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Mathematics is not only the collection of Numbers of different types(i.e, natural numbers, whole numbers, fractions, integers, rational and irrational numbers and real numbers) but also includes the combination of mathematical operators(i.e, addition, subtraction, multiplication and division) which actually increase relevancy of existence of the numbers.

The basic operations of addition are stated below. Basically addition word is significant for adding, joining, bringing together, increasing one value by another, combining  and  many more. The '+' sign is used  to represent the operations of addition.

Addition can be done by forward counting, which is the most easy and beginners method of addition.  If we simply need to add 5 to 23, then  we count 5 forward towards right of the number line to get the desired result.  So, after 23 we have 24, 25, 26, 27, and 28 as next 5 numbers. So we get 28 as the sum of 23 and 5.

23 + 5 = 28

To do some complex calculations of addition i.e, for higher digits row method was developed in which addition process became easy.  Here we start addition from ones place and proceed towards left of the place value as tens, hundreds... and so on .

Example 1:

Example 2:

## What will be the result of 9 + 8 = ?

The answer to this question is 17. As both Numbers have single digits so no carry will be generated and result of 9 + 8 = 17.

9
+    8
----------
1 7

## What will be the result of 87 + 7 = ?

The answer to this question is 94. Here we will first add digits at ones place and carry 1 will be added to digit at tens place result of 87 + 7 = 94.

8 7
+  7
-------
9  4
Step 1 ) Add 7 + 7 this gives 14, keep 4 and add carry to digit at tens place.
Step 2 ) Add carry 1 to 8 we get 9.
Step 3) Our final result is 94.

## Calculate the result of 92 + 65 = ?

Result of 92 + 65 = 157. Here first we add digits at ones place that are 2 and 5 and gives 5 + 2 = 7. Now add Digits at tens place that are 9 and 6 we get 9 + 6 = 15, so our final result will be equals to 157. This process is shown below:

9 2
+  6 5
--------
1 5 7

Step 1 ) Add 5 and 2, we get 5 + 2 = 7.
Step 2 ) Add 9 and 6, we get 9 + 6 = 15.
Step 3 ) Our final result is 157.

## Find the result of 23 + 34 +98 = ?

Result of above question that is 23 + 34 + 98 = 155 , here we have three Numbers to be added, so first we will add 23 and 34, we will get 57 and now we will add 57 to 98, in this when we add 7 and 8 a carry will be generated which will be added to the digits at tens place and our final result will be 155. This process is shown below:

2 3
3 4
+    9 8
------------
1 5 5

Step 1 ) Add 3 + 4 + 8 = 15, add carry 1 to digit at tens place.
Step 2 ) Now add 1 + 2 + 3 + 9 = 15.
Step 3 ) Our final result will be 155.

## Calculate the result of 157 + 3 + 1000 = ?

The result of above question is 1160. First we will add 157 and 3 together that is 157 + 3 = 160. Now we will add 160 to 1000 that is 1000 + 160 = 1160 , so our final result will be 1160, this process is shown below-

1 5 7
3
+  1 0 0 0
------------------
1  1  6 0

Step 1 ) Add 7 + 3 + 0 = 10, keep 0 and add carry 1 to digit at tens place.
Step 2 ) Now add 1 + 5 + 0 = 6.
Step 3 ) Now add 1 + 0 = 1.
Step 4 ) Now add 1.
Step 5) Our final answer is 1160.

## Find the result of 34.5 + 83.6 + 45.8 = ?

The result of above operation is 163.9. First we will add 34.5 and 83.6 that is 34.5 + 83.6 = 118.1. Now add 118.1 to 45.8 we get 118.1 + 45.8 = 163.9 which is our final result .

This process is shown below-

3 4 . 5
8 3 . 6
4 5 . 8
-----------
1 6 3  . 9

Step 1 ) First add digits after Decimals we get 5 + 6 + 8 = 19, keep 9 and add carry 1 to next higher place digit.
Step 2 ) Now add 1 + 4 + 3 + 5 = 13. Transfer carry 1 to next higher place digit.
Step 3 ) Now add 1 + 3 + 8 + 4 = 16.
Step 4 ) Our final result is 163.9.

## Find the result of 4876 + 908 + 459 = ?

The result of above operation is 6243. First we will add 4876 and 908 that is 4876 + 908 = 5784. Now add 5784 to 459 we get 5784 + 459 = 6243 which is our final result .

This process is shown below-

4  8  7  6
9  0  8
4  5  9
-------------
6  2  4   3

Step 1 ) First add digits at ones place we get 6 + 8 + 9 = 23, keep 3 and add carry 2 to next higher place digit.
Step 2 ) Now add 2 + 7 + 0 + 5 = 14. Transfer carry 1 to next higher place digit.
Step 3 ) Now add 1 + 8 + 9 + 4 = 22. Transfer carry 2 to next higher digit.
Step 4 ) Our final result is 6243.

## Find the result of 1.2 + 7.8 + 8.1 = ?

The result of above operation is 17.1. First we will add 1.2 and 7.8 that is 1.2 + 7.8 = 9.0. Now add 9.0 to 8.1 we get 9.0 + 8.1 = 17.1 which is our final result .

This process is shown below-

1 . 2
7 . 8
8 . 1
-----------
1 7 . 1

Step 1 ) First add digits after decimal and we get 2 + 8 + 1 = 11, keep 1 and add carry 1 to next higher place digit.
Step 2 ) Now add 1 +1 + 7 + 8 = 17.
Step 3 ) Our final result is 17.1.

## Find the result of 111.1 + 83.26 + 4.8 = ?

The result of above operation is 199.56. First we will add 111.1 and 83.26 that is 34.5 + 83.6 = 194.36. Now add 194.36 to 4.8 we get 194.36 + 4.8 = 199.6 which is our final result .

This process is shown below-

1 1 1 . 5 0
8 3 . 2 6
4 . 8 0
-----------
1 9 9 . 5 6

Step 1 ) First add digits after Decimals we get 0 + 6 + 0 = 6.
Step 2 ) Now add 5 + 2 + 8 = 15. Transfer carry 1 to next higher place digit.
Step 3 ) Now add 1 + 1+ 3 + 4 = 9.
Step 4 ) Now add 1 + 8 = 9.
Step 5 ) Our final result is 199.56.

## Find the result of 237 + 908 + 690 = ?

The result of above operation is 1835. First we will add 237 and 908 that is 237 + 908 = 1145. Now add 1145 to 690 we get 1145 + 690 = 1835 which is our final result .

This process is shown below-

2 3 7
9 0 8
+ 6 9 0
-----------
1 8 3  5

Step 1 ) First add digits at ones place we get 7 + 8 + 0 = 15, keep 5 and add carry 1 to next higher place digit.
Step 2 ) Now add 1 + 3 + 0 + 9 = 13. Transfer carry 1 to next higher place digit.
Step 3 ) Now add 1 + 2 + 9 + 6 = 18.
Step 4 ) Our final result is 1835.

## The sum of two numbers is 15. If one of the numbers is x, the other would be best represented by which of the following?

In mathematical word problems involvement of operations like addition, subtraction, multiplication and division seem to be much in use. Word problems are basically expressed in the form of statements. These statements are essentially not mathematical expressions or Numbers. We ourselves have to understand complete word problem properly and then extracting the necessary information that can be used for evaluation purpose. Next part of word problems is the solution. In a word problem all dimensions for various quantities have to be handled in a proper way. If conversions are required, do them purposefully. Let us consider an example of such problems to understand their working in Math properly.
Suppose we have following example word problem:

Q. The sum of two numbers is 15 if one of the numbers is X, the other would be best represented by which of the following? Options are:
A.      X + 15
B.      X – 15
C.      15 – X
D.     X
Solution: Word problem says that numbers when added give result 15 and one number out of two is X. Let us assume that second number is given as Y. According to the word problem, only information we are available with is their sum, i.e.
X + Y = 15,
Taking 'X' to another side as it is also a known quantity; we get value of 'Y' as:
Y = 15 – X,

Thus correct representation of value of 'Y' is given by option C i.e. 15 – X. Thus we see, to find the value of one missing variable in the problem we need just relevant information. Similarly, for word problems involving more than 1 variables, we need that information.

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