Calculators are amazing, but depending on them even for the basics will hamper your math skills. Just like addition, subtraction, and multiplication, you should know how to divide manually, at least for small numbers. This can come handy during tests that do not allow a calculator and, at times when you don’t have one.
How to divide without a calculator?
Don’t worry, it is not hard!
We will you through basic steps so that you understand how to divide without the help of a calculator.
Things to remember
To get the process right, you must learn the terminology.
- The number below the division sign is the dividend
- The number outside the division sign (left) is the divisor
- The answer you get is the quotient
Basic steps for manual division
Divide – 6492/4
4 is the divisor and 6492 is the dividend.
- Find out how many times 4 will go into 6 (the first digit of the dividend). So, put 1 in the quotient and write 4 below 6.
- You have to subtract them for the remainder. You will get 2.
- Now, bring the second digit of the dividend (4) below and write it beside 2.
- The number that you get now is 24.
- Follow the same steps. Find out how many times 4 will go into 24. The answer is 6. Write 6 in the quotient beside 1 and then subtract the numbers. You will now get 0.
- Bring the third digit down, beside 0. That’s 9.
- Since 4 will go into 9 2 times, write 2 in the quotient and 8 below 9. Subtract.
- You get 1.
- Bring the last digit, 2, down. Write it beside 1.
- The remainder now is 12.
- 4 goes into 12, 3 times. Write 3 in the quotient and 12 below 12.
- Subtract 12-12 to get 0.
- So, the quotient now is 1623. That’s your answer.
If all numbers are done, and the remainder is not zero yet, you will have to add a decimal in the quotient and write 0 beside the remainder. Continue with your division until you get 0 or a recurring number.
Many tests ask for an answer until 2 or 3 decimal places. So you don’t have to worry beyond that.
What if the divisor has a decimal?
Sometimes, the problem may look like this – 2367/3.5
In such a case, you can remove the decimal from the divisor by adding a 0 to the dividend. After doing this, you can follow the steps mentioned above.
Some quick rules about division
We would like to help you a little more with long division by telling you about a few basic rules. Here they are:
- 0 divided by any number is always 0. You may have learned the same about multiplication as well. For example, there are 40 oranges in the basket and 0 oranges were distributed among 3 children. How many does each child get? 0.
- On the flip side, you will never divide a number by 0. You can’t ask the remainder of the problem 24/0. There’s no answer. If you come across such a problem, just write the infinity symbol as the answer.
- If you divide any number by itself, the answer will always be 1.
- Anything divided by 1 is the number itself.
- Every fraction is a division sum.
- When you divide any number by 2, you get its half. For example, 20/2 is 10. 10 is half of 20.
- Divide 1 by any number and the answer will be the same as that number. 4/1 is 4. 2576/1 is 2576.
BONUS: Can we solve remainder problems without using long division?
We are speaking about this because a lot of students studying for SAT, GRE, and ACT find themselves stuck. They are unable to figure out how to solve remainder problems without using long division.
The good news is that it is possible. You can totally crack these problems without touching long division. But how?
Here, you will need a calculator. However, simply pressing the numbers in will not help you. You will need to work with calculator algorithms to get to the remainder. Below are the steps:
- Start with the basic division. You will get a decimal number (Example: 2.4 or 7.8).
- Now use the integral and multiple it with the divisor.
- The answer you get should be subtracted from the dividend.
- Voila. There’s your remainder!
When you are doing it for the first time, remember to punch in the numbers correctly. We see many students get confused between a divisor and a dividend or an integer. This is where basics and terminology come handy.
We hope we helped you understand long division. Practice with a few small numbers and move up to get it thoroughly. In math, like in many other things, practice is the key to success!
All the best.