Addition And Subtraction

We use addition to calculate the total or sum of two or more numbers. Addition can be used to find the sum of whole numbers, integers, algebraic expressions, and fractions. On the other hand, subtraction is used to determine the difference between two or more numbers. In the addition process, the symbol (+) is used to indicate the operation and the sum is its result. The addition formula is: Addend + Addend = Sum. 

Here, addend is the number that is added to another number. 
On the other hand, the symbol (-) is used to represent the subtraction method, and the difference is the result of the operation. The subtraction formula is: Minuend - Subtrahend = Difference. 

Here, subtrahend is the number being subtracted, and minuend is the number from which subtrahend is deducted.  For example, if we subtract 10 from 20: 
20 - 10 = 10

Here, minuend = 20 (the number from which the other number is subtracted)

Subtrahend = 10 (the number being subtracted)
Difference = 10 (the result)

Two-digit addition and subtraction can be done with or without regrouping. It can be done without regrouping if the sum of the numbers from any of the place value column is equal to or less than 9. For a better understanding, take a look at this: 
Adding the numbers, 25 and 34,

Adding the values in the ones place, we get: 5 + 4 = 9. Similarly, adding the values in the tens place: 2 + 3 = 5. Hence, 25 + 34 = 59.
Now, let us calculate 2-digit subtraction without regrouping. 
Subtract 32 from 74.
 

Here, the place value arrangement is similar to the addition method. We have 4 -2 = 2 in ones column, and 7 - 3 = 4 in the tens column. Hence, 74 - 32 = 42.  

If the sum of the numbers in a column is greater than 9, we have to carry over (regroup) when adding or subtracting. In this instance, first, we arrange the two digits in columns as ones and tens. Then start the addition with the ones column. If the result has two digits, write the last digit in the ones place and carry over the first digit to the tens column. For example, if the sum is 15, write 5 in the ones place and carry over 1 to the tens column. Then, add the tens column along with the carried-over (1).

Let us take another example. Add numbers 366 + 455.

Step 1: Start with the digits in ones column. 
6 + 5 = 11 
The sum is 11. Carry over 1 to the tens place. 

Step 2: Now, we will add the tens place digits along with the carry-over 1. 
6 + 5 + 1 = 12
The sum is 12. The sum’s tens place digit (1) will be carried over to the hundreds column. 

Step 3: Add the digits in the hundreds place along with the carry-over 1. 
3 + 4 + 1 = 8
The sum is 8. 

Step 4: Thus, 366 + 455 = 821 

The subtraction with regrouping:

When a digit in the minuend is less than the matching digit in the subtrahend, we borrow 1 from the next preceding column and add it to the minuend to make it greater than the subtrahend. In this case, subtraction with regrouping occurs. For example, subtract the numbers 321 - 164.

     321 
  -  164 = 157

Step 1: Start the subtraction with the ones place digits. Here 1 is smaller than 4. So, we will borrow 1 from the tens column and make it 11. Now, 11 - 4 = 7. 

Step 2: Now, we can move to the tens column. After giving 1 to the ones column, 2 becomes 1. Next, we can subtract 1 and 6. Here, 1 is smaller than 6, so again we borrow 1 from the hundreds column. This makes 1 as 11. So, 11 - 6 = 5. 

Step 3: We borrow 1 from the hundreds column and 3 becomes 2. Now subtract the digits in the hundreds place. So, 2 - 1 = 1. 

Step 4: Thus, 321 - 164 = 157. 

A number line is a horizontal line consisting of all numbers from 0 to infinity. Using a number line, we can perform addition and subtraction. For addition, just count the positive numbers from left to right. For instance, look at the example given below to calculate 1 + 2. 

Addition using a number line:  

Mark the first number (1) and move by 2 units towards the right-hand side of the number line and we land at 3. Thus, 1 + 2 = 3. 
 

Subtraction using a number line: 

Using the number line, we can easily subtract smaller numbers step-by-step. Unlike addition, we should move from right to left on the number line to subtract numbers. Take a look at the example below where we subtract 3 from 5.  

Mark 5 and move towards the left-hand side by 3 units and we land at 2. Thus, 5 - 3 = 2. 

Fractions are a part of a whole number. The process of addition and subtraction of fractions depends on the denominators (bottom numbers). When we add or subtract fractions with like denominators (the same denominator), just perform the operations without changing the denominator.

For example, add 2/7 +  4/7
 2/7 +  4/7 = 2 + 4/7 = 6/7

Subtraction of like fractions: Subtract 6/8 - 3/8 
6/8 - 3/8  = 6 - 3/8 = 3/8

Addition and subtraction of unlike fractions: We should find the least common denominator (LCD) of the given denominators before adding or subtracting unlike fractions. Then, convert each fraction and add them to get the result. For e.g., add 3/5 + 2/7

Step 1: Find the LCD of 5 and 7, which is 35. It is the smallest multiple of 5 and 7. 

Step 2: Convert each fraction. To make sure the fraction stays the same, we multiply numerator and denominator by the same number.

So, here we multiply both of them by 7. 
3/5 = 3 × 7/5 × 7 = 21/35
   
2/7 = 2 × 5/7 × 5  = 10/35

Step 3: Add the fractions. 
21/35 + 10/35 = 21 + 10/35 = 31/35

The answer is 31/35

Subtraction of unlike fractions: Subtract 3/4 - 2/6

Step 1: Find the LCD of 4 and 6 is 12. 

Step 2: Convert each fraction. 

3/4 = 3 × 3/4 × 3 = 9/12 
2/6  = 2 × 2/6 × 2 = 4/12

Step 3: Subtract the fractions. 
9/12 - 4/12 = 9 - 4/12 = 5/12

Final answer is 5/12

We perform addition and subtraction of decimals similarly to whole numbers. But we need to properly align the decimal points before the operation. Also, to match the decimal places, we add zeros where needed. Once the addition or subtraction is done, we should ensure the final answer has the appropriate decimal point. For example, add 4. 12 + 1.7

    4.12 
+  1.7 

Add a zero next to 7 to match the decimal places. 
    4.12 
+  1.70
   5.82

So, the final result is 5.82

Next, we can subtract two decimal numbers.
Subtract 5.32 - 2.14 
Here, we can remove the decimal points and consider it as a whole number. 
So, 532 - 214 = 318 

Now, we can count the decimal places in the original number and apply it to the final result. Since 5.32 and 2.14 have two decimal places, the final answer also should have two decimal places. Hence, the answer will be 3.18.

We use addition and subtraction in our everyday lives to determine prices, quantities, and measurements. The real-life applications of these two fundamental mathematical operations are countless. Here are some real-life applications:

• We can calculate our expenses and profit from different sources using addition and subtraction. It will help to manage our personal finances effectively.

• When we go shopping, we can estimate the total price of multiple items we buy. Also, we can subtract the discounts and other offers from the price to calculate the final amount.

• Addition and subtraction help us estimate the total time spent on different tasks and projects, improving time management.

• In engineering and construction, addition is used to calculate the total amount of required materials. Likewise, using subtraction engineers can calculate the remaining length or width of a room or a construction site.

• The addition method can be used to determine the total number of steps we take during a walk. Also, we can subtract how many calories are burned during exercise or any fitness programs. It will help us to maintain good health and physical fitness.