Addition and Subtraction

The first few math operations that children learn are addition and subtraction. The other two math operations are multiplication and division. 

Addition and subtraction are operations to add and subtract mathematical values or numbers respectively. Addition and subtraction are known as inverse operations. Let’s understand it with the help of an example, If 2 is added with 4 then it results as 6 and if 2 is subtracted from 6 then it results as 4. 

Similarly, multiplication and division are also known as inverse operations.

Addition

The addition is a mathematical operation that adds two numbers together. A sum is a result or response obtained after adding. 

⇒ For example, when we add 2 and 5, we get 7.  We used the addition operation on two numbers, 2 and 5, to get the total, which is 7.

⇒ 2 + 5 = 7

Symbol

Different symbols are used in mathematics. One of the most commonly used math symbols is the addition sign. We read about adding two numbers 2 and 5 in the above definition of addition. The symbol (+) connects the two numbers and completes the specified statement if we observe the pattern of addition (2 + 5 = 7). One horizontal line and one vertical line make up the addition sign. The plus sign is another name for the addition symbol.

Addition Formula

To solve any addition problem, we utilize the formula Addend + Addend = Sum. 

Let’s understand the following terms:

• Addends: The numbers to which the addition operation will be applied.

• Sum: The result of the addition.

• When doing addition, we employ two symbols: a plus sign (+) and an equal sign (=).

Solving Addition Problems

One-digit numbers can be added easily, but bigger numbers require splitting the numbers into columns using their appropriate place values, such as ones, tens, hundreds, thousands, and so on. 

According to the place value system, we always start adding from the right side. While solving such problems, we may come across some examples that have carryover and others that do not. 

Addition without regrouping is an addition that involves the sum of digits less than or equal to 9 at each place value. In addition with regrouping is a type of addition that involves a sum of digits higher than 9 at any of the place values. To add two numbers using regrouping, first find the total of the digits, then write only the unit place digit in the appropriate column, while taking the tens place digit in the column to the immediate left.

Let’s understand the addition of 2 digit number:

Addition without regrouping: Assume the number are 12 and 16 then:

Here the sum of 2 and 6 is 8 and the sum of 1 and 1 is 2. So both 8 and 2 are less than 9. So we can simply add the numbers.

Addition with regrouping: Assume the number are 15 and 26 then:

Here the sum of 5 and 6 is 11 which is more than 9 so we have written only 1 at the unit’s place and took 1 carryover then added carry to the sum of 1 and 2. So the sum occurs as 41.

Subtraction

The process of reducing one number from another is known as subtraction. It's a basic arithmetic operation that's represented by a minus sign (-) and is used to calculate the difference between 2 numbers.

For example, you purchased 10 chocolates for your birthday celebration and your guests consumed 5 of them. You're down to 5 chocolates now. This can be expressed as a subtraction expression: 10 - 5 = 5.  We get 5 when we subtract 5 from 10 (10 - 5). To get the difference of 5, we used the subtraction operation on two numbers, 10 and 5.

Subtraction Symbol

The sign (-) connects the two numbers and completes the given expression in this subtraction: (10 - 5 = 5). The minus sign is another name for this symbol.

Subtraction Formula

We will learn some of the terms included in the subtraction expression:

• Minuend: The number from which the other number is to be subtracted.

• Subtrahend: The number that is subtracted from the other number.

• After subtracting the subtrahend from the minuend, the difference is the final result.

• The formula for subtraction is as follows: Minuend - Subtrahend = Difference

Solving Subtraction Problems

One-digit numbers can be subtracted easily, but for larger numbers, we divide the numbers into columns based on their place values, such as ones, tens, hundreds, thousands, and so on. 

While subtracting larger numbers, we may come across some situations that require borrowing and others that do not. Subtraction with regrouping is another name for subtraction with borrowing. We apply the regrouping approach when the minuend is less than the subtrahend. To make the minuend bigger than the subtrahend, we borrow 1 number from the preceding column while regrouping.

Let’s Understand the Subtraction with Regrouping: 

Assume the number are 35 and 16 then:

Here 5 is less than 6, So we have borrowed 1 from 3 then numbers became 15 and 6 so the difference for the unit’s place is 9. For ten’s place numbers will be 2 and 1 now and the difference is 1.

Rules

The rules while solving questions of Addition and Subtraction are given below:

• When two positive numbers are added together, the result is always positive.

• When two negative numbers are added together, the result is always negative.

• The result of subtracting two positive numbers can be positive or negative.

• The result of subtracting two negative numbers can be positive or negative.

Did You Know?

• If we have 2 single-digit numbers then their addition can be a two-digit number but subtraction can be a two-digit number. For example, 6 and 5 are two numbers and the addition is 11 which is a two-digit number but the difference is 1 which is a single-digit number.

Solved Examples

Let us see examples of addition, and subtraction to understand the concepts better. 

1. Amit has 2 chocolates and 6 sweets then how many items does Amit have?

Ans: Here we have to add both chocolates and sweets. We have both numbers as single-digit numbers. So we can simply add 6 and 2.

So, 6 + 2 = 8.

Hence, Amit has total 8 items.

2. Arun has 6 books and he gave 2 books to his friend then how many books are left with Arun?

Ans: When two one-digit positive numbers are subtracted, the outcome is always a single-digit number.

We have both numbers as single-digit numbers. So we can simply subtract 2 from 6.

So, 6 - 2 = 4

Hence, Arun has 4 books.

3. Find the result of the followings:

1. 15 + 20 = ?

2. 99 + 10 = ?

3. 95 - 10 = ?

4. 90 - 15 = ?

Ans: We can add and subtract two-digit positive and negative numbers. A three-digit value can be obtained by adding two-digit positive numbers, but a three-digit value cannot be obtained by subtracting two-digit positive numbers.

1. 15 + 20 = 35

2. 99 + 10 = 109

3. 95 - 10 = 85 

4. 90 - 15 = 75

4. Anuj has 10 Tennis balls and his friend has 6 Tennis balls. How many more Tennis balls does Anuj have than his friend?

Ans: Here, Anuj has 10 Tennis balls & his friend has 6 Tennis balls.

⇒ 10 - 6 = 4

Anuj has 4 more Tennis balls than his friend.

Practice Questions

1. If Arun has 49 apples and 37 oranges, then find the number of fruits.

2. If Seema has 39 sweets and she gave 21 sweets to her friends then how many sweets does Seema have?

Conclusion

Before starting school, young children begin studying maths. They learn to count and can use counting to solve simple problems. Many different types of problems are represented and solved using addition and subtraction. Math Addition and Subtraction can be used to represent a wide range of situations. It's necessary to learn how to recognize these circumstances and symbolically represent them.