How to do divisions with a comma? The complete guide to perform this operation with the comma at the divisor, at the dividend and with both commas.
Comma Division: Introduction
Division problems that include decimals can be difficult for younger students to understand. Adults often have difficulty with these operations if they are not used to practicing mathematics regularly, or if they did not have a solid background during their elementary school years, they may not be able to do it or take longer to solve them.
It is essential to ensure that children receive a clear and complete explanation of these divisions from the very beginning, thus avoiding any room for uncertainty. Although they may seem complicated, with the right practice and exercise, these divisions are not at all unsolvable and can also be done mentally. Now, we will explore the method for performing divisions with decimals and provide you with some guidance on how to proceed. Read on to learn more!
Whole numbers and decimal numbers
Let’s start with some basic notions, just to understand: in mathematics, numbers can be whole (without a comma) or decimal, that is, provided with a comma and other numbers after it; these numbers are called “decimals” and identify the number with 1, 2 or more decimal places (or more precisely tenths, hundredths, thousandths).
For example: 9 is a whole number, 9.5 is a number with only 1 decimal, 9.55 with 2 decimals (hundredths) and so on. Solving a division means finding how many times a number , which is called the Divisor (the number on our right) is contained in another number called the Dividend (the number on our left) and the method for solving the operation changes depending on whether one of the 2 factors has a decimal point or not. Three cases can therefore arise, which we will address one by one. It is very important to learn to recognize and understand them, so as to know which procedure to ado.
Whole Dividend and Decimal Divisor
First case : Integer Dividend, Decimal Divisor . Let’s start by making the divisor an integer too, so the first question to ask is: how many decimals are there? So multiply both by 10, 100, 1000, as many zeros as there are decimals.
Example: 840:4.2. The divisor has 1 decimal place so we will multiply both by 10, obtaining 8400:42. The 42 goes into 84 twice with a remainder of 0, then the 42 goes into 0 zero times with a remainder of 0, once again the 42 goes into 0 zero times with a remainder of 0 and the result is 200. Both are decimal numbers.
In this case, the number with the greatest number of decimals prevails. Let’s say 1.02:3.4, the dividend wins having 2 decimals against 1 of the divisor; therefore I will have to multiply both by 100, obtaining 1020:340. Both are integers so let’s proceed: 34 goes into 102 three times with a remainder of 0.
Decimal Dividend and Integer Divisor
Second case : Decimal Dividend and Integer Divisor , that is, the opposite case to the previous one. We begin to carry out the operation normally, writing how many times the integer divisor is in the integer dividend, then once we reach the decimal point we will simply have to add it to the result or “quotient” and continue with the division, adding the decimals.
If we do not obtain a remainder equal to 0, we can be more or less precise or approximate depending on how many decimal places we want to assign to our quotient.
For example: 28.4:12. The 12 goes into 28 twice with a remainder of 4, so I insert the decimal point; I lower the 4 and get a remainder of 44; the 12 goes into 44 three times with a remainder of 8; I add a 0 and get 80; the 12 goes into 80 six times with a remainder of 8 and so on.
The result rounded to two decimal places will be 2.36.
Decimal Dividend and Decimal Divisor
The last and most complex case is that of the Dividend and the Divisor both decimal . The first step to take is to remove the decimal point from the Divisor; at the same time, you have to move the decimal point of the Dividend as many times as there are decimal places in the Divisor.
Let’s take a clarifying example right away: 1.83:0.3. The Divisor has only one decimal place, so you need to move the Dividend comma just once. We therefore have 18.3:3. Did you notice that, now, we are faced with a division with a decimal Dividend and an integer Divisor, i.e. the first case addressed in the guide? At this point, we proceed as explained previously. The final result will be 6.1 with a remainder of 0.
As you can see, a good initial setup helps a lot to solve these operations. At the beginning it will take you more time to do them, however perseverance and training will make everything easier.
