2-Digit Addition

When adding two-digit numbers, we need to consider their place values: ones and tens. We write the numbers in columns, lining up the ones under ones and the tens under tens. We first add the digits in the ones place. If the sum is 10 or more, we carry over (regroup) to the tens place.

Next, we add the tens. If no digits are carried over, it is called 'no regrouping'. If we carry over, it’s called “regrouping”. The numbers we add are called addends, and the answer is called the sum. Observe the figure below, which shows that 60 and 25 are the addends and 85 is the sum.

The 2-digit addition with regrouping follows specific rules for carrying digits between place values. When the sum of numbers exceeds 9, the digits are carried over to the next place value, i.e., the tenth place. Regrouping for two-digit numbers begins with the ones column and proceeds to the left, toward the tens column. Let’s take, for example, 67 and 34. 

Step 1: The given addends are arranged based on their place value, i.e., ones and tens in a column. So, 7 and 4 will be placed under the ones column, and 6 and 3 will come under the tens column. 

Step 2: Add numbers from right to left, starting with the ones place. Here, the numbers in the ones place are 7 and 4, 7 + 4 = 11

Step 3: When the sum in the ones place is 10 or more. From the sum, we place the one digit in the ones place, and carry the tens digit to the tens place. As 11 is greater than or equal to 10, we carry forward 1 to the tens column and write 1 as the sum in the ones place. 

Step 4: While adding the tens column, we include the number that was carried over from the ones column. Hence, we add 6 + 3 + 1 (carry-over) = 10. 

Step 5: Therefore, the sum of 67 and 34 is 101.

The most basic type of addition is two-digit addition without regrouping, as we use it in our everyday shopping and financial transactions, and many more. In this case, we record the number beneath the appropriate place value column and do not carry forward any numbers to the next column when the sum is less than or equal to 9. Let’s take, for example, 68 and 31.

Step 1: Arrange the addends based on their place value, i.e., ones and tens. When adding 68 and 31, 8 and 1 will be under the ones place, and 6 and 3 will be placed under the tens place. 

Step 2: Start adding the numbers from right to left, i.e., from ones to tens. This means 8 + 1 = 9. We write 9 in one place and then add 6 + 3 = 9.

Step 3: Adding both columns gives 68 + 31 = 99. Therefore, the sum is 99 

Adding two-digit decimals is just like adding numbers. We arrange the numbers based on their place value and decimal point. We add from right to left, and if a column adds up to more than 9, we carry over the extra digit to the next column. Let’s learn how to add two-digit decimals with and without carrying over. 

We follow the same steps for decimal additions that we do for whole numbers. Let’s look at an example to understand this better. For example, let’s take 4.7 and 2.5.

Step 1: Arrange the numbers based on their place value. The digits 7 and 5 go under the tenths column, while 4 and 2 go under the ones column.

Step 2: We start adding from the right to the left. 7 + 5 = 12. Write 2 in the tenths column and carry over 1 to the ones column. 

Step 3: Add the ones column along with the carried-over number. 4 + 2 + 1 = 7.

Step 4: The final sum is 7.2. Add tenths: 7 + 5 = 12; write 2 in the tenths place and carry over 1 to the ones place.

Adding two-digit decimals without regrouping follows the same steps as whole numbers. Let’s understand this with an example: 5.3 and 2.4.

Step 1: Write 5.3 and 2.4, aligning them by place value. The digits 3 and 4 should be placed under the tenths column, while 5 and 2 go under the ones column.

Step 2: Start adding from the right. 3 + 4 = 7 in the tenths column. Then, add the ones column: 5 + 2 = 7.

Step 3: After adding both columns, the final sum is 7.7. So, 5.3 + 2.4 = 7.7.

Adding two digits numbers can be very easy and simple by following these simple tips and tricks. Here are a few tips and tricks that will help you grasp the concept of 2-digit addition:

• Always write the numbers in different rows, aligning digits of the same place.
   
• Round to 10, when adding numbers closer to 10. Perform addition as regular. From the final answer, add or subtract the number you rounded.
  Example: 23 + 30
  23 can be written as 20 + 3
  23 + 30 = 20 + 3 + 30 = 50 + 3 = 53.
   
• Break the number into tens and ones.
   
• Practice adding numbers using real objects.
   
• Remember the carry always goes to the number on the left.

We use two-digit addition in many real-life situations. Some of the applications are mentioned below:

• Shopping: In shopping, 2-digit addition is used to calculate the total cost. For example, if a toy costs $25 and a book costs $18, you add $25 + $18 = $43 to find the total cost.

• Travel: To calculate the total time or cost, we use a 2-digit addition. For example, if a bus ride takes 45 minutes and a train ride takes 30 minutes, adding 45 + 30 = 75 minutes helps you know the total travel time. 

• Sports: If a basketball player scores 27 points in one game and 34 points in another, adding 27 + 34 = 61 gives the total points.

• Academics: To calculate the overall performance of students in a test, two digit addition is used. For example: if a student scores 23 marks in one subject and 32 in the other out of 50. The total marks will be 55 out of 100.

• Cooking: To calculate the amount of ingredients to use in a recipe, 2-digit addition is used. For example: a recipe requires 12 grams of flour for making a cake for 2 servings. If you need to increase the serving by two, then the amount of flour needed will be 12 + 12 = 24 grams.