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Short division is a fundamental mathematical technique that enables us to divide one number by another quickly and efficiently. It is commonly used when dividing larger numbers or solving complex arithmetic problems. By mastering short division, individuals can simplify calculations and find accurate solutions without the need for lengthy methods such as long division. This guide will provide a step-by-step explanation of how to perform short division, empowering individuals to divide numbers effortlessly and develop their mathematical skills. Whether you are a student aiming to excel in math or an individual seeking to enhance your problem-solving abilities, learning how to do short division is a valuable skill that will prove useful in various contexts of your life.
This article was co-written by David Jia. David Jia is a tutoring teacher and founder of LA Math Tutoring, a private tutoring facility based in Los Angeles, California. With over 10 years of teaching experience, David teaches a wide variety of subjects to students of all ages and grades, as well as college admissions counseling and prep for SAT, ACT, ISEE, etc. scoring 800 in math and 690 in English on the SAT, David was awarded a Dickinson Scholarship to the University of Miami, where he graduated with a bachelor’s degree in business administration. Additionally, David has worked as an instructor in online videos for textbook companies such as Larson Texts, Big Ideas Learning, and Big Ideas Math.
This article has been viewed 27,276 times.
Short division is similar to long division, but allows you to write fewer calculations and do more mental calculations. The general method for both short and long division is the same, but in short division you don’t need to write a lot of calculations and just do the subtraction and multiplication operations mentally. [1] XResearch Resources To do short division, you must know how to do basic addition and subtraction. Short division is only applicable when the divisor – the number used to divide, must be less than 10.
Steps
Performing short division [2] XResearch Source
![Image titled Do Short Division Step 1](https://www.wikihow.com/images_en/thumb/c/c0/Do-Short-Division-Step-1-Version-5.jpg/v4-728px-Do-Short-Division-Step-1-Version-5.jpg)
- For example, with 847/5 division, the number 5 is the divisor, so you would write it outside the division. The number 847 is the divisor, so it should be placed inside the divisor.
- The quotient remains blank because you haven’t done the division.
![Image titled Do Short Division Step 2](https://www.wikihow.com/images_en/thumb/d/d3/Do-Short-Division-Step-2-Version-5.jpg/v4-728px-Do-Short-Division-Step-2-Version-5.jpg)
- If you were to do a long division, you would write 8 minus 5 as 3, and bring down the 4 in the divisor. Short division shortens this part of the calculation.
![Image titled Do Short Division Step 3](https://www.wikihow.com/images_en/thumb/2/2f/Do-Short-Division-Step-3-Version-5.jpg/v4-728px-Do-Short-Division-Step-3-Version-5.jpg)
- In the example above, the next divisor is 34.
![Image titled Do Short Division Step 4](https://www.wikihow.com/images_en/thumb/f/f3/Do-Short-Division-Step-4-Version-5.jpg/v4-728px-Do-Short-Division-Step-4-Version-5.jpg)
- Now, divide 34 by 5. Thus, 34 divided by 5 equals 6 (5 x 6 = 30) with a remainder of 4.
- Write the quotient as 6 on the division sign, just to the right of 1.
- Again, you’ll do some mental math.
![Image titled Do Short Division Step 5](https://www.wikihow.com/images_en/thumb/d/db/Do-Short-Division-Step-5-Version-5.jpg/v4-728px-Do-Short-Division-Step-5-Version-5.jpg)
- Now, divide 47 by 5. The number 47 divided by 5 equals 9 (5 x 9 = 45) with a remainder of 2.
- Write the quotient as the 9 above the division sign, and to the right of the 6.
![Image titled Do Short Division Step 6](https://www.wikihow.com/images_en/thumb/0/08/Do-Short-Division-Step-6-Version-5.jpg/v4-728px-Do-Short-Division-Step-6-Version-5.jpg)
Perform division in special cases
![Image titled Do Short Division Step 7](https://www.wikihow.com/images_en/thumb/6/66/Do-Short-Division-Step-7-Version-4.jpg/v4-728px-Do-Short-Division-Step-7-Version-4.jpg)
- For example: 567/7. In this case, 5 cannot divide 7, but 56 divides 7 equals 8. When you do the calculation, you will write the first quotient of the quotient on the number 6 instead of the number 5 and continue to do the division. The final result is 81.
![Image titled Do Short Division Step 8](https://www.wikihow.com/images_en/thumb/e/e2/Do-Short-Division-Step-8-Version-3.jpg/v4-728px-Do-Short-Division-Step-8-Version-3.jpg)
- For example: 3208/8. Where 32 divided by 8 equals 4, but zero cannot be divided by 8. Thus, you will add a zero to the quotient and perform the division with the next divisor. Since 8 divided by 8 equals 1, the final result is 401.
![Image titled Do Short Division Step 9](https://www.wikihow.com/images_en/thumb/f/f9/Do-Short-Division-Step-9-Version-3.jpg/v4-728px-Do-Short-Division-Step-9-Version-3.jpg)
- Divide 748 by 2. So what is 7 divided by 2? Definitely 3 and remainder 1. Write 1 next to 4. Next, what is 14 divided by 2? Even 7. Finally, 8 is divisible by 2 and is 4; so the final answer is 374.
- Divide 368 by 8. The number 3 cannot be divided by 8, but the number 36 can. So 36 divided by 8 equals 4 and remainder 4 (8 x 4 = 32, 36 – 32 = 4). Write 4 next to 8. Since 48 divided by 8 equals 6, the answer to the calculation is 46.
- Divide 1228 by 4. The number 1 cannot be divided by 4, but 12 divided by 4 equals 3. The number 2 cannot be divided by 4, so you have to add 0 to the quotient and take 28 divided by 4. The number 28 divided by 4 equals 7, so the result you get is 307.
Advice
- Check answers. You can check by multiplying the quotient by the divisor and adding the remainder (if any).
This article was co-written by David Jia. David Jia is a tutoring teacher and founder of LA Math Tutoring, a private tutoring facility based in Los Angeles, California. With over 10 years of teaching experience, David teaches a wide variety of subjects to students of all ages and grades, as well as college admissions counseling and prep for SAT, ACT, ISEE, etc. scoring 800 in math and 690 in English on the SAT, David was awarded a Dickinson Scholarship to the University of Miami, where he graduated with a bachelor’s degree in business administration. Additionally, David has worked as an instructor in online videos for textbook companies such as Larson Texts, Big Ideas Learning, and Big Ideas Math.
This article has been viewed 27,276 times.
Short division is similar to long division, but allows you to write fewer calculations and do more mental calculations. The general method for both short and long division is the same, but in short division you don’t need to write a lot of calculations and just do the subtraction and multiplication operations mentally. [1] XResearch Resources To do short division, you must know how to do basic addition and subtraction. Short division is only applicable when the divisor – the number used to divide, must be less than 10.
In conclusion, short division is a highly effective method for dividing numbers that allows individuals to quickly find the quotient and remainder. It is a straightforward process that involves breaking down the dividend into smaller chunks and repeatedly dividing by the divisor, which helps to simplify complex divisions. By following the steps of short division, one can easily solve division problems and obtain accurate results. It is a valuable technique to master, especially for quick mental calculations and problem-solving in various mathematical situations. With practice and familiarity, individuals can become proficient in performing short division, saving time and effort in their mathematical endeavors.
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