A division with decimals is a mathematical operation that consists of dividing into equal parts numbers that are made up of an integer part and a decimal part, both separated by a period or a comma, also called a decimal.
We can find different combinations:
decimal dividend and integer divisor
4.50 ÷ 2 = 2.25
integer dividend and decimal divisor
5 ÷ 1.25 = 4
dividend and divisor are decimal numbers
3.3 ÷ 1.1 = 3
Depending on the case, the quotient It can be a decimal number or an integer.
How to divide with decimals in the dividend
This division is done like a division between whole numbers, we just have to pay attention to place the decimal point in the correct place.
Division with a decimal number in the dividend, whole number in the divisor and decimal result.
We begin by looking for a number that, multiplied by the divisor, results in the figure taken from the dividend or an approximate one (2×2=4). We write down the product of said multiplication below the dividend figure. We will subtract both figures (4-4=0) and write down the difference (0) below and separated by a horizontal line. Then we will lower the next figure (5). If, as in the example, this number is to the right of the comma, we are dealing with a decimal figure and it is time to place the comma in the quotient. We proceed to look for a number that, when multiplied by the divisor, gives us this figure or an approximation (2×2=4). We write down the product below and subtract both numbers (5-4=1). The difference is noted (1) and separated by a horizontal line. When we no longer have any more figures in the dividend, zeros will be placed until the result is complete. Once placed (10), we look for the number that, multiplied by the divisor, brings us closer to this new figure (5×2=10). We write down the result below and subtract, writing down the difference separated by the horizontal line (10-10=0). This division is exact because it has left a remainder of 0.
How to divide with decimals in the divisor
To solve this type of division, the essential thing is to convert the decimal divisor into an integer. To do this, we eliminate the comma and add to the dividend the same number of zeros as the decimal figures in the divisor.
Division with a whole number in the dividend and a decimal number in the divisor. The result is an integer.
First thing to divide 5 ÷ 1.25 is to remove the comma from the divisor and add as many zeros as there are decimal figures in the divisor. In this case we will add two zeros to the dividend, leaving 500 ÷ 125. We need a number that, when multiplied by the divisor, results in or is close to the dividend. We write down the result of the multiplication (4×125=500) below the dividend, subtract and separate the difference (0) with a horizontal line. This division is exact because it gives 0 as the remainder.
How to divide with decimals in dividend and divisor
It is necessary to convert the divisor to an integer. The elimination of the comma from the divisor is compensated by moving the comma of the dividend as many places as the divisor has decimal places (for example, 3.3 ÷ 1.1 becomes 33 ÷ 11), the comma is moved by one place.
Division with a decimal number in the dividend, a decimal number in the divisor, and an integer in the result.
We eliminate the comma from the divisor and move the comma of the dividend to the right, as many places as there are decimal places in the divisor. In 3.3 ÷ 1.1 we delete the comma of the divisor and move that of the dividend one place to the right, obtaining 33 ÷ 11We look for the number that, multiplied by the divisor, results in or approximates the dividend. We write down the result (3×11=33) below the dividend, subtract and write down the difference separated with a horizontal line. The division is exact because its remainder is 0.
If there are not enough figures in the dividend, we will add zeros until the number of decimals in the divisor is equal (for example, 25.4 ÷ 3.826 will become 25400 ÷ 3826). Since there was only one figure after the dividend comma and we needed to move it three places, we added two zeros to compensate.
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