Before calculators became common, people had to be quick with numbers in their heads. Our grandparents and their parents used clever mental math tricks to solve problems fast. These tricks weren’t for showing off but were essential for daily life, from shopping to running a business.

In this blog, I’ll share 15 popular mental math tricks before calculators took over.

## Multiplication by 11

Multiply any two-digit number by 11 quickly in your head. Add the two digits of the original number, then place that sum between the original digits. If the sum is over 9, carry the 1 to the left digit. This trick works because of the pattern in the 11 times table.

## The 9 Times Table Finger Trick

Use your fingers to solve multiplication problems with 9. Hold up all ten fingers, then lower the finger that matches the number you’re multiplying by 9. The fingers to the left show the tens’ place, while those on the right show the ones’ place. This visual method makes the 9 times table much easier to remember and use.

## Squaring Numbers Ending in 5

Square numbers ending in 5 without a calculator. Multiply the tens digit by itself plus 1, then add 25 to the end. For example, 35 squared is 1225 because 3 x 4 = 12, and 1225. This shortcut works for any number ending in 5 and saves time on larger calculations.

## Calculating Percentages

Percentages can be tricky, but there’s a simple trick to make them easier. Instead of finding a percentage of a number, try switching the order. For instance, to find 8% of 50, calculate 50% of 8 instead, which is 4. This trick works because of the commutative property of multiplication, making percentage calculations much simpler to do in your head.

## Multiplying by 5

Multiplying by 5 can be quick and easy with this trick. Simply divide the number by 2, then multiply by 10. For odd numbers, round down when dividing, then add half the original number to your result. This method is often faster than traditional multiplication and works because 5 is half of 10.

## The Rule of 72

Want to know how fast your money can grow? Try the “Rule of 72.” Just take the number 72 and divide it by your interest rate. The result tells you roughly how many years it’ll take for your money to double. This handy trick works thanks to the power of compound interest. It’s a quick way to get a good idea of your investment’s growth without complex math.

## Adding Large Numbers

When adding big numbers, try working from left to right instead of right to left. Start with the hundreds place, then move to the tens, and finally the ones, keeping a running total as you go. This method allows for quicker estimates and is especially useful when exact precision isn’t required. It can also help you catch errors more easily since you’re dealing with the largest numbers first.

## Subtracting from 1000

Subtracting any number from 1000 can be done with a simple trick. Subtract all digits except the last from 9, then subtract the last digit from 10. For example, 1000 – 648 = 352 because 9 – 6 = 3, 9 – 4 = 5, 10 – 8 = 2. This method works due to the properties of our base-10 number system and can speed up mental calculations involving change from $10.

## Multiplying by 25

Multiplying by 25 doesn’t have to require a calculator. Instead, divide the number by 4, then multiply by 100. This shortcut works because 25 is one-fourth of 100 and can save time on mental calculations involving quarters or percentages. It’s particularly useful when dealing with money or time calculations.

## The Butterfly Method for Fractions

The “butterfly” method simplifies adding or subtracting fractions. To use it, multiply diagonally across the fractions, add the results for the numerator, and multiply the denominators for the new denominator. This visual technique makes fraction operations easier without needing to find common denominators first. It’s a great tool for students learning fractions or anyone who needs to do quick fraction calculations.

## Doubling and Halving

Doubling and halving can make multiplication easier. For example, to multiply by 25, you can multiply by 100 and divide by 4. This method works for many number combinations and can simplify difficult multiplications. It’s based on the principle that multiplying by 2 and dividing by 2 cancel each other out, allowing you to adjust the numbers to easier-to-handle values.

## The 3 Times Table Hand Trick

Your fingers can help you with the 3 times table too. Hold up the finger that matches the number you’re multiplying by 3, then count by tens for fingers to the left and by ones for fingers to the right. This visual aid turns your hand into a 3 times table calculator. It’s especially helpful for younger learners or anyone who finds memorizing times tables challenging.

## Divisibility Rules

Divisibility rules help you quickly determine if a number is divisible by 2, 3, 4, 5, 6, 9, or 10. For example, a number is divisible by 3 if the sum of its digits is divisible by 3. These rules can help with mental factoring and simplifying fractions without a calculator. Knowing these rules can save time on math tests or in everyday calculations.

## Estimating Square Roots

You can estimate the square roots of non-perfect squares without a calculator. Find the nearest perfect square, then adjust your guess based on how far the original number is from that square. This method provides quick approximations for square roots without needing exact calculations. It’s useful in situations where a rough estimate is sufficient, such as in some physics or engineering problems.

## Cross Multiplication for Proportions

Cross multiplication is a powerful tool for solving proportions. To use it, multiply diagonally across the proportion and set the products equal to each other. This technique simplifies ratio and proportion problems, making them easier to solve mentally or on paper. It’s particularly useful in fields like chemistry, physics, and finance where proportional relationships are common.

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