What is Division?
Division is the process of splitting numbers into equal parts or groups.
The general form of division is, \(\frac{\text{Dividend}}{\text{Divisor}}=\text{Quotient}\)
Division can also be written as, \(\text{Dividend} \div \text{Divisor}=\text{Quotient}\)
In the case of a remainder after division, we can write out the division operation as, \(\text{Dividend}=\text{Divisor}\times \text{Quotient} + \text{Remainder}\)
Division of a Decimal by a Whole number
We begin by dividing the two numbers without taking into account the decimal point. The decimal point of the quotient is then placed in the same position as that of the dividend.
Divide Decimals by one-digit numbers
Example 1: Divide the decimal value of 6.65 by 5.
We will divide the value as we do in the case of whole numbers. The decimal point is ignored in this case, and the value is divided until you get 0 as the remainder or a value less than the divisor. Finally, place the decimal point at the same position as given in the quotient.
\( =~\frac{6.65}{3}~=~1.33\)
Example 2: Divide 60.3 by 6.
\( \frac{6.63}{6}~=~10.05\)
You must note that when the dividend does not have enough digits to divide, we proceed with the division by adding zeros at the right of the end of the decimal numbers. This is known as the process of inserting zeroes.
Divide the Decimals by two-digit numbers
Example 3: Divide the decimal value of 120.63 by 30.
We will divide the value as we do in the case of whole numbers. Ignore the decimal part and divide the value until you get 0 as the remainder or get a remainder less than the divisor. The decimal point of the quotient is placed in the same place above the dividend.
\( =~\frac{120.63}{30}~=~4.021\)
4.021
_________
30 ) 120.63
-120
_________
63
-60
_______
30
-30
_______
0
Division of a Decimal by a Decimal
To divide a decimal by a decimal, we first need to convert the divisor into a whole number. To do this, we multiply the divisor by a power of 10, and the same value is multiplied by the dividend. Then the division is carried out.
Example 4: Divide the decimal value of 1.25 by the decimal 2.5.
Move the decimal of the divisor to the right as many times as necessary to make it a whole number. We have 1 decimal place, so we need to multiply by 10.
\(\frac{1.25~\times~10}{2.5~\times~10}~=~\frac{12.5}{25}\)
Divide the dividend (12.5) by the divisor (25).
\(=~\frac{12.5}{25}~=~0.5\)
0.5
_______
25 ) 12.5
– 0
———-
125
– 125
———-
0
Example 5: Divide the decimal value of 66.6 by the two-digit number 33.3
Convert the divisor to a whole number by multiplying the numerator and the denominator by 10.
\(=~\frac{66.6~\times~10}{33.3~\times~10}~=~\frac{666}{333}~=~2\)
2
_______
333 ) 666
– 666
———-
0
Real-life Examples
Example 6: Jack has a stamp collection. Each stamp weighs 0.4 ounces. If the total weight of his stamps is 26 ounces, how many stamps does he have?
The weight of one stamp is 0.4 ounces. The total weight of all of the stamps combined is 26 ounces. To figure out the number of stamps, divide the total weight by the weight of one stamp:
\(26~\div~4\)
\(=~\frac{6~\times~10}{0.4~\times~10}\) Convert the divisor into a whole number
\(=~\frac{260}{4}\)
= 65
65
_______
4 ) 260
– 24
———-
20
– 20
———-
0
Hence, Jack has 65 stamps in his collection.
Example 7: Tom runs 45.5 miles in 6.5 hours a day. How many miles does he cover in 1 hour?
To calculate the miles that Tom covers in 1 hour, we need to divide the total distance by the time taken to cover the given distance:
\(45.5~\div~6.5\)
\(=~\frac{45.5~\times~10}{6.5~\times~10}\)
\(=~\frac{455}{65}\)
= 7
7
_______
65 ) 455
– 455
———-
0
Tom covers 7 miles in an hour.
The number being divided is known as the dividend. The number that divides the dividend is known as the divisor. We call the result of the division operation as the quotient.
Let us say you have five apples, which would be 5.0. So far, no one has eaten any of the apples. However, if you have only half an apple, you do not have a full apple; instead, you have half an apple and five full apples. We can write this in decimal form as 5.5, or we can use terms such as five and five-tenths of an apple.