How does the bus stop method work?

Decoding the Bus Stop: A Simple Guide to Long Division

Long division can seem daunting, but a simple visual aid can transform the process from a confusing jumble of numbers into a manageable, step-by-step procedure. This aid is the “bus stop” method, so named for its resemblance to a bus stop shelter. Understanding its structure and application is key to mastering long division.

The bus stop method provides a clear, organized framework for tackling division problems. Unlike other methods that might scatter numbers across the page, the bus stop keeps everything neatly in its place. Let’s break down the structure:

• The “Bus Stop”: This is the long division symbol itself, usually drawn as a curved line above a horizontal line. Think of it as the shelter where the numbers take refuge during the calculation.

• The Divisor (Outside the Bus Stop): This is the number you’re dividing by. It sits outside the “bus stop” on the left, patiently waiting to be used. Imagine it as the bus itself, ready to pick up the numbers and transport them through the calculation.

• The Dividend (Inside the Bus Stop): This is the number being divided. It resides neatly inside the “bus stop,” ready to be processed. Think of this as the passengers waiting for the bus (the divisor).

• The Quotient (Above the Bus Stop): This is the result of the division—the answer. It’s written above the bus stop, appearing step-by-step as the calculation progresses. It’s the destination of the passengers.

How it Works: A Step-by-Step Example

Let’s illustrate with the problem 675 ÷ 5.

1. Setup: We write the problem as follows:

       _____
   5 | 675

2. Divide the first digit: We begin by dividing the first digit of the dividend (6) by the divisor (5). 5 goes into 6 once (1). We write the ‘1’ above the ‘6’ in the quotient.

       1___
   5 | 675

3. Multiply and Subtract: We multiply the quotient digit (1) by the divisor (5), resulting in 5. We subtract this from the first digit of the dividend (6 – 5 = 1).

       1___
   5 | 675
       5
       -
       1

4. Bring Down: We bring down the next digit from the dividend (7), placing it next to the remainder (1), creating the number 17.

       1___
   5 | 675
       5
       -
       17

5. Repeat: We repeat steps 2-4. 5 goes into 17 three times (3). We write the ‘3’ in the quotient above the ‘7’. We multiply 3 by 5 (15) and subtract it from 17 (17 – 15 = 2).

       13__
   5 | 675
       5
       -
       17
       15
       --
        2

6. Final Step: We bring down the last digit (5), creating the number 25. 5 goes into 25 five times (5). We write the ‘5’ in the quotient. We multiply 5 by 5 (25) and subtract it from 25 (25 – 25 = 0).

       135
   5 | 675
       5
       -
       17
       15
       --
        25
        25
        --
         0

The remainder is 0, meaning the division is complete. Our quotient, the answer, is 135.

The bus stop method, with its clear visual structure, makes long division more accessible. By systematically following these steps, even complex division problems become manageable. Its straightforward approach makes it a valuable tool for anyone learning the fundamentals of arithmetic.