How Do You Divide Whole Numbers by Whole Numbers?

Dividing whole numbers by whole numbers involves finding out how many times one whole number (the divisor) fits completely into another whole number (the dividend). The result is called the quotient.

Here's a breakdown of the process:

• Understanding the Terms:

  • Dividend: The number being divided (the larger number, generally).
  • Divisor: The number you are dividing by.
  • Quotient: The result of the division (the answer).
  • Remainder: If the divisor doesn't divide the dividend evenly, there's a remainder - the amount "left over."

• Methods of Division:

  • Equal Sharing/Partitioning: Imagine you have a certain number of items (the dividend) and want to share them equally among a certain number of people or groups (the divisor). The quotient represents how many items each person/group receives.

  • Repeated Subtraction: Keep subtracting the divisor from the dividend until you reach zero or a number smaller than the divisor. The number of times you subtracted is the quotient, and any number remaining is the remainder.

  • Long Division: This is a formal method for dividing larger numbers. Here's a simplified overview:

    1. Set up the problem: Write the dividend inside the division symbol and the divisor outside.
    2. Divide: Determine how many times the divisor goes into the first digit(s) of the dividend. Write that number (part of the quotient) above the dividend.
    3. Multiply: Multiply the part of the quotient you just wrote by the divisor.
    4. Subtract: Subtract the result from step 3 from the corresponding part of the dividend.
    5. Bring down: Bring down the next digit of the dividend.
    6. Repeat: Repeat steps 2-5 until all digits of the dividend have been used. The number at the top is the quotient, and the number remaining (if any) is the remainder.

• Example:

  Let's divide 17 by 3 (17 ÷ 3).

  • Using repeated subtraction:

    • 17 - 3 = 14
    • 14 - 3 = 11
    • 11 - 3 = 8
    • 8 - 3 = 5
    • 5 - 3 = 2
      We subtracted 3 five times, and we have 2 left over. So, 17 ÷ 3 = 5 with a remainder of 2.

  • Using long division:

         5  R2
      ------
    3 | 17
       15
       --
        2

    The quotient is 5, and the remainder is 2.

• Key Considerations:

  • When the divisor is larger than the dividend, the quotient is 0, and the remainder is the dividend. For example, 5 ÷ 7 = 0 R5
  • Any number divided by 1 is itself. For example, 8 ÷ 1 = 8.
  • Dividing by zero is undefined.