Addition: Definition, Meaning, Properties & Examples

Addition is one of the basic arithmetic operations used for the purpose of calculations in Mathematics. We have four arithmetic operations that are widely used for the purpose of performing calculations and solving different problem sums. Addition is considered to be one of the most common operations that can be used for the purpose of performing different tasks in our day to day life. So, addition is to bring two or more numbers together. This article will highlight the function and properties of addition in details.

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Addition: Basic Details

Now, let us see a small conversation about addition.
Ram: I have \(3\) chocolates in my pocket.
Sham: I have \(5\) chocolates in my pocket.
Ram: So, how many chocolates do we have in total?
Sham: It is easy to find, let us add them together.
Ram: Add? What is that?
Sham: You have \(3\) chocolates with you, so keep \(3\) in your mind. I have \(5\) chocolates with me. Keep \(5\) fingers open in your hand. Now, start counting the finger starting from the number which comes after \(3\). That is \(3\) in mind \(5\) in fingers, after \(3\) it is \(4,\,5,\,6,\,7,\,8\).
Yes, we have \(8\)  chocolates in total with us.

Addition: Definition

Addition, generally indicated by the \(+\) sign, is a method of combining two or more numbers. In other words, finding the sum of two or more numbers or objects is known as an addition.

For example, to find the sum of \(5\) and \(7\) we will write it as \(5+7\).

Addition: Process and Example

Now, let us see the method of counting the objects. The addition is bringing two or more objects or numbers or things together.
Below here is shown how \(3\) pens are added to \(2\) pens to make them as \(5\) pens.

Like this, we can add many such objects like fruits, vegetables, stationeries, etc., to find the total numbers of objects.

How to Add Large Numbers?

Now let us learn how to add a large number above two digits. To add numbers of more than two digits, we will follow the below steps.
Step 1: We need to arrange the given numbers in columns, such as units placed under the unit’s place, tens under tens, hundreds under hundreds, and so on.
Step 2: We add the numbers in each column taking the carryover, if any, to the next column to the left, and adding it along with the number in that column. We continue this process till we add the numbers in all the columns.

Example: Add \(156\) and \(108\).
Solution: We arrange the given numbers in columns and start adding as follows.

Step 1: Add units place i.e., \(6+8=14\). So, write \(4\) and carry \(1\) to the ten’s column.

Step 2: Add ten’s place including carrying \(1\). So, it will be \(1+5+0=6\). Now there is no carryover and we can directly write 6 in the ten’s column.

Step 3: Now add the hundredth’s place i.e., \(1+1=2\).
So, \(156+108=264\)

Addition: Using a Number Line

The number line is the horizontal line in which the numbers are placed in equal breaks. It is the visual representation of numbers on a straight horizontal line. All the numbers in a pattern can be represented in a number line.

The numbers in a number line are shown below with zero in the middle and positive numbers to the right of the zero and negative numbers to the left side of a straight line.

There are two steps to be followed to add numbers on a number line.
\(\to\) Move right from zero to add the positive numbers.
\(\to\) Move left from zero to add the negative numbers.
Example: Let us add \(5\) and \(7\) using the number line.

First, mark point \(5\) on the number line. Then move \(7\) points to the right since we are adding positive numbers.

From the above number line, we find that \(5+7=12\).

Now, let us consider a negative number \(-6\) and add \(3\) to it and find the value. We know that \(-6\)  lies left to zero in a number line and \(3\) lies to the right side of zero in a number line. So, mark the point \(-6\) on the number line and move points to the right.

So, from the above number line, we can write \(-6+3=-3\).

Now, let us add \(-6\) and \(-3\) using a number line. Since, both are negative numbers, mark the point \(-6\) to the left of zero. Because \(-6\) lies left to zero in a number line. Now, move points to the left of \(-6\) on the number line (\(-3\) is a negative number).

So, from the above number line, we can write \(-6-3=-9\)

So, we have learned how to add the given numbers using a number line.
Wait, we observed some unique rules of addition while adding the numbers with different signs. What is that?

1. \(5+7=12\Rightarrow\) When we add two positive numbers or integers, we will get the answer as positive.
2. \(-6+3=-3\Rightarrow\) When we add a positive and a negative number, then subtract the given numbers and keep the sign of the larger number to the answer.
3. \(-6-3=-9\Rightarrow\) When we add two negative integers add the given absolute values and write the answer with a negative sign.

Addition: Properties

In the addition equation, we have addends and a sum.

When we put the addends together, the answer we receive is known as a sum.
There are three properties of addition:
1. Identity property
2. Commutative property
3. Associative property

Identity Property

The identity property states that, if we add any number to zero or if zero is added to any number the result is the same value of the number.
Example: \(8+0=0\) or \(0+8=8\)

Commutative Property

The commutative property of addition states that, if we change the order of addends the answer remains the same.
Example: \(6+9=15\) or \(9+6=15\)

Associative Property

The associative property of addition states that when we add three or more numbers the change in the order of the addends does not change the sum.
Example: \((4+3)+5=12\) and \(4+(3+5)=12\)

Till now, we have learned how to add the numbers normally, using number lines and using different properties. Let us extend our learning regarding addition.
The addition is not only the sum of integers. The addition is also used in finding the sum of fractions, a sum of decimals, etc. Now, let us learn how to find the sum of fractions and decimals.

How to Add Fractions?

The term which is used to represent the part of the whole is called a fraction. There are two parts in a fraction namely, numerator and denominator. There are three types of fractions:
1. Proper Fractions
2. Improper Fractions
3. Mixed Fractions
Example of Fraction: If an apple is divided into two equal parts, then each part is equal to half of the whole apple.

We can add the proper and improper fractions by making the denominator common. But to add mixed fractions, first, we need to convert the mixed fraction into an improper fraction and then add those fractions by making the denominator the same.

To add the given fractions, we need to know how to take the lowest common multiple (LCM) of the denominators or make the denominator of the given fractions the same and add the numerator.

LCM: The smallest positive integer that is divisible by both given numbers is called the Lowest Common Multiple or LCM.
Example: To find LCM of \(2\) and \(5\) we will use the below step.

So, the LCM of \(2\) and \(5\) is \(2 \times5=10\)
Now let us see some examples of adding the fractions.
1. \(\left({\frac{1}{4}}\right)+\left({\frac{2}{4}}\right)\)
Solution: In the given question the denominators are the same. So, add the numerators and put the answer over the same denominator.

\(\Rightarrow\frac{{1+2}}{4}=\frac{3}{4}\)

2. \(\left({\frac{1}{2}}\right)+\left({\frac{1}{3}}\right)\)
Solution: Here we can see the denominators are different, so first let us find the LCM of the denominators.

The LCM of \(2\) and \(3\) is \(6\). So, we know that \(2\times3=6\) and \(3\times2=6\). So, multiply the numerator and denominator of the first fraction by \(3\) and the second fraction by \(2\), we get.

\(\frac{{1\times3}}{{2\times3}}+\frac{{1\times 2}}{{3\times2}}\)
\(=\left({\frac{3}{6}}\right)+\left({\frac{2}{6}}\right)\)
\(=\frac{{3+2}}{6}\)
\(=\frac{5}{6}\)

So, from the above examples, we came to know that, to add two fractions, first make the denominators the same and add the numerators to find the answer.

How to Add Decimals?

A decimal number can be defined as a number whose whole number part and the fractional part are separated by a decimal point. The dot in a decimal number is called a decimal point. The digits following the decimal point show a value smaller than one.

The representation of integers and non-integers in their standard form is known as decimals.
Example: \(2.5, 3.6, 7.88, 1.33, \ldots  \ldots \)

To add these decimals, we need to follow the below steps:
1. Write the decimal numbers according to their place values.
2. Put zeroes if necessary, to complete the required number of decimal places.
3. Add the decimal numbers like the addition of whole numbers.

Example: Add \(130.1+53.24\)
Solution: We can see there are two digits after a decimal point in \(53.24\) and only one digit after the decimal point in \(130.1\). So, we need to add a \(0\) to \(130.1\).
Therefore, \(130.1+53.24 \Rightarrow 130.10+53.24=183.34\)
In the same way, we can add the decimal by adding zeros if necessary, based on their place values.

Solved Examples – Addition

Q.1. Add \(1538\) and \(236\).
Ans:

Q.2. Add \(3507468\) and \(6641007\).
Ans:

Q.3. Add \(3\) and \(4\) using the number line.
Ans: To add \(3\) and \(3\) using the number line, we need to mark a point \(3\) to the right side of \(0\) and start moving \(4\) points to the right.

So, \(3+4=7\)

Q.4. Add \(6\) and \(5\) using the number line.
Ans: To add \(6\) and \(5\) using the number line, we need to mark a point \(6\) to the right side of \(0\) and start moving \(5\) points to the right.

So, \(6+5=11\)

Q.5. Find the sum of \(13+17\) and \(17+13\) and write your decision.
Ans:

So, \(13+17=17+13 \Rightarrow30=30\)

Q.6. Find the sum of \(\frac{3}{4}\;\) and \(\frac{5}{3}.\)
Ans: Given \(\left( {\frac{3}{4}} \right) + \left( {\frac{5}{3}} \right)\)
We know that the common multiple of \(3\) and \(4\) is \(12\). So, multiplying the numerator and denominator of the first fraction by \(3\) and the second fraction by \(4\), we get
\(\frac{3}{4} + \frac{5}{3}\)
\( \Rightarrow \,\;\frac{{3 \times 3}}{{4 \times 3}} + \frac{{5 \times 4}}{{3 \times 4}}\)
\( = \frac{9}{{12}} + \frac{{20}}{{12}}\)
\( = \frac{{9 + 20}}{{12}}\)
\( = \frac{{29}}{{12}}\)

Q.7. Add \(23.45\) and \(345.5\).
Ans: To add the decimal, write the decimal numbers according to their place values. Put zeroes if necessary, to complete the required number of decimal places. Add the decimal numbers like the addition of whole numbers.

Summary

In this article, we can understand the definition of addiction, how to add the given objects, an example of addition, the addition of large numbers, the addition of numbers using a number line, and the addition of fractions and decimals. Also, we have learned the different properties of addition.

Frequently Asked Questions (FAQs) – Addition

Q.1. What are addition and subtraction?
Ans: Addition is a process of finding the sum of two or more numbers or objects or something else. The Addition is a mathematical operation that uses \(+\) as the symbol to add the given things.Subtraction is the process of deducting from a group of numbers or finding the difference between numbers.

Q. What are the different properties of addition?
Ans: The different properties of addition are:
1. Identity property
2. Commutative property
3. Associative property

Q: How do you do addition?
Ans: Addition is the process of adding the given numbers or it is the process of finding the sum. Example: If we have given two numbers then, we need to place that number column like the unit’s place under the unit’s place and tens place under the ten’s place and so on. Then add the respective digits. If we have a carryover left in the unit’s place, then add to the tens column and add the respective numbers.

Q. What are the strategies of addition?
Ans: The strategies for addition are Breaking apart/Separation, Compensation and Transformation.

Q. What are addition and subtraction?
Ans: Addition is a process of finding the sum of two or more numbers or objects or something else. The Addition is a mathematical operation that uses + as the symbol to add the given things. Subtraction is the process of deducting from a group of numbers or finding the difference between numbers.

Q. What is addition?
Ans: Addition is a process of finding the sum of two or more numbers or objects or something else. The Addition is a mathematical operation that uses + as the symbol to add the given things.

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