problem by rounding or using benchmarks.

Solving problems involving fractions, decimals, or percentages by using equivalent forms or proportions.

Using patterns, properties, or rules to simplify calculations.

The skills involved in mental math include:

Remembering math facts, such as times tables or basic operations.

Visualizing numbers and their relationships, such as place value or magnitude.

Manipulating numbers and expressions, such as regrouping or expanding.

Applying strategies and techniques, such as shortcuts or tricks.

Checking the reasonableness of the answer, such as using estimation or inverse operations.

## Why is mental math important?

Mental math has many benefits for students and adults alike. Some of the benefits are:

It enhances the ability to concentrate and focus on the task at hand.

It stimulates the interest and curiosity in math and other subjects.

It improves the self-confidence and self-esteem of the learner.

It helps with the application skills in math and other domains, such as science, engineering, or finance.

It helps to reduce mistakes and errors in problem-solving.

It is strongly associated with better memory skills and cognitive functions.

It stimulates both sides of the brain, which are responsible for logic and creativity.

There is also research evidence that supports the importance of mental math. For example, a study of first-grade students found that those who could quickly recall addition facts had more cognitive resources to learn other skills and concepts. Another study of fifth-grade students found that there was a significant positive correlation between mental computation and mathematical reasoning. A third study of college students found that engaging the brains prefrontal cortex during mental math exercises was linked to better emotional health.

## How to improve mental math skills?

The good news is that mental math skills can be improved with practice and guidance. Here are some strategies and techniques that can help you improve your mental math skills:

### Break addition and subtraction problems into parts

### Add or subtract two-digit numbers by splitting them into tens and ones. For example, to add 37 and 46, you can do: 37 + 46 = (30 + 40) + (7 + 6) = 70 + 13 = 83 To subtract 46 from 83, you can do: 83 - 46 = (80 - 40) - (3 - 6) = 40 - (-3) = 43 Use the distributive property for multiplication

### Multiply two-digit numbers by using the distributive property of multiplication over addition. For example, to multiply 37 by 12, you can do: 37 x 12 = (30 + 7) x 12 = (30 x 12) + (7 x 12) = 360 + 84 = 444 Use the power of ten for division

### Divide by powers of ten by moving the decimal point to the left. For example, to divide 444 by 100, you can do: 444 100 = 4.44 To divide by other multiples of ten, you can use the same principle. For example, to divide 444 by 20, you can do: 444 20 = (444 10) 2 = 44.4 2 = 22.2 Estimate the answer before calculating

### Estimate the answer to a problem by rounding or using benchmarks. This can help you check the reasonableness of your answer and avoid mistakes. For example, to estimate the answer to 37 x 12, you can do: 37 x 12 40 x 10 = 400 The actual answer is 444, which is close to the estimate. Use patterns and rules to simplify calculations

Use patterns and rules that apply to certain numbers or operations to make calculations easier. For example, you can use these rules:

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Any number multiplied by zero is zero.

Any number multiplied by one is itself.

Any number multiplied by ten is the same number with a zero added at the end.

Any even number multiplied by five is half of the number with a zero added at the end.

Any odd number multiplied by five is half of the number minus one with a five added at the end.

The sum of two odd numbers or two even numbers is even.

The sum of an odd number and an even number is odd.

The difference of two odd numbers or two even numbers is even.

The difference of an odd number and an even number is odd.

## Conclusion

Mental math is a valuable skill that can help you in many ways. It can improve your concentration, curiosity, confidence, application, accuracy, memory, and creativity. It can also make math more fun and enjoyable. To improve your mental math skills, you can practice using strategies and techniques such as breaking problems into parts, using the distributive property, using the power of ten, estimating the answer, and using patterns and rules. You can also use resources and games that are available online or offline to challenge yourself and have fun with mental math.

So what are you waiting for? Start practicing mental math today and see how it can change your life!

## FAQs

#### Q1: What are some common mental math tricks?

A1: Some common mental math tricks are:

To square a two-digit number that ends in five, multiply the first digit by itself plus one, and put 25 at the end. For example, to square 35, you can do: 35 x 35 = (3 x (3 + 1))25 = 1225 To multiply two numbers that are close to 100, subtract each number from 100, add the differences, and subtract the product of the differences from 10000. For example, to multiply 96 by 97, you can do: 96 x 97 = 10000 - ((96 - 100) + (97 - 100)) - ((96 - 100) x (97 - 100)) = 10000 - (-4 + -3) - (-4 x -3) = 10000 - (-7) - (12) = 10000 + 7 - 12 = 9995 To divide a large number by five, multiply it by two and move the decimal point one place to the left. For example, to divide 876 by five, you can do: 876 5 = (876 x 2) 10 = 1752 10 = 175.2

#### Q2: How can I help my child with mental math at home?

A2: Some ways to help your child with mental math at home are:

Encourage your child to use mental math in everyday situations, such as shopping, cooking, or playing games.

Ask your child to explain their mental math strategies and techniques, and praise their efforts and achievements.

Provide your child with feedback and guidance on their mental math skills, and help them correct their mistakes.

Challenge your child with different types of mental math problems, such as word problems, puzzles, or riddles.

Use online or offline resources and games that are designed for mental math practice and fun.

#### Q3: Is mental math tested in standardized exams?

A3: Yes, mental math is tested in some standardized exams, such as the SAT, ACT, GRE, GMAT, or MCAT. These exams often include questions that require quick and accurate mental calculations, such as arithmetic operations, fractions, decimals, percentages, ratios, proportions, exponents, roots, or algebra. Therefore, practicing mental math can help you improve your score and performance on these exams.

#### Q4: What are some challenges or difficulties with mental math?

A4: Some challenges or difficulties with mental math are:

Lack of confidence or motivation to use mental math.

Lack of pr