Addition Operation on Multi Digit Numbers
The term addition operation with reference to numbers with multiple digits points to adding numbers that have 2 or more than 2 digits.
The numbers on which the addition operation is performed are called addends, and the result of adding two or more numbers is called the sum.
For example:
Consider adding the following numbers: 245 and 327
Below are Some Terms Related to Addition
- Addend: The numbers on which addition is performed
(In the above example, numbers 245 & 327 are addends.)
- Sum: It is the result of addition operation.
(In the above example 562 is sum.)
- Carry over: When the sum of two digits is greater than 9 then the digit in tens place is shifted one position to the left and is added to the digit preceding it. The digit which is being added is called carry.
In the above example, the sum of the digits in the ones place exceeds 9 i.e. 12, and here 1 is shifted one position to the left to the tens place, and this “1” is called carry.)
When Adding Multi-Digit Numbers, we will need to Follow these Steps:
Step 1: Write the numbers with the same place value one below the other.
Step 2: Add the digits in the ones place and if needed, regroup.
Step 3: Add the digits in the tens place and if needed, regroup.
Step 4: Repeat the above process until you have added all of the numbers in each specific place value.
Continue to move to the next largest place and regroup as needed, which results in the final result or the sum of the addends.
Adding Two Digit Numbers with Regrouping:
Sometimes, you need to regroup while adding numbers.
Let’s try it with
17
+35
____________
1. Write the digits with same place values lined up.
7
5
2. Add the digits in ones place.
7
+5
_______
12
Since the sum of the digits in the ones place is greater than 9, you need to regroup.
Regroup 12 as 1 ten and 2 ones.
Then arrange 1 in the tens column and 2 in the ones column.
Next, add the digits in the tens place and remember that you’ll need to add the regrouped ten!
So, we have 5 tens and 2 ones i.e. 52.
17
+35
______
52
How to Check Whether a Sum is Reasonable?
Estimation of the sum of addends can be used to check whether a sum is reasonable or not. It can be done by rounding off the addends to arrive at a rough estimate as the sum, and if it is close to the actual sum we can say that the estimated sum is reasonable, otherwise the process of rounding off will need to be repeated.
Let’s understand this with the help of an example.
Consider the sum,
199 + 252
Lets first calculate the actual sum
199
+252
__________
451 (Add the ones, then tens, and then the hundreds and regroup)
Now let’s estimate,
take a look at the first number, 199
What will be the number if it is rounded off to the nearest hundreds.
It will be either 100 or 200. Since 200 is very close to 199, we will round the number 199 to 200.
Similarly, number 252 is rounded off to the nearest tens. It will be either 250 or 260. 250 is closer to 252. Hence, 252 is rounded off to 250.
Estimate of 199 + 252 is 200 + 250
Then the rough estimated sum of given numbers is,
200
+250
__________
450 (Add the ones, then tens, and then the hundreds and regroup)
And 450 is quite close to the actual sum of 451.
Therefore the sum is reasonable in this example.
Solved Examples:
Example 1:
Find the sum for the following:
(i) 142 + 213 = _________
(ii) 512 + 241 = __________
Solution:
(i) Using place value to line up the addends,
142
+213
________
355 (Add the ones, then tens, and then the hundreds)
(ii) Using place value to line up the addends,
512
+241
________
753 (Add the ones, then tens, and then the hundreds)
Example 2:
Noah walked 215 m in 12 minutes and covered 931 m in 5 minutes while running.
What is the distance he traversed in a total of 17 minutes?
Solution:
Total distance traveled by Noah,
215 m + 931 m
Using place value to line up the addends,
215
+931
_________
1146 (Add the ones, then tens and then the hundreds)
Hence, the total distance Noah traveled is 1146 m.
Example 3:
There were 400 more people watching a movie on Saturday than on Sunday. On Sunday, 300 people watched the same movie. How many people watched the movie on Saturday?
Solution:
On Sunday, 300 people watched the movie.
On Saturday, there were 400 people more than Sunday who watched the movie. So,
(300 + 400) people watched the movie on Saturday.
Using place value to line up the addends,
300
+400
_________
700
_________
So a total of 700 people watched the movie on Saturday.
Example 4:
House A costs $ 24,000 less than house B. If the cost of house A is $ 123,000, then what do you do to calculate the cost of house B?
Solution:
Since house A costs $ 123,000 and it is $ 24,000 cheaper than house B. So in this case, house B costs,
$ 123,000 + $ 24,000
123,000
+ 24,000
_________
147,000 (Add the ones, then tens, then the hundreds and so on)
Hence, house B actually costs $ 147,000.
Place value of a digit in a number represents its individual value in that number.
For e.g. in number 52, the place value of 2 is 2 ones, or 2 × 1 = 2.
Similarly, the place value of 5 is 5 tens, or 5 × 10 = 50.
It is the process of replacing a number with another number of approximately the same values. Rounding off can be done to the nearest tens, hundreds, thousands and so on.
We use regrouping in addition when the sum of digits in a place value column is greater than 9.