Addition And Subtraction of Decimals

 Addition of decimals is the process of finding the sum of numbers that contain decimal points. Subtraction of decimals is the process of finding the difference between such numbers.

In these methods, check whether the numbers have the same number of digits after the decimal point (i.e., are "like decimals"). If not, add trailing zeros to make them like decimals. If not, convert the unlike terms to like terms by adding additional zeroes after the decimal point.

As we have learned, decimal numbers can be classified as like or unlike. To find the sum of two decimals, we need to apply the following steps:

1. Check whether the decimal points are vertically aligned.

2. If necessary, add trailing zeros to make the numbers have the same number of digits after the decimal point.

3. Add as whole numbers, then place the decimal point in the result directly under the other decimal points.

Adding Unlike Decimals

Unlike decimals, values always have a different number of digits after the decimal point.
They can be easily converted to like decimals by adding extra zeroes after the decimal point. Note that adding extra zeros does not change the value of the number.

Add 10.22 and 3.5

Step 1: Here, the given decimal values are not aligned correctly, so they are unlike.
 10.22
+  3.5  

Step 2: To make them alike, we add extra zeroes as shown below:
  10.22
+  3.50  

Step 3: We now add the values to find the sum.
  10.22
+  3.50
   13.72

Adding Like Decimals

Since the like decimals have the same number of digits after the decimal point, they can be aligned correctly and added just like whole numbers. The decimal point must be placed accurately in the final result.

Example: Add 95.7 and 82.3
    95. 70
+  82. 30
   178.00

To find the difference between two decimals, we use the following steps:

• Verify if the decimal point of the number is correctly aligned in a vertical line.

• Place zeroes where the numbers differ in length.

• Now, we find the difference between the numbers by subtracting them.

Subtraction of Like Decimals

The subtraction of like numbers is calculated in the same way as whole numbers, by subtracting the smaller number from the larger one.

Subtract 40.32 from 98.25
    98.25
-  40.32  
    57.93

Subtraction of Unlike Decimals

To subtract unlike decimals, first, add extra zeroes to the shorter decimal.
Then, subtract the numbers in the same way as, like decimals. 

Subtract 20.486 from 78.6

    78.600
-   20.486
    58.114

Decimals are significant components of mathematics. They are widely used in real-life scenarios beyond math, where the precision of numbers matters. Here are a few real-life applications of addition and subtraction of decimals:

• Shopping: We use decimals in shopping to calculate the exact amount of money spent or the discount amount.

• Cooking: In cooking, precise measurement of ingredients is often required in decimals.

• Distance/height measurements: They can be applied in measuring the accurate distance or height.

• Fuel consumption: Decimals help calculate fuel consumption or estimate the required fuel amount by using addition or subtraction.

•  Time: We use decimals to measure time in sports or when going on a trip.