How to Divide a Number by a Number?

Dividing one number by another involves determining how many times the second number (the divisor) fits into the first number (the dividend). There are several methods to accomplish this, depending on the complexity of the numbers involved.

1. Basic Understanding

• Dividend: The number being divided (the larger number typically).
• Divisor: The number you are dividing by.
• Quotient: The result of the division.
• Remainder: The amount left over if the divisor doesn't divide evenly into the dividend.

Formula: Dividend ÷ Divisor = Quotient (+ Remainder)

2. Simple Division (Mental Math or Basic Facts)

For simple division problems with small numbers (e.g., 12 ÷ 3), you can often use mental math or recall basic multiplication/division facts. In this example, 3 goes into 12 four times (3 x 4 = 12), so the answer is 4.

3. Long Division

Long division is a method used for dividing larger numbers, especially when the divisor has multiple digits.

Steps for Long Division:

1. Set up the problem: Write the dividend inside the division symbol (the long division bracket) and the divisor outside to the left.
2. Divide: Determine how many times the divisor goes into the first digit(s) of the dividend. Write this number (the quotient) above the division symbol.
3. Multiply: Multiply the quotient by the divisor and write the result below the portion of the dividend you used.
4. Subtract: Subtract the result from the portion of the dividend.
5. Bring down: Bring down the next digit of the dividend to the right of the result.
6. Repeat: Repeat steps 2-5 until all digits of the dividend have been used.
7. Remainder (if any): If there's a number left over after the last subtraction, that's the remainder.

Example: 518 ÷ 4

    129 R 2
4 | 518
   - 4
   ----
    11
   -  8
   ----
     38
   - 36
   ----
      2

In this example, 518 divided by 4 equals 129 with a remainder of 2.

4. Short Division

Short division is a condensed version of long division, typically used when the divisor is a single-digit number. It involves less writing, with intermediate calculations done mentally. While it is similar to long division, short division is more compact and requires a good understanding of multiplication facts and mental arithmetic.

5. Using a Calculator

For quick calculations, especially with decimals or large numbers, a calculator is the easiest tool. Simply enter the dividend, press the division symbol (÷), enter the divisor, and press the equals (=) button.

6. Division with Fractions

Dividing by a fraction is the same as multiplying by its reciprocal.

• Reciprocal: The reciprocal of a fraction is found by swapping the numerator and denominator (e.g., the reciprocal of 2/3 is 3/2).

Example: 4 ÷ (2/3)

1. Find the reciprocal of 2/3, which is 3/2.
2. Multiply 4 by 3/2: 4 * (3/2) = 12/2 = 6

In summary, dividing a number by a number can be performed through mental math for simple cases, long division for more complex calculations, short division as a condensed form of long division (when the divisor has one digit), or using a calculator for efficient calculations. Understanding the concept of reciprocals is crucial for dividing by fractions.