How to do bus stop division

There are three main methods to solve a division problem. You have the long division method, the chunking method, and the bus stop division method. All three methods will enable you to reach the same answer, but it will do so at varying speeds.

It’s best to start with the long division method. As suggested by its name, it’s the longest method out of the three, but it takes you through each calculation step-by-step. Once you have mastered that, you can move on to the chunking method and then finally progress to the bus stop method.

The bus stop method of division, also called the short division method, can be tricky at the beginning – particularly if you’re used to writing out each individual step one by one. However, you will fly through division problems once you get the hang of it.

But what is the bus stop method, how do you do it, and why is it called that? Let’s find out.

To use the bus stop method, simply divide each digit of the dividend by the divisor, adding your answers in the quotient as you work your way across.

If the divisor is bigger than the dividend digit, combine it with the next digit in the dividend to create a larger number. Remainders are carried over to the next digit, going up in place value.

The bus stop division method, also known as the short division method, is a formal written method to divide two numbers together. It is a form of progression for kids. As they become more comfortable with their times tables and multiplication of two and three-digit numbers, they’ll be able to divide numbers quicker without the tedious steps involved in long division and chunking.

However, they may still need to write their calculations down so they don’t get confused. As such, the bus stop method works as an intermediary step between solving division problems with the long division method and doing it entirely in their head – which is the end goal.

It’s called the bus stop method due to the use of a division bracket. With a bit of imagination, you can picture the division bracket looking like a bus stop shelter from the front. One could argue whether it really looks like a bus stop or not, but the main purpose of this name is that it makes the method easy to remember for primary school kids and allows them to differentiate it from other division methods, such as long division.

Also, the division bracket isn’t just there for looks. It actually serves a role. It separates the dividend from the divisor – with the dividend going inside the bracket and the divisor outside the bracket to the left – and allows space for the quotient to be written at the top.

• Step 1: Write the dividend inside the division bracket and the divisor outside the division bracket to the left.
• Step 2: Divide the first digit of the dividend by the divisor and write the answer above the division bracket as the quotient. If the divisor is too big for the first digit, follow step 3. Otherwise, move on to step 4.
• Step 3: Combine the first and second digits of the dividend to create a larger number. Divide the dividend by the divisor, and write the answer in the quotient.
• Step 4: If there is a remainder, add it to the next digit in the tens column. It’s important to interpret remainders appropriately, so be sure to get this step right.
• Step 5: Repeat steps 1 to 4 again until you have no more remainders left.

This can sound quite confusing when explained in words. The best way to understand it is to see it in practice, so let’s take a look at a few simple examples, starting with dividing two-digit numbers by a one-digit number.

Example 1 – two digit dividend and a one-digit divisor

Suppose you want to solve the equation 24 ÷ 2:

1. Write 24 inside the division bracket and 2 outside the division bracket to the left.
2. The first calculation is 2 ÷ 2. This equals 1, which means we can write 1 in the quotient.
3. Do the same for the second digit, so our next calculation is 4 ÷ 2. This equal 2, which means we can write 2 as the next digit in the quotient.
4. There are no more digits left in the dividend. Therefore, we have completed the bus stop method.
5. The final answer to our equation is 24 ÷ 2 = 12.

That seemed simple enough, right? Let’s do another one.

Example 2 – two digit dividend and a one-digit divisor

Suppose you want to solve the equation 68 ÷ 4:

1. Write 68 inside the division bracket and 4 outside the division bracket to the left.
2. The first calculation is 6 ÷ 4. 4 goes into 6 at least 1 time but has a remainder of 2. So we can write 1 in the quotient.
3. Write the remainder 2 next to the second digit of the dividend (8) to create the number 28.
4. This means that our next calculation is 28 ÷ 4. Using our times tables, we know that 4 goes into 28 exactly 7 times. This means we can write 7 as the next digit in the quotient.
5. There are no more digits left in the dividend. Therefore, we have completed the bus stop method.
6. The final answer to our equation is 68 ÷ 4 = 17.

You should be getting the hang of it now, so let's raise the stakes and use larger numbers. Let’s take a look at how we would divide a three-digit dividend by a single-digit divisor.

Example 1 – three-digit dividend and a one-digit divisor

Suppose you want to solve the equation 126 ÷ 3:

1. Write 126 inside the division bracket and 4 outside the division bracket to the left.
2. The first calculation is 1 ÷ 3. 3 is bigger than 1, which means you can’t divide it into a whole number. Therefore, combine the first and second digits of the dividend to create 12 and try again.
3. This gives us the calculation 12 ÷ 3. 3 goes into 12 exactly 4 times, which means we can write 4 as our first digit in the quotient.
4. The next calculation is 6 ÷ 3. 3 goes into 6 exactly 2 times, which means we can write 2 as our next digit in the quotient.
5. There are no more digits left in the dividend. Therefore, we have completed the bus stop method.
6. The final answer to our equation is 126 ÷ 3 = 42.

Let's do another one.

Example 2 – three-digit dividend and a one-digit divisor

Suppose you want to solve the equation 492 ÷ 6:

1. Write 492 inside the division bracket and 6 outside the division bracket to the left.
2. The first calculation is 4 ÷ 6. 6 is bigger than 1, which means you can’t divide it into a whole number. Therefore, combine the first and second digits of the dividend to create 49 and try again.
3. Our calculation is 49 ÷ 6. 6 goes into 49 at least 8 times, but has a remainder of 1. Write 8 in the quotient, and write 1 next to the last digit of the dividend (2) to create the number 12.
4. This means our next calculation is 12 ÷ 6. 6 goes into 12 exactly 2 times, which means we can write 2 as our next digit in the quotient.
5. There are no more digits left in the dividend. Therefore, we have completed the bus stop method.
6. The final answer to our equation is 492 ÷ 6 = 82

So far, we’ve only been dividing with one-digit numbers. What happens if you want to divide with two-digit numbers?

Nothing, we use the same steps as we’ve been using. Let’s see it in practice.

Example 1 – three-digit dividend and a two-digit divisor

Suppose you want to solve the equation 250 ÷ 10. You may know the answer to this question instinctively, but let’s solve it using the bus stop method:

1. Write 250 inside the division bracket and 10 outside the division bracket to the left.
2. The first calculation is 2 ÷ 10. 10 is bigger than 2, which means you can’t divide it into a whole number. Therefore, combine the first and second digits of the dividend to create 25 and try again.
3. Our calculation then becomes 25 ÷ 10. 10 goes into 25 at least 2 times, but has a remainder of 5. Write 2 in the quotient, and write 5 next to the last digit of the dividend (0) to create the number 50.
4. This means our next calculation is 50 ÷ 10. 10 goes into 50 exactly 5 times, which means we can write 5 as the next digit in the quotient.
5. There are no more digits left in the dividend. Therefore, we have completed the bus stop method.
6. The final answer to our equation is 250 ÷ 10 = 25.

As you can see, it's exactly the same steps. The only difference is that since the divisor is a two-digit number, you will always have to combine the first and second digits of the dividend together to create a larger number. Let’s see another example.

Example 2 – three-digit dividend and a two-digit divisor

Suppose you want to solve the equation 891 ÷ 27:

1. Write 891 inside the division bracket and 27 outside the division bracket to the left.
2. You can combine the first and second digits of the divisor straight away to create the number 89.
3. The first calculation is 89 ÷ 27. 27 goes into 89 at least 3 times, but has a remainder of 8. Write 3 in the quotient, and write 8 next to the last digit of the dividend to create 81.
4. Our next calculation is 81 ÷ 27. 27 goes into 81 exactly 3 times, which means you can write 3 as the next digit in the quotient.
5. There are no more digits left in the dividend. Therefore, we have completed the bus stop method.
6. The final answer to our equation is 891 ÷ 27 = 33.

At this point, this short-hand division method should be pretty easy for you. But to really drive it home, let’s look at an example including a four-digit dividend.

Example 1 – four digit dividend and a two-digit divisor

Suppose you want to solve the equation 7220 ÷ 38:

1. Write 7220 inside the division bracket and 38 outside the division bracket to the left.
2. Combine the first and second digits of the dividend to create 72. The first calculation is 72 ÷ 38. 38 goes into 72 at least 1 time, but has a remainder of 34. Write 1 in the quotient, and 34 next to the third digit of the dividend (2) to create the number 342.
3. The next calculation is 342 ÷ 38. 34 goes into 342 exactly 9 times, but has a remainder of 2. Write 9 as the next digit in the quotient.
4. We still have one digit left in the dividend, 0. But 0 cannot be divided by a number, which means you can simply write it as the next digit in the quotient.
5. There are no more digits left in the dividend. Therefore, we have completed the bus stop method.
6. The final answer to our equation is 7220 ÷ 38 = 190.

So far, all the examples we’ve looked at have been wholly divisible, meaning it has no remainders left over. What do we do when this isn’t the case? You simply leave it as a remainder. Let’s see this in action.

Example 1 – remainder left over

Suppose you want to solve 86 ÷ 5

1. Write 86 inside the division bracket and 5 outside the division bracket to the left.
2. Our first calculation is 8 ÷ 5. 5 goes into 8 at least 1 time but has a remainder of 3. Write 1 in the quotient, and write 3 next to the last digit of the dividend (6) to create the number 36.
3. The next calculation is 36 ÷ 5. 5 goes into 36 at least 7 times, but has a remainder of 1. Write 7 as the next digit of the quotient. There are no more digits left to carry the remainder across to. Therefore, we leave it as it is.
4. The final answer to our equation is 86 ÷ 5 = 17 remainder 1.

The bus stop method for division is a shortcut to the more detailed long-divison method. It follows the same steps but combines some of them together to create a quicker process. Using the divisor, simply work your way across each digit of the dividend until you no longer have any digits left.

It requires a good knowledge of your times tables and multiplications, so if you’re not comfortable with multiplying two and three-digit numbers together, it will be best to practice that first before moving on to the bus stop method.