Operations on Decimal Fractions- Addition and Subtraction of Decimal Fractions

In mathematics, various operations on decimal fractions are performed to evaluate the values, equations, and data. Operations like “addition and subtraction of decimal fractions” and division and multiplication of decimal fractions are some of the procedures to be followed to evaluate mathematical expressions. There are various other procedures while evaluating the decimal fractions such as division of decimal fraction with a counting number, division of decimal fraction with a decimal fraction, for instance, 0.0204/17 can be written as 204/17 which is equivalent to 12? Now the 0.0204/17 can be easily written down as 1.0012.

Addition and subtraction

Addition and subtraction can be considered as primary operations in arithmetic. It is used to adding and subtracting the two or more values of numbers or any arithmetic values. Apart from this other two basic operations are the multiplication and division. It can be easily stated that subtraction is quite opposite of addition, for instance, 10+2 is equal to 12 whereas 12-2 is equal to 10. The mathematical operation of adding numbers means summing up 2 or more values or numbers to obtain another number or value, for example by adding 1 and 9, 10 will be obtained. Similarly, subtraction denotes the reduction of number from another number to obtain the final value such as 5 subtracted from 8 will result in 3.

Operations on decimal fractions 

A decimal value or number is a fractional number or value whose denominator has the power of 10 for instance the number 6/10 can be expressed in the form of decimal as 0.6 where:

• The dot denotes the point of the decimal.
• The following number placed right to the point of the decimal expresses the numerator of the fractional number or fractional part.
• The number placed left to the point of decimal expresses the whole portion of the fractional value.
• For instance, 5+3/10 can be denoted as 5.3 where 5 denotes the whole number part and 0 denotes fractional part.
• The point of the decimal segregates the rational part from the whole number part.

The “addition and subtraction of decimal fractions” can be observed and is dealt in everyday life regarding Temperature, Money, and Measurement.

“Addition and subtraction of decimal fractions” are significantly easy if one is comfortable with forwarding and borrowing. The first step is to line up the decimal point along with the addition of zeroes if necessary at the end of the last integer, it will create the same integers of decimal places. Now do the addition and subtraction like a normal procedure.

Addition of decimal fractions

 Before the addition and subtraction of any fractional values, it is necessary to find a common denominator, which means one has to find the smallest numeric value which can make both of the denominators evenly. A simple trick to this problem is by multiplying both denominators together to obtain a new denominator, for example, ⅝ + ⅗ can give us denominator 40 by multiplying 8 and 5 together.

Now, to find a new numerator one has to look at the numerator of each fraction individually. It can be observed that for obtaining the denominator 40, factors 8 and 5 have been used. Now we use this factor to multiply it with each numerator to make it even, for example, ⅝ + ⅗ can be expressed as (5*5 + 3*8)/ 40. Now the denominator is the same, the above numerator can be easily evaluated by simply adding and subtracting. The following value will be 1.225.

Subtraction of decimal fractions

In the procedure of subtraction in decimal fractions, one has to simply subtract one decimal from another decimal. It is observed that subtracting a decimal value is similar to subtracting a whole numeric value. First, it has to be converted into decimals and the numbers are placed one above the other separated by a common line. There are two simple rules of subtracting decimal fraction which are:

• Write the integers of the numbers one below another in such a way that decimals are in the same vertical line.
• Now follow the simple subtraction procedure of Addition and subtraction of decimal fractional values

Conclusion 

From the above discussion, it can be concluded that both decimals and fractions are two different forms of ways to express the numbers. When the fractional numbers are transformed into decimals it makes it convenient for carrying mathematical operations of decimal operations. The addition and subtraction of decimal fractions can be easily observed in everyday life which can be in the form of monetary values, measurement, and temperature. Both the operation addition and subtraction of decimal fractions have similar procedures and provide accurate values. The mathematical operation of addition and subtraction simply means summing up numbers and reducing numbers from one another.