Online Math Center

# Mental Math: 5 Tricks You Can Do in Your Head Without a Calculator

Quick, just off the top of your head, what’s 84% of 25?

If you have to answer this type of question without a calculator, chances are you’re not going to be quick about it all. Chances are, you might also experience some math anxiety that makes you feel overwhelmed, apprehensive, or as if you’re having a mental block that prevents you from solving the exercise.

Whether you’re a parent or a student, you can easily gain some confidence and boost your math skills using a few mental tricks for solving math problems in your head at lightning speed. But first, let’s see why mental math is important and how it helps expedite the problem-solving process.

## Why is mental math important?

Doing basic mental math using low numbers or amounts is a reality of everyday life for most people. For some people, this is almost second nature and it is very useful when shopping, paying a cashier, counting items, or scheduling something.

But beyond these simple applications in daily life, mental math can help solve more complex problems that many students fear. Knowing a few mental math tricks helps students gain more confidence and overcome math anxiety when they are called to solve problems on the blackboard at school. Also, there are several other benefits that mental math provides, including:

• Solving math problems faster, especially during competitions or exams when calculators are not allowed and time is limited;
• Increasing mental agility, by keeping the brain engaged in exercises and problem-solving rather than relying on technology for every answer;
• Enhancing number sense, which allows students to mentally manipulate numbers in different ways to successfully solve a problem.

To enable you to make the most of these benefits, here are a few mental math tricks that you can practice every day without a calculator.

## Tips and tricks you should know

1. The simple rules of divisibility

When you want to evenly split things, knowing these simple divisibility rules can help you quickly solve problems before you even have a chance to whip out a calculator.

• All multiples of 2 are divisible by 2 and they always end in 0, 2, 4, 6, or 8.
• All multiples of 3 are divisible by 3 and the digits always add up to 3 or multiples of 3 like 6, 9, 12, 15, etc.
• All multiples of 4 are divisible by 4 and the last two digits are always divisible by 4 and pass the rule for multiples of 2.
• All multiples of 5 are divisible by 5 and always end in 5 or 0.
• All multiples of 6 are divisible by 6 and pass the same rules for both 2 and 3.
• All multiples of 9 are divisible by 9 and the sum of the digits is always divisible by 9.
• All multiples of 10 are divisible by 10 and the number always ends in a 0.
• All multiples of 12 are divisible by 12 and they pass the divisibility rules for 3 and 4.

2. Think-of-a-number tricks

If you want to make an impression, think-of-a-number tricks are a great way to show your math skills and make any mental math practice fun. As a student, you can try them with your peers or parents, and as a parent, you can definitely make your child more interested in math with these captivating tricks. For example, here’s one such trick:

1. Think of a number.
2. Multiply it by 3.
4. Divide this number by 3.
5. Subtract the original number from the result obtained after dividing by 3.

Here’s another cool think-of-a-number trick you can practice and use to impress your friends:

1. Think of a number.
3. Double that.
4. Subtract 4.
5. Cut that in half.

3. Adding 9 to any number

Adding 10 to any number is easier than adding 9. So do exactly that and then subtract 1. For example, if you have to solve 9 + 8, you can add 1 to 9 and make it 10, and then subtract 1 from 8 and make it 7. So instead of solving 9 + 8, you’re solving 10 + 7 which has the same result.

You can apply this trick to bigger numbers as well. For example, you can transform 87 + 99 into 86 + 100 and get the same results. The same goes when you have to add any number that ends in 9.

4. Multiplying numbers that end in zero

This is a great trick, especially when you deal with bigger numbers. First, you multiply the numbers without the zeros. Next, you add the zeros at the end for the final result.

For example, if you want to calculate 300 times 500, you start by multiplying 3 times 5, which is 15. Now, all you have to do is add all the zeros you left out. In this case, your answer would be 150,000.

5. Calculating percentages

If calculating X% of Y doesn’t come easy, try swapping those numbers and calculate Y% of X. For example, if 84% of 25 seems harder to solve, try solving 25% of 84. In this case, you would divide 84, which represents 100% by 4, which represents 25% and get 21.

To make calculating percentages even easier, you can memorize the basic fractions they equal. For example, 10% is 1/10, 12.5% is 1/8, 20% is 1/5, 25% is 1/4, 50% is 1/2, and 75% is 3/4.

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