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Addition And Subtraction Of Two-Digit Numbers

What are two-digit numbers? 

Two-digit numbers begin with 10 and end at 99. The digits in the tens position of a two-digit number must be between 1 and 9. The largest two-digit number is 99 and the least two-digit number is ten. 

The place value of a number is the position of each digit. When dealing with two-digit numbers, we have two distinct place values called the ones and tens place.

Consider the number 86. 

In the given example, 8 is at the tens place which means the value is 80 and 6 is at the one place, which has the value of 6. 

How to add two-digit numbers?

Whenever we add two-digit numbers, we always start the process at the outmost right digit, or the ones place. 

Adding two-digit numbers without regrouping

To add two-digit numbers, follow these steps:

  1. Write the numbers with the place values lines up. 
  2. Add the digits in the ones place. 
  3. Add the digits in the tens place. 

Example #1 

What is the sum of 13 and 11?

Solution

Addition ProcessStep-by-Step Explanation
Arrange the numbers in a column form with the place values lined up.
Add the digits in the column of the ones place. Thus, 1 + 3 = 4
Then, write the sum of 1 and 3 below the bar. 
Get the sum of the numbers in the tens place. Hence,1 + 1 = 2
Then, write the 2 below the bar.
Therefore, the sum of 13 and 11 is 24

Example #2

Find the sum of 24 and 33.

Solution

Addition ProcessStep-by-Step Explanation
Arrange the numbers in a column form with the place values lined up.
Get the sum of the numbers in the ones place. Hence,4 + 3 = 7
Then, write the 7 below the bar.
Add the numbers in the tens place. Thus, 2 + 3 = 5
Then, write the sum of 2 and 3 below the bar. 
Therefore, the sum of 24 and 33 is 57.

Example #3

Determine the sum of 16 and 42.

Solution

Addition ProcessStep-by-Step Explanation
Arrange the numbers in a column form with the place values lined up.
Add the numbers in the ones column. Thus, 6 + 2 = 8
Then, write the sum below the bar. 
Get the sum of the numbers in the tens place. Hence,1 + 4 = 5
Then, write the sum of 1 and 4 below the bar. 
Therefore, the sum of 16 and 42 is 58.

Example #4

What is the result when 21 is added to 58?

Solution

Addition ProcessStep-by-Step Explanation
Arrange the numbers in a column form with the place values lined up.
Get the sum of the numbers in the ones column. Hence, 8 + 1 = 9
Then, write the sum of 8 and 1 below the bar. 
Add the numbers in the tens place. Thus, 5 + 2 = 7
Then, write 7 below the bar. 
Therefore, the sum of 58 and 21 is 79.

Example #5

What is the result of adding 73 and 22? 

Solution

Addition ProcessStep-by-Step Explanation
Arrange the numbers in a column form with the place values lined up.
Get the sum of the numbers in the column of the ones place. Thus, 3 + 2 = 5
Then, write 5 below the bar. 
Add the numbers in the tens place. Hence,7 + 2 = 9
Then, write the sum of 7 and 2 below the bar. 
Therefore, the sum of 73 and 22 is 95.

Adding two-digit numbers with regrouping

To add two-digit numbers that need regrouping, follow these steps:

  1. Write the numbers with the place values lines up. 
  2. Add the digits in the ones place. If the sum exceeds 10, then carry over the digit to the tens place.
  3. Add the digits in the tens place. If the sum exceeds 10, then carry over the digit to the hundreds place.

Example #1 

What is the sum of 23 and 19?

Solution 

Addition ProcessStep-by-Step Explanation
Arrange the numbers in a column form with the place values lined up.
Get the sum of the numbers in the units’ column. Thus, 3 + 9 = 12
Since the sum exceeds 10, write 0 below the bar of the ones column and put the carry over of 1 on top of the tens place column. 
Add the carry over and the tens digit of 23 and 19. Hence, 1 + 2 + 1 = 4
Then, write 4 below the bar of the numbers in the tens column. 
Therefore, the sum of 23 and 19 is 42.

Example #2 

Determine the result of adding 48 and 36. 

Solution

Addition ProcessStep-by-Step Explanation
Arrange the numbers in a column form with the place values lined up.
Add the numbers in the ones’ column. Thus, 8 + 6 = 14
Since the sum is 14, write 4 below the bar of the numbers in the units digit and put the carry over 1 on top of the tens digit column. 
Get the sum of the carry over and the tens digit of 48 and 36. Thus, 1 + 4 + 3 = 8
Then, write 8 below the bar of the tens digit column.
Therefore, the sum of 48 and 36 is 84.

Example #3 

What is the result of adding 56 and 63?

Solution

Addition ProcessStep-by-Step Explanation
Arrange the numbers in a column form with the place values lined up.
Add the numbers in the ones’ column. Hence, 6 + 3 = 9
Then, write 9 below the bar.
Get the sum of the numbers in the tens’ column. Thus, 5 + 6 = 11
Since the sum is 11, write 1 below the bar of the numbers in the tens column and put the carry over in the column of hundreds’ place. 
Since there is no hundreds digit in the numbers 56 and 63, simply bring down the carry over of 1.
Therefore, the sum of 56 and 63 is 119.

Example #4

What is the sum of 73 and 87?

Solution 

Addition ProcessStep-by-Step Explanation
Arrange the numbers in a column form with the place values lined up.
Get the sum of the numbers in the ones’ column. Thus, 3 + 7 = 10
Since the sum is 10, write 1 below the bar of the numbers in the units column and put the carry over in the column of tens’ place. 
Add the carry over and the numbers in the tens’ column. Hence, 1 + 7 + 8 = 16
Since the sum is 16, write 6 below the bar of the numbers in the tens column and put the carry over on top of the hundreds’ place column.
Since there is no hundreds digit in the numbers 78 and 67, simply bring down the carry over of 1.
Therefore, the sum of 73 and 87 is 160

Example #5 

Find the sum of 98 and 19.

Solution

Addition ProcessStep-by-Step Explanation
Arrange the numbers in a column form with the place values lined up.
Get the sum of the numbers in the ones’ column. Thus, 9 + 8 = 17
Since the sum is 17, write 7 below the bar of the numbers in the units column and put the carry over in the column of tens’ place. 
Add the carry over and the numbers in the tens’ column. Hence, 1 + 9 + 1 = 11
Since the sum is 11, write 1 below the bar of the numbers in the tens column and put the carry over on top of the hundreds’ place column.
Since there is no number in the hundreds digit column, simply bring down the carry over of 1.
Therefore, the sum of 98 and 19 is 117.

How to subtract two-digit numbers?

Whenever we subtract two-digit numbers, we always start the process at the outmost right digit, or the ones place.

Subtracting two-digit numbers without regrouping

To subtract two-digit numbers, follow these steps:

  1. Arrange the numbers one above the other so that the tens’ and ones’ place digits are aligned. 
  2. Subtract the units digit of the number on the second row from the units digit of the number on the first row.
  3. Subtract the tens digit of the number on the second row from the tens digit of the number on the first row.

Example #1

What is the difference between 45 and 14? 

Solution

Subtraction ProcessStep-by-Step Explanation
Align the digits of the 45 and 14 in a column form with the place values lined up.
Subtract 4 from 5. Thus,5 – 4 = 1
Then, write the difference of 5 and 4 below the bar.  
Subtract the numbers in the tens digits. Thus, 4 – 1 = 3
Then, write 3 below the bar.
Therefore, the difference of 45 and 14 is 31.

Example #2

Determine the result of subtracting 59 from 99. 

Solution

Subtraction ProcessStep-by-Step Explanation
Align the digits of the 99 and 59 in a column form with the place values lined up.
Subtract the number in the units digit. Hence,9 – 9 = 0
Then, write 0 below the bar of the units column.  
Subtract the number in the tens column. Thus, 9 – 5 = 4
Then, write the difference of 9 and 5 below the bar of the tens column. 
Therefore, the result of subtracting 59 from 99 is 40

Example #3

Find the difference of 63 and 21. 

Solution

Subtraction ProcessStep-by-Step Explanation
Align the digits of the 63 and 21 in a column form with the place values lined up.
Subtract the number in the units digit. Hence,3 – 1 = 2
Then, write the difference of 3 and 1 below the bar of the units column.  
Get the difference of the number in the tens column. Thus, 6 – 2 = 4
Then, write 4 below the bar of the tens column.
Therefore, the difference of 63 and 21 is 42.

Example #4

What is the result of 84 – 33?

Solution

Subtraction ProcessStep-by-Step Explanation
Align the digits of the 84 and 33 in a column form with the place values lined up.
Subtract the number in the units digit. Hence,4 – 3 = 1
Then, write the difference of 4 and 3 below the bar of the units column.  
Get the difference of the number in the tens column. Thus, 8 – 3 = 5
Then, write 4 below the bar of the tens column.
Therefore, the difference of 84 and 33 is 51.

Example #5

Find the difference of subtracting 18 from 79. 

Solution

Subtraction ProcessStep-by-Step Explanation
Align the digits of the 79 and 18 in a column form with the place values lined up.
Subtract the number in the units digit. Hence,9 – 8 = 1
Then, write the difference of 9 and 8 below the bar of the units column.  
Get the difference of the number in the tens column. Thus, 7 – 1 = 6
Then, write 6 below the bar of the tens column.
Therefore, if we subtract 18 from 79, the result will be 61.

Subtracting two-digit numbers with regrouping

To subtract two-digit numbers, follow these steps:

  1. Arrange the numbers one above the other so that the tens’ and ones’ place digits are aligned. 
  2. Subtract the units digit of the number on the second row from the units digit of the number on the first row. If the units digit of the subtrahend is greater than the units digit of the minuend, then borrow 1 in the tens digit. 
  3. Subtract the tens digit of the number on the second row from the tens digit of the number on the first row. If the tens digit of the subtrahend is greater than the units digit of the minuend, then borrow 1 in the hundreds digit.

Example #1

What is the difference of 33 and 17?

Solution

Subtraction ProcessStep-by-Step Explanation
Align the digits of the 33 and 17 in a column form with the place values lined up.
Since 7 is higher than 3, we need to borrow 1 from the tens digit. Thus, we will add 10 in the units digit, and we will subtract 1 from the tens digit.  
Subtract 7 from 13. Thus,13 – 7 = 6
Then, write the difference below the bar in the units column.
Subtract 1 from 2. Hence,2 – 1 = 1
Then, write 1 below the bar in the tens column.
Therefore, the difference of 33 and 17 is 16.

Example #2

Find the result of subtracting 13 from 21.

Solution

Subtraction ProcessStep-by-Step Explanation
Align the digits of the 21 and 13 in a column form with the place values lined up.
Since 3 is higher than 1, we need to borrow 1 from the tens digit. Thus, we will add 10 in the units digit, and we will subtract 1 from the tens digit.  
Get the difference of 11 and 3. Thus,11 – 3 = 8
Then, write 8 below the bar in the units column.
Subtract the numbers in the tens column. Hence, 1 – 1 = 0
Since the difference is 0, and it is the last column that we are going to subtract, you can opt to write 0 below the bar.
Therefore, the difference between 21 and 13 is 8.

Example #3

Determine the difference of subtracting 25 from 91.

Solution

Subtraction ProcessStep-by-Step Explanation
Align the digits of the 91 and 25 in a column form with the place values lined up.
Since the units digit of the subtrahend is greater than the units digit of the minuend, we need to borrow 1 from the tens digit. Thus, we will add 10 in the units digit, and we will subtract 1 from the tens digit.  
Get the difference of 11 and 3. Thus,11 – 5 = 6
Then, write 6 below the bar in the units column.
Subtract the numbers in the tens column. Hence, 8 – 2 = 6
Then, write the difference of 8 and 2 below the bar in the tens column.
Therefore, the difference between 91 and 25 is 66.

Example #4

What is the difference of 87 – 59?

Solution

Subtraction ProcessStep-by-Step Explanation
Align the digits of the 87 and 59 in a column form with the place values lined up.
Since the units digit of the subtrahend is greater than the units digit of the minuend, we need to borrow 1 from the tens digit. Thus, we will add 10 in the units digit, and we will subtract 1 from the tens digit.  
Get the difference of 11 and 3. Thus,17 – 9 = 8
Then, write 8 below the bar in the units column.
Subtract the numbers in the tens column. Hence, 7 – 5 = 2
Then, write the difference of 7 and 5 below the bar in the tens column.
Therefore, the difference between 87 and 59 is 28.

Example #5

Find the difference between 76 and 49.

Solution

Subtraction ProcessStep-by-Step Explanation
Align the digits of the 33 and 17 in a column form with the place values lined up.
Since 9 is higher than 6, we need to borrow 1 from the tens digit. Thus, we will add 10 in the units digit, and we will subtract 1 from the tens digit.  
Subtract 9 from 16. Thus,16 – 9 = 7
Then, write the difference below the bar in the units column.
Subtract 1 from 2. Hence,6 – 4 = 2
Then, write 1 below the bar in the tens column.
Therefore, the difference of 76 and 49 is 27.

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