Addition

Addition

The process of adding is putting two or more things together. In math, adding is the way to figure out how much two or more numbers add up. It is a basic math operation that we use all the time in our daily lives. We use addition a lot when we work with money, figure out how much we owe for groceries, or figure out the time.

What is Addition?

In math, adding is the process of putting two or more numbers together. The result of adding two or more numbers together is called the sum of the given numbers. For example, if we add the numbers 2 and 4, (2 + 4), we get 6. Here, we added the numbers 2 and 4 together to get the sum, which is 6.

Addition Symbol

There are different symbols in math. One of the math symbols that is used a lot is the symbol of addition. In the above definition of addition, the numbers 2 and 4 are brought together. If we look at how adding works (2 + 4 = 6), we can see that the symbol (+) connects the two numbers and finishes the expression. The addition symbol is made up of one line across and one line up. It is also called the plus sign (+) or the sign for addition.

Parts of Addition

A statement about adding can be broken down into the following parts.

Added: These are the numbers that are added together.

Addition Symbol: The (+) sign is used to show that two numbers are being added together. If the statement is written horizontally, like in the example below, we put an equals sign (=) right before the sum.

Sum: It is the final number you get when you add up all the numbers.

Addition Formula

The statement that shows an addition fact is called the “addition formula,” and it looks like this: addend + addend = sum. This can be understood by looking at the example in the figure below. Here’s how to explain the basic formula for adding or the math equation for adding.

In this case, the addends are 4 and 2, and the sum is 6. It’s important to remember that an addition fact can have more than one addend. 5 + 4 + 2 + 7 = 18, for instance.

How to Add Numbers Together?

When solving addition problems, it’s easy to add up numbers with one digit, but for bigger numbers, we divide them into columns based on their place values, such as ones, tens, hundreds, thousands, etc. Based on the place value system, we always start adding from the right side. This means we start with the one’s column, then move to the tens column, then the hundreds column, and so on. When solving these kinds of problems, we might run into some cases with carry-overs and some without. Let’s look at what it means to add with regrouping and what it means to add without regrouping.

Addition Without Regrouping

Addition without regrouping is when the sum of the digits in each column is less than or equal to 9. Let’s use an example to see how to add two or more numbers without regrouping.

Example: Add together 12311 and 53213.

Solution: We’ll use the given steps and try to link them to the figure below.

Step 1: Look at the numbers in the one column. (1 + 5 = 6)

Step 2: Move to the column with the tens. (2 + 3 = 5)

Step 3: Add the numbers in the hundreds column together. (3+ 2 = 5)

Step 4: Now, add up the numbers in the thousands column. (1 + 1 = 2)

Step 5: Add the numbers in the “ten thousand” column. (1 + 3 = 4)

Step 6: 12311 + 53213 = 65524.

When adding, we don’t have to regroup. Instead, we just add the numbers in each place value column and add the totals together to get the answer. Now, let’s figure out how to add with regrouping.

Addition With Regrouping

When adding numbers, if the sum of any of the addends is more than 9 in any of the columns, we regroup this sum into tens and ones. Then, we move the sum’s tens digit to the column before it and write the sum’s ones digit in that column. In other words, we only write the number in the “ones place digit” in that column. The “tens place digit” goes in the column to the left. Let’s use an example to learn how to add two or more numbers by regrouping.

Example: Add 18794 and 54856.

Solution: Let’s try to figure out what the steps have to do with the picture below.

Step 1: Put the numbers in the ones place. (4 + 6 = 10). Here, 10 is the total. The sum’s tens digit, which is 1, will be moved to the column before it.

Step 2: Add the tens column numbers together with the carryover 1. This means that 1 (carry-over) + 9 + 5 = 15. The total here is 15. The number 1 will be moved from the tens place to the hundreds place.

Step 3: Add the numbers in the hundreds place to the carryover number 1. This means that 1 + 7 + 8 equals 16. The total here is 16. The number 1 will be moved from the tens place to the thousands place.

Step 4: Now, add the numbers in the thousands place to the carryover digit 1. For example, 1 (carryover) + 5 + 2 = 7.

Step 5: 5794 + 2856 = 8650, so the total is 8650.

Changing the order of the numbers does not change the answer. This is an important property of addition. For example, if we switch the addends in the example above, we still get the same total, which is 6340 (2865 + 3475). This is called the commutative property of addition.

Addition on Number Line

Using number lines is another way to add numbers. Let’s use an example and the number line below to figure out how to add on a number line. If we want to figure out what 8 + 4 is, we start by putting 8 on the number line. When we use a number line to add, we move one number to the right of the number as we count. Since we are adding 8 and 4, we will move four steps to the right. Now we’re up to number 12. Hence, 8 + 4 = 12.

Addition Properties

Most of the time, we use the following properties when doing addition:

Commutative Property: This property says that the sum of two or more addends stays the same no matter how they are put together. For instance, 8+7 = 7+8 = 15

Associative Property: This property says that the sum of three or more addends stays the same no matter how they are put together. 5 plus 7 plus 3 equals 5 plus 7 plus 3 equals 15.

Additive Identity Property: This property of addition says that if we add 0 to any number, the sum is always the number itself. Adding 0 and 7 equals 7.

Addition Word Problems

Every day, we use the idea of adding to figure out how to do things. We should look at the situation carefully and use the tips and tricks that come next to figure out what to do. Let’s use an interesting example to learn how to solve addition word problems.

Example: A School has 410 boys and 289 Girls. How many Students are there in the School? 

Solution: Number of Boys in a School = 410 and 

  Number of Girls in a School = 289 

To find the total of number of Students in the school we need to Add the Boys and Girls. Now, Let’s find the total number of Students

So Total Number of Students = 410 + 289 

Therefore Total Number of students in the Class = 699 

Tips and Tricks in Addition

• When you see words like “put together,” “in all,” “altogether,” and “total,” you know you need to add the numbers.
• Start with the bigger number and add the smaller number to it. For example, it’s easier to add 12 to 43 than 43 to 12.
• Putting numbers into groups based on their place values makes adding easier. For example, 22+64 can be broken up into 20+2+60+4 parts. Even though this looks hard, it makes it easier to add in your head.
• When adding numbers with more than one digit, make sure to put the numbers in the order of their place value.
• When you add 0 to any number, you get that number.
• Adding 1 to any number makes the sum the next number after that number.
• “+” is used to show that something is added.
• When you add up a set of numbers, it doesn’t matter what order you do it in. The sum will always be the same. For instance, 2+5+3 = 10 and 5+3+2 = 10. The name for this is the associative property of addition.

☛Related Links

What is regrouping in math addition?

Addition Calculator

Addition of Algebraic Expressions

Addition of Fractions

Adding Decimals

Some More Addition Examples : 

Question : 1 

A Fruit Seller Sold 564 Apples and 269 Mangoes . How many Fruits did he sell together ? 

Ans – Number of Apples Sold = 564

Number of Mangoes Sold = 269 

Total Fruits Sold Together = 564 + 269 

So the Total Fruits he Sold = 833 

Question 2 : A train carrying 679 people on a journey. It carried 500 people in the return journey. How many people travelled in all?

Ans – Train Carried People in first Journey = 679 

Train Carried People in Return Journey = 500 

To Find the Total People a Train carried = 679 + 500 

Total People Travelled = 1179 

Frequently Asked Questions FAQs on Addition