Addition and Subtraction: Solved Examples

Addition and Subtraction is the most basic and simple arithmetic operation. Addition involves the summing up of two or more numerical values giving the total value of the numbers. While subtraction is the main Mathematical operation of reducing a certain numerical value from another to find the difference between them. Both addition and subtraction are completely opposite of each other. 

• Numbers that are added together are called addends. 
• The first number in a subtraction equation is called the minuend and the second number is named as subtrahend. 
• The subtrahend should always be smaller than the minuend.
• When two positive numbers are added, the sum is always positive. 
• On adding two negative numbers, the total will always be negative.
• If the minuend is negative, the result of subtraction will be negative 
• If the minuend is positive, the difference will be positive as well.

Key terms: Adding, Subtracting, Minuends, Subtrahends, Numerical values, Numbers, Addition, Subtraction

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Addition

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Addition is the totaling of two or more numerical values. It is denoted by the '+' sign called a plus. The addition equation is laid out as- addend + addend = sum. 

For example if we add 3 and 5, we get eight. It'll be shown as-

3 + 5 = 8

Lets understand this in daily life practice. 

Alina had 3 chocolates. Sama gave her 5 more chocolates. How many chocolates does Alina have now?

3= 1+1+1 

5= 1+1+1+1+1 

The chocolates all together,

1+1+1+1+1+1+1+1= 8

Hence, the sum of chocolates with alina is 8. 

Make two columns for tens and ones. Write the units of addends accordingly. For example-

Add 24 + 43

In tens place, 2+4=6 

In ones place, 4+3=7

The sum total equals to 67. 

One more example is Addition of 63 and 22 :

In tens place, 6+2 = 8

In ones place, 3+2 = 5

The sum total equals to 85. 

Carrying Over

In some cases the addition of numbers in one place will be more than 9. Then use the carrying over process. For example-

Let's add 69 + 26 

• On adding the ones one can get 15 which is more than 9. Therefore change it to tens and ones. 

Hence, 15 ones= 1 ten + 5 ones 

• Write 5 in one place.
• Now add the tens. 6 tens + 2 tens + 1 ten carried over. It equals 8 tens.
• Sum total turns out to be 85.

Another example of Addition of 58 + 19

• On adding the ones we get 17 which is more than 9. Therefore we change it to tens and ones. 

Hence, 17 ones= 1 ten + 7 ones 

• Write 7 in one place.
• Now add the tens. 5 tens + 1 tens + 1 ten carried over. It equals 7 tens.
• Sum total turns out to be 77. 

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Addition of 3 digit numbers 

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The same process has to be used to find the sum of three digit numbers. Arrange the numbers in hundreds and tens of places. Add the respective numericals in the same place. Write the sum as an answer. 

For example- Lets add 318 and 271

In hundreds place 3+2=5 

In tens place, 1+7=8

In ones place, 8+1=9

The total sum is 589.

Another example is Addition of 452 and 326

In hundreds place 4+3=7

In tens place, 5+2=7

In ones place, 2+6=8

The total sum is 778.

Carrying Over

There might be some questions in which the sum of numbers in ones and tens places will be exceeding 9. In such cases we use the carrying over method as follows.

Lets add 568 and 297

• On adding the ones one can get 15 which is more than 9. Therefore change it to tens and ones. 

Hence, 15 ones= 1 ten + 5 ones 

• Write 5 in one’s place.
• Now add the tens. 6 tens + 9 tens + 1 ten carried over. It equals 16 tens.
• Therefore change it to hundreds and tens. 

Hence 16 ten’s= 1 hundreds and 6 tens.

• Write 6 in ten’s place. 
• Add the numbers in hundreds places. 5 hundreds + 2 hundreds + 1 hundred carried over equals 8 hundreds. 
• The sum total is 865.

Another example is Addition of 786 and 147

• On adding the ones one can get 13 which is more than 9. Therefore change it to tens and ones. 

Hence, 13 ones= 1 ten + 3 ones 

• Write 3 in ones place.
• Now add the tens. 8 tens + 4 tens + 1 ten carried over. It equals 13 tens.
• Therefore change it to hundreds and tens. 

Hence 13 tens= 1 hundreds and 3 tens.

• write 3 in tens place. 
• Add the numbers in hundreds places. 7 hundreds + 1 hundreds + 1 hundred carried over equals 9 hundreds. 
• The sum total is 933.

Now let's add 278 to 860

• Add the digits in one place. One can get 8+0=8. 
• Now add the digits in tens place. 7+6=13 Tens.
• Therefore we'll change it to hundreds and tens. 

Hence 13 tens= 1 hundreds and 3 tens.

• Write 3 in tens place. 
• Add the numbers in hundreds places. 2 hundreds + 8 hundreds + 1 hundred carried over equals 11 hundreds. 
• Therefore change it into thousands. Hence 11 hundreds= 1 thousands and 1 hundreds.
• The entire sum total is 1138.

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Subtraction 

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Subtraction is the reduction of a particular numerical value from a larger number. It is denoted by a "-" symbol called a minus sign. The simple subtraction formula is- 

minuend - subtrahend = difference 

Where minuend is the former larger number from which the subtrahend is subtracted.

For example if one reduces 4 from 9,one gets 5.

It'll be shown as 9-4=5.

Let's take an example from our real life-

Suppose you had 9 oranges. You gave 4 to your friend. How many oranges will you have left?

4=1+1+1+1

9=1+1+1+1+1+1+1+1+1

Cutting out 4 from 9, you have 1+1+1+1+1=5 oranges left. 

Read more: Addition and subtraction on number lines

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Subtraction of 2 digit numbers 

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Arrange the units according to their places. Subtract the respective numbers simply and write the difference in the answer row. Let's take an example of 65-32

In tens place, reducing 6 by 3 gives 3 

In one place, subtracting 2 from 5 equals 3. 

Therefore, the difference is 33.

Now let's take an example from practical life. Rina buys 78 candies for her two sisters 

Seema and tina. She gave 38 candies to seema. Now how many candies will Tina get? 

Ans: The total number of candies was 78. It is the larger number so it is the minuend. Out of it 38 were given to seema so tina will get 

78-38=?

Therefore Tina will get 40 candies.

Note- Always start from the one's place for both addition and subtraction.

Subtraction With Borrowing 

There are several questions in which the value of the unit in one's place of minuend is smaller than the one's place unit of the subtrahend. In such cases we may use the borrowing technique to find the difference.

For example let's take an example of subtracting 28 from 51

• Here, in the ones place 1 is smaller than 8 so it cannot be subtracted. But we can borrow from the unit in tens places. 
• Instead of considering 51 as 5 tens and 1 ones, we may consider 51 as 4 tens and 11 ones. Either way the value remains the same. Now we can easily subtract 8 from 11 which equals to 3. 
• In the tens place we will minus 2 from 4 as shown and we will get a 2.
• Hence the difference turns out to be 23.

Word problem-  There are 70 balls in a basket. There are only two colours of ball- white and orange. If 39 of the balls are orange. How many white balls are there?

Ans- total number of balls= minuend.

Number of orange balls- 39 

Number or white balls= 70-39

• As 9 could not be subtracted by 0. We borrowed a ten from the tens place changing the unit in tens place from 7 to 6.
• In one place one gets 10 borrowed+0= 10. 
• Subtracting 9 from 10 we get 1. 
• In the tens place 6 is reduced by 3 giving 3. 
• The difference turns out to be 3. 
• Therefore there are 31 white balls in the basket.

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Subtraction of 3-digit numbers

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Subtraction of 3 digit numbers are carried out with the same method. Just a few hundred columns will be added. Let's take a simple example of reducing 241 from 679-

• Subtracting 1 from 9 we get an 8 in one place.
• 7 minus four gives 3 in the tens place. 
• Reducing 2 from 6 equals to 4 in the hundreds place.
• Therefore arranging it all we get 438 as the answer.

In real life we often see piles of things at market places. Clothes,accessories, books and more. Let's take an example from here

There were 750 books at a shop at the beginning of the month. At the end of month 430 were sold. How many books are left in the shop? 

• On subtracting 0 from any number we always get the same number. In the ones place we get 0.
• In the tens place get 2 by subtracting 3 from 5. 
• In the hundreds place 7 is reduced to 3 by subtracting 4 from it.

Also Read:

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Things to Remember

• Addition and subtraction are the fundamental concepts of Mathematics. All other and higher calculations are indifferently based on it.
• The sign for Addition is a a cross symbol "+" called a plus.
• The symbol for subtraction is a minus sign which is "-"
• Adding gives the sum total of two numbers while subtraction shows the difference between them.
• Always start calculation from the ones place while either subtraction or Addition.
• In addition if the answer is more than 9 use the carrying over method.
• In subtraction if the minuend is lesser use the borrowing over method.

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Previous Year Questions

1. Nascent hydrogen consists of..
2. In which of the following reactions the hydrogen peroxide acts as a reducing agent?..[JEE MAIN 2023]
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