How to do short division
Short division is a mathematical method that helps you divide large numbers quickly and efficiently. It is a key skill in arithmetic and can be used to solve various real-life problems. Whether you’re a student learning division or an adult refreshing your math skills, knowing how to do short division can make calculations much easier.
Short division involves dividing a large number, known as the dividend, by a smaller number, known as the divisor. The result, known as the quotient, is the answer to the division problem. The process of short division breaks down the division into smaller steps, making it easier to calculate.
To do short division, start by writing the dividend and divisor in the division format. Then, divide the first digit of the dividend by the divisor. Write the quotient above the dividend, and multiply the quotient by the divisor. Subtract the product from the first digit of the dividend, and bring down the next digit of the dividend. Repeat this process until you have divided all the digits of the dividend. Finally, write the remainder, if any, beside the quotient to give the complete answer.
Short division is a useful skill to have in everyday life. It can be used to split bills among friends, calculate unit prices at the grocery store, or solve problems in various fields such as engineering, finance, and science. By mastering short division, you can become more efficient in your calculations and improve your problem-solving abilities.
Step-by-Step Guide
Short division is a method used to divide large numbers quickly and accurately. Follow these steps to perform short division:
Step 1: Setup
Write the dividend (the number being divided) inside the long division symbol, and write the divisor (the number the dividend is being divided by) outside the symbol. Also, make sure to leave enough space for the quotient (the answer).
Step 2: Divide
Look at the leftmost digit of the dividend. This will be your first digit of the quotient. See how many times the divisor can be multiplied to obtain a product that is less than or equal to the dividend. Write this digit above the long division symbol as the first digit of the quotient.
Step 3: Multiply and Subtract
Multiply the divisor by the first digit of the quotient and subtract this product from the dividend. Write the result below the subtraction line.
Step 4: Bring Down
Bring down the next digit of the dividend and place it next to the result obtained in step 3. This will be the new dividend for the next step.
Step 5: Repeat
Repeat steps 2-4 until there are no more digits left in the dividend. At each step, keep writing the new digit above the long division symbol as the next digit of the quotient.
Step 6: Remainder (Optional)
If there are any digits left in the dividend after completing step 5, they represent the remainder. Write them as a fraction or a decimal to indicate a remainder.
By following these steps, you can perform short division to divide large numbers efficiently.
Step 1: Divide the Dividend by the Smallest Possible Divisor
Short division involves dividing a larger number, known as the dividend, by a smaller number, called the divisor. The goal is to determine the quotient, which is the answer to the division problem.
To begin, identify the smallest possible divisor that can divide evenly into the dividend. This is usually the smallest single-digit number that can divide into the first digit of the dividend.
For example, let’s say we have the following problem:
Divide 784 by 4.
In this case, 4 is the smallest divisor that can divide into 7. Divide 7 by 4 to find the first digit of the quotient.
Result:
- 7 ÷ 4 = 1
Write the quotient 1 above the dividend, next to the digit that was divided.
Then, multiply the divisor (4) by the quotient (1) to get the product.
Result:
- 1 × 4 = 4
Write the product 4 below the dividend, subtract it from the dividend, and write the difference below the line.
Result:
-
- 7
- ─
- 4
- ─
- 3
The next step is to bring down the next digit of the dividend (in this case, the digit 8). This creates the new dividend, which is 38. Repeat the process until there are no more digits left to bring down.
Step 2: Write the Quotient Above the Dividend
After you have identified the divisor and dividend, the next step is to write the quotient above the dividend. The quotient is the result of division, and it will be written above the long division symbol.
To find the quotient, divide the first digit or the first few digits of the dividend by the divisor. Write the result above the line, aligned with the corresponding digit or digits in the dividend. If the quotient is not a whole number, you can round it to the nearest whole number or express it as a decimal.
Once you have written the quotient, you can start dividing and finding the remainder. This step is crucial to completing the short division process correctly.
For example, if the dividend is 945 and the divisor is 5, the quotient would be 1. You would write “1” above the first digit of the dividend:
1 ----------- 945
Remember, the quotient helps in determining how many times the divisor goes into the dividend, and it directly impacts further steps of the short division process.
Step 3: Multiply the Quotient by the Divisor
After you have determined the quotient in step 2, you need to multiply it by the divisor to get your result.
To do this, write the quotient as a whole number, without decimals or remainders. Then, multiply the quotient by the divisor, placing the product under the dividend. This will give you the result of the division.
| 7 | |
| x | 142 |
| — | — |
| 994 |
In this example, we multiply the quotient of 142 by the divisor 7. The product, 994, is written below the dividend.
Now, you can proceed to the next step which is subtracting the product from the dividend.
Step 4: Subtract and Bring Down
After completing the division in the previous step, you will need to subtract and bring down digits until there are no more digits left to bring down.
To subtract, you start with the quotient digit you have just found and multiply it by the divisor. Next, you write the result below the dividend, aligning it with the current dividend digit. Subtract this result from the current dividend digits to get a new dividend.
Repeat the process by bringing down the next digit from the dividend and perform the division again. Continue subtracting and bringing down digits until there are no more digits left to bring down.
Here’s an example:
363
--------
x 9
--------
-27
-
---
51
In this example, the quotient is 40 and the remainder is 51. You have successfully completed the short division!
Tips for Effective Short Division
Short division is a method used to divide larger numbers quickly and efficiently. Here are some tips to help you master this arithmetic technique:
1. Understand the Process
In short division, you divide the dividend (the number being divided) by the divisor (the number you’re dividing by) to get the quotient (the answer). Make sure you understand the basic process and terminology before attempting short division.
2. Set Up Your Division
To set up a short division problem, write the dividend on the inside, and the divisor on the outside as shown in the example below:
Example: 345 ÷ 5
____
5 | 345
Divide the first digit of the dividend (3) by the divisor (5) and write the quotient (0) above the line:
Example: 345 ÷ 5
0
5 | 345
3. Repeat and Bring Down
Next, bring down the next digit of the dividend (4) to the right of the 0, and divide the new number (34) by the divisor (5). Write the quotient (6) above the line:
Example: 345 ÷ 5
06
5 | 345
Bring down the final digit (5) and continue dividing until you reach the end of the dividend.
4. Check Your Answer
After completing the short division, double-check your calculations by multiplying the quotient and divisor together and adding any remainder to the result. The final answer should be equal to the dividend.
Remember: Short division takes practice, so keep practicing until you feel comfortable using this method for rapid calculations!
Example: 345 ÷ 5 = 69 (remainder 0)
Short division is a valuable skill to have, especially when working with larger numbers. By following these tips, you can enhance your efficiency and accuracy in performing short division.
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