Division is the mathematical operation of splitting a quantity into equal groups or determining how many times one number (the divisor) fits into another number (the dividend). Here's how to perform division, primarily focusing on long division:
Understanding the Basics of Division
Division has several key components:
- Dividend: The number being divided.
- Divisor: The number by which the dividend is divided.
- Quotient: The result of the division (how many times the divisor fits into the dividend).
- Remainder: The amount left over if the divisor does not divide the dividend evenly.
Long Division Method
Long division is a structured method for dividing larger numbers. Here's a step-by-step process:
- Setup: Write the dividend inside the division symbol and the divisor outside to the left.
- Divide:
- According to Cuemath the first step is to take the first digit of the dividend from the left.
- Divide the first digit (or the first set of digits if the first digit is smaller than the divisor) of the dividend by the divisor.
- Write the result (the quotient) above the dividend, aligned with the digit you just divided. This is step 2.
- Multiply: Multiply the quotient you just wrote by the divisor.
- Subtract: Subtract the result from the part of the dividend you were dividing. This result is written below according to step 3.
- Bring Down: Bring down the next digit of the dividend to the right of the remainder. This is step 4 of long division according to Cuemath.
- Repeat: Repeat steps 2-5 with the new number you formed by bringing down a digit until there are no more digits to bring down.
Example
Let’s divide 672 by 21 using long division:
| Step | Calculation | Result |
|---|---|---|
| 1 | Setup: 21 | 672 |
| 2 | 67 ÷ 21 = 3 | Quotient is 3 |
| 3 | 3 x 21 = 63 | |
| 4 | 67 - 63 = 4 | |
| 5 | Bring down the 2 | |
| 6 | 42 / 21 = 2 | Quotient is 2 |
| 7 | 2 x 21 = 42 | |
| 8 | 42-42 = 0 | Remainder is 0 |
Therefore, 672 divided by 21 is 32.
Tips for Success
- Estimation: Estimate how many times the divisor fits into the dividend to help you get the correct quotient in each step.
- Place Value: Ensure you align digits correctly when performing the subtraction and bring down steps.
- Check your Work: Multiply the quotient by the divisor and add the remainder. This result should equal the dividend if your division is accurate.
Division with Remainders
Sometimes, division doesn’t result in a whole number. The leftover is known as the remainder:
- If, after the long division process, you're left with a number smaller than the divisor, that's your remainder.
- The remainder can be expressed as a fraction (remainder over the divisor), or as a decimal.
Different Forms of Division
Division can be expressed in various ways:
- Using the division symbol: ÷ (e.g., 10 ÷ 2)
- Using the forward slash: / (e.g., 10 / 2)
- As a fraction: (e.g., 10/2)
By following these steps, you can effectively solve various division problems.
