Useful Tips and Tricks for Division

By Alex David

April 8, 2025

Are you struggling with division? Whether you’re dealing with large numbers, decimals, or complex equations, division can be tricky. But with the right mental math strategies, you can divide quickly and efficiently—without needing a calculator! In this guide, you’ll learn powerful tips and tricks for division to boost your calculation speed.

There are different tips and tricks for division that are designed to overcome a situation like this. These strategies simplify calculations, build confidence, and make problem-solving faster and less intimidating. But with a few astute tips and tricks for division can become amazingly simpler and easier to handle.

Quick Tips and Tricks of Division

There are some basic techniques of division that mentally help you to understand the story behind the division. These tips and tricks for division boost the ability to improve mathematical skills.

For better understanding, start with simple tips and tricks for division, like dividing by 0 and 1. Follow the natural process and build a strong conceptual foundation for complex problems. This step-by-step technique reduces the confusion and also fosters confidence, showing how division evolves from basic ideas to advanced methods.

Such a positive and simple tips and tricks for division can transform division from a daunting task into a skillful mental exercise, empowering learners to solve problems with ease and efficiency.

Useful Tips and Tricks for Division

Dividing by 0

If you want to divide a number by 0, then it does not get a meaningful result. As you should remember, division by 0 is always undefined. Teach children this concept as a non-possibility in division. This tips and tricks for division make the work super easy.

Example:

$\frac{1025}{0} = \text{undefined}$

Dividing by 1

Although 1 is also a multiplicative identity, here in division, any number divided by 1 remains the same.

Example:

$\frac{12}{1} = 12$

Reinforce the idea that division by 1 doesn’t change the original value.

Dividing by 2 (Halving)

Dividing by 2 means splitting the number in half.

Mental Math Trick:

If the number is even, halve it directly. If it’s odd, first subtract 1, halve it, then add 0.5.

Example:

For Even: $\frac{16}{2} = 8$

For Odd: $\frac{17}{2}$

$\frac{16}{2}$ 8 + 0.5 = 8.5

Dividing by 3

Dividing by 3 is one the best tips and tricks for division. It involves breaking a number into smaller, manageable parts. Sometimes it is better to check the divisibility. Split the number into smaller, easier chunks and divide each part separately. Add the results to get the final answer.

Example:

To divide 273 by 3, split it into 270 and 3:

270 ÷ 3 = 90

3 ÷ 3 = 1

at the end 273 ÷ 3 = 91

Dividing by 4 (Quartering)

This tips and tricks for division is the same as halving the number twice.

Example:

48 ÷ 4 = (48 ÷ 2) ÷ 2

= 24 ÷ 2

= 12

Dividing by 5

As 5 is a prime number, if you want to divide a number by 5, just remember in your mind that a number divisible by 5 either ends in 0 or 5.

Mental Math Trick:

For divided by 5, multiply by 2 and then divide by 10.

Example:

35 ÷ 5 = (35 × 2) ÷ 10 = 70 ÷ 10 = 7

showing mental math tips and tricks for division.

Dividing by 6

For dividing by 6, first check its divisibility. If a number is divisible by both 2 and 3, it is divisible by 6.

Mental Math Trick:

Use the tricks of divide by 2 and divide by 3 to get the result of dividing by 6

Dividing by 7

7 is also a prime number. If you want to get the result of dividing by 7, use the approximation trick. This can be tricky. Use a mental trick; approximate by multiplying nearby numbers and adjust.

Example:

50 ÷ 7 = 7 remainder 1, because 7 × 7 = 49.

Dividing by 8

Dividing by 8 is like halving three times.

Example:

64 ÷ 8 = (64 ÷ 2) ÷ 2 ÷ 2

= 32 ÷ 2

= 16.

Dividing by 9

Numbers divisible by 9 have digits that add up to 9 or a multiple of 9.

Mental Math Trick:

Approximate using ÷ 10 and adjust. Sometimes the dividend is a large number, then use the approximation method and adjust the number.

Example:

81 ÷ 9 = 9 (since 8 + 1 = 9).

Dividing by 10

One of the simple and best tips and tricks for division is dividing by 10. Dividing by 10 is simple—remove the last digit or move the decimal point one place left.

Example:

250 ÷ 10= 25

Dividing by 11

11 also belongs to the prime number group. Dividing by 11 may seem challenging at first, but there is a simple tips and tricks for division to make it easier. The key idea lies in alternating sums and differences of the digits of the number you’re dividing.

Example:

121 ÷ 11 = 11

Dividing by 12

Check divisibility by 3 and 4, then combine results.

Mental Math Trick:

Use divided by 6, then divide again by 2.

General Tips and Tricks of Division

Use Compatible Number

One of the easy and simple tips and tricks for division is to divide large numbers mentally is to use compatible numbers. These are the numbers that are easy to work with and have round or simple easy factors. The main concept of using compatible numbers in division involves adjusting the dividend or divisor to numbers that are easier to work with while staying close to the original values.

Example:

Suppose you want to solve 195 ÷ 6
Round 195 to 192, which is close to the original value and divisible by 6.
192 ÷ 6 = 32
Since 195 is slightly larger than 192, the exact result will be a little more than 32.

This approach helps approximate the answer quickly and provides insight into the result without lengthy calculations.

Use Chunking

The best tips and tricks for division is to divide large numbers mentally is to use chunking, which is a way of breaking down the large number into smaller parts or chunks that are easy to divide by the divisor.

Example

For 1548 12, you can use chunking to split 1548 into two chunks: 1200 and 348. Then, you can divide each chunk by 12 separately and add the results. Dividing 1200 by 12 gives you 100, and dividing 348 by 12 gives you 29. Adding 100 and 29 gives you 129, which is the answer.

Estimation

Round to the nearest multiple of the divisor and adjust.

Example:

Use Known Facts

Recall multiplication tables to guide division.

Example:

For 144 ÷ 8, think 8 × 18 = 144.

Shortcut for Powers of 10

For numbers like divided by100, or divided by 1000, simply move the decimal point left by as many places as there are zeros.

Example:

2500 ÷ 100 = 25

Mental Visualization

Picture groups being formed as you divide.
Relate division to sharing equally to build intuition, especially in kids.

This image is about visualization of numbers.

Conclusion:

Division, though a fundamental mathematical operation, can sometimes appear daunting when dealing with complex numbers, equations, or decimals. However, with these tips and tricks for division, strategies, and mental techniques, it can be simplified and mastered. Starting from the basics, such as dividing by 0 or 1, and gradually building towards more intricate scenarios fosters confidence and understanding.

Frequently Asked Questions (FAQs)

Q # 01: Why is division considered one of the hardest operations in math?

Division is often looking difficult because:

It involves multiple steps (especially in long division).
It’s not always straightforward, unlike addition or multiplication.
Some numbers don’t divide evenly, leading to remainders or decimals.

Q # 02: What is the difference between long division and short division?

Long division is a step-by-step method used for dividing large numbers. It involves writing down all calculations.
Short division is a simplified method, useful when divisors are small and easy to work with mentally.

Example:

Long Division: 125 ÷ 5 = 25
Short Division: Simply divide 1212 by 55 (quotient = 2), then divide 55 by 55 (quotient = 1). Answer = 25.

Q # 03: How do I teach best tips and tricks for division to kids?

Best strategies for teaching kids division:

Use real-life examples (sharing pizza slices, dividing candies).
Introduce visual aids (draw groups to show division).
Use games and puzzles to make division fun.

Q # 04: Why is estimation important in division?

Estimation helps to:
Quickly approximate answers before solving completely.
Check if your answer is reasonable.
Avoid calculation mistakes.

Example:

393 ÷ 7→ Round 393 to 400→ 400 ÷ 7 ≈ 57 (actual answer is 56.1).

Q # 05: What are some real-life examples where division is used?

Daily life Applications of Division:
Splitting Expenses:

Example: Dividing a restaurant bill.
Work Schedules:

Example: Dividing tasks among employees

Q # 06: How can I divide large numbers without using a calculator?

Best strategies for mental division:
Break the number down (use chunking).
Use approximation (round to nearest 10 or 100).
Think in multiples (find the closest multiple of the divisor).

Q # 07: What are the fastest mental math tricks for division?

Divide by 5: Multiply by 2, then divide by 10.
Divide by 9: Use the digit sum trick (if the sum of digits is a multiple of 9, it is divisible by 9).
Divide by 4: Halve the number twice.