In mathematics, we are taught to solve long addition, subtraction, and multiplication problems by working through the numbers from the units column on the right and then proceeding to the left. However, with long division questions, the opposite is true; we move from left to right.
Although this is the most common method of solving long division questions, it is possible to begin with the units column of the dividend and solve the problem from right to left.
So why do we start division from the left?
Read on as we attempt to answer this question and explore some of the ins and outs of long division.
Division can technically be started from either the left or right side of the dividend. However, starting from the left is far more efficient and requires fewer steps than if started on the right.
The standard method of long division is taught starting from the left of the dividend and uses a combination of division and subtraction to arrive at the quotient. It also requires some basic mental arithmetic skills.
So let's now jump in and explore some common division terminology.
- Dividend. This is the number that gets divided. In the question 40 ÷ 5, the dividend is 40.
- Divisor. This is the number that the dividend is divided by. In the question 40 ÷ 5, the divisor is 5.
- Quotient. This is the answer to a division question. In the question 40 ÷ 5 = 8, the quotient is 8.
- Integer. This is another word for a whole number, one that does not have a decimal point.
- Quotition. This is a form of division that looks at how many parts of a whole there are.
- Partition. This is a form of division that looks at the size of each part that forms the whole.
- Remainder. This is the value that is left over once one integer has been divided by another.
In mathematics, division is the process of splitting a number into equal parts to find how many times a split of that size can be made.
There are two ways of thinking about division. The first is in terms of "quotition," and the second is in terms of "partition."
Quotition concerns the number of equal parts that comprise a whole, and partition considers the size of each equal part.
If, for example, you have 24 eggs, quotition division can find that your total basket of eggs can be split into groups of 2, 4, 6, 8, and 12. Partition division, on the other hand, would consider the size of each group - so two groups of 12 eggs.
Quotition and partition arrive at the same answers, but they look at division problems from different angles.
Long division is a mathematical method of dividing large numbers into equal parts. Long division helps to break down a complicated problem into small, simple steps.
When performing the long division method, you usually start by dividing the furthest number on the left of the dividend by the divisor.
How to perform long division
Here we will look at how to perform long division, using the usual approach of starting from the first digit of the dividend from the left.
- Take the first digit of the dividend from the left and check whether it is greater than or equal to the divisor. If it is, then progress to the next step. If it isn't, then combine this digit with the next digit to the left of the dividend.
- Next, divide this digit by the divisor and write the answer on top of your division box as the quotient.
- Then subtract the result from the digit and write the difference below dividend.
- Now bring down the next digit of the dividend.
- Repeat the same method until all the digits of the dividend have been used.
The process is best illustrated through the use of an example. Let's say our question is 900 / 5. So, in this example, 900 is the dividend and 5 is the divisor.
- The first digit on the left of the dividend is 9. So we will divide 9 by 5.
- 9 is not divisible by 5, but there is one lot of 5 in 9. So write 1 above the dividend as the first digit in the quotient.
- Write 5 beneath 9 and subtract it. 9 - 5 = 4.
- Now we must try and divide 4 by 5. But we can't because 5 is greater than 4.
- So we bring down the first 0 from the dividend to make it 40 and divide that by 5 instead.
- 40 / 5 = 8. So we write 8 as the next digit of the quotient above the dividend.
- Then, we write 40 below 40 and subtract 40 - 40 = 0.
- Next, we bring down the remaining 0 from the dividend.
- 0 / 5 = 0. So we write 0 as the remaining quotient.
- The quotient is now 180.
- So 900 / 5 = 180.
It is possible to divide from the right. However, dividing from the left is more efficient. Therefore, over many years of human ingenuity, we have come to start from the left as a means of efficiency rather than because the numbers dictate it.
With division, we are splitting a number into smaller and smaller pieces. So it makes sense to start dividing by splitting the biggest part of that number before moving to the smaller parts.
In the same way that we can consider multiplication as repeated addition (4 x 2 = 4 + 4), we can also consider division as repeated subtraction.
For example, 12 / 4 can be conceived as subtracting 4 from 12 until it is no longer possible and then counting the number of times you were able to do so.
This is one way of dividing from the right.
In this method, you work down the number line until you either reach 0 or can no longer subtract the divisor.
Let's say, for example, we want to divide 18 by 3. So we need to subtract 3 from 18 until it is impossible to subtract it anymore.
- Starting from the right, we do 8 - 3 = 5. We then carry the 1 from the tens column to get 15.
- 5 - 3 = 2. We then carry the 1 from the tens column to get 12.
- 2 - 3 cannot be done, so we carry the 1 to get 12 - 3 = 9
- 9 - 3 = 6
- 6 - 3= 3
- 3 - 3 = 0
- We then tally how many times we were able to subtract the divisor (3), which is 6 in our example.
- So, 18 ÷ 3 = 6.
Dividing numbers from right to left using this basic method works with single digits and smaller numbers. However, with larger numbers, left to right is far more efficient.
Division is the mathematical process of evenly splitting a number by another number. Long division is a method that simplifies dividing bigger numbers that cannot be done using mental arithmetic.
The traditional long division method starts by dividing the largest digit in the dividend, which is always the furthest to the left. Although this is the most commonly practised and efficient method of performing long division, some alternatives start with the smallest digit, which is always furthest to the right.
