Long Division is a Myth

Thank you to everyone who made contact with us regarding ‘new’ subtraction.  The response was overwhelming.  Many of you have told me that long division is a bit of a bug bearer as well and asked if I would write about it.

In the Hummingbird Learning Centres, the word we hear mostly associated with long division is ‘hate’ as in ‘I hate long division’.  My stock reply – how can you hate something that doesn’t exist? It’s a myth!

The response I get then is generally a look that is both one of surprise and withering at the same time.  Long division does exist Elaine – I got it for home work!!

But think about it – there is no division in long division.  There is estimation, multiplication and subtraction, but no division. Long division does not exist, so it is impossible to hate it as you cannot hate something that isn’t there. So now that you no longer hate it, it’s going to be easy and the wonderful thing about maths is that there is often more than one way to do it.

We use two methods – the classic long division method  and our alternative, easy, method.  We usually start with the classic, as it is how it is taught in school, but if that concept is proving difficult we quickly switch to the easy method.

Let’s start with understanding the terms used in the process of division. Take for example the following question: 793÷13=61

793 is called the dividend, ÷ is the symbol for division, 13 is the divisor, = is the symbol for equals and 61 is the answer or quotient. These terms are true for both short and long division.

Before beginning any maths question, it is very important to rule the page with a small margin on the left for the question number and a considerably larger one on the right for rough work.  Rough work & estimation play a large part in the long division process and having a specified area just for this is essential. When learning long division, graph paper or a good maths copybook can be very useful, to ensure that the numbers in the dropdown method that I will be explaining below remain very clear, thus minimising mistakes.

Example:  793 ÷ 13 =


Classic Long Division Method  – E DM S B R

Long Division Classic MethodThis is the Hummingbird Learning Method® classic approach to long division.

Estimate: Good guessing will go a long way in long division and this is where your rough work column comes into its own.

Division: First question, how many times will 13 go into 7?  The answer will be 0. So move onto the next number which becomes 79. I find it good to put the answer 0 over the 7.

 Multiplication: Using your knowledge of Multiplication, look at the tens digit of each number – the 7 in the 79 & the 1 in the 16.  A good guess here would be 13×7, so use your rough work column to work that out. The answer to that estimate is 112. That is way too big, so we know that the answer is going to be less than 7. So we start again and guess a lower number until we arrive at a number that is less than 79.  In this example it is 6; 13×6 is 78. You put the answer 6 over the 9.

Subtraction:  Write 78 under 79 and subtract.  Your answer will be 1.

Bring Down:Then bring down your next number, in this case, 3. The number is now 13.  13 goes into 13 once. Place a 1 on top beside the 6 and your final answer is 61

Repeat or remainder:  In the example above, we didn’t have to keep repeating the process as it was a short question, but if the question is longer, just keep estimating, multiplying and subtracting until it either works out evenly or you are left with number at the end that is smaller than the divisor.  This is called the remainder.


Easy Long Division Method – Easy with 5s and 10s

Long Division EasyMethodThis is the Hummingbird Learning Method®easy, alternative approach to long division.  It is especially good if confidence around maths tables is low.  Everyone finds multiplying by 5 or 10 easy so we use them mostly in this method, together with subtraction, repeating and addition.

Using the previous example:  793 ÷ 13 =

Multiplication: Multiply 130 by 10 (130).Write 130 under 793.  To the right of it put the number 10 and circle it.

Subtraction:  Subtract 130 from 793.  Your answer will be 663.

Repeat or remainder:  Keep repeating the process, multiplying and subtracting until it either works out evenly or you are left with number at the end that is smaller than the divisor. This is called the remainder. In this case it takes 6 goes until you have 13 left. 13 goes into 13 once. Put a 1 into a circle on the right hand side, underneath all the encircled 10s.(If multiplying by 10 is too high, then multiply by 5 instead. Once that gets too high, use 2s.)

Addition: Add up all of the numbers in the circles.  You will get the answer 61. Easy!


Hummingbird Learning Centre has just launched its new Successful Studying course.  This course will be held over 4 weeks on Monday evenings in Adare and is suitable for secondary & college students. Places are limited.  For further information contact Elaine on 087 2996054

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