What is meant by a Partial Sum in math?
When adding large numbers, addition of partial sums helps in breaking the calculation apart and putting the numbers together in accordance with their place values. The partial sum method in math involves calculating the partial sums of one place value column at a time and then adding all the partial sums together to find the total sum. Usually, partial sums are added from left to right.
How do we add using the Partial Sums method?
The partial sums method begins by adding up the numbers in the hundreds place (if it’s a three-digit number), then adding up the numbers in the tens place, and then the numbers in the ones place. Finally, we add up all the partial sums.
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Solved Examples
Example 1: Find: 652 + 346 = ____
Solution: First, arrange the numbers as per their place values.
Hundreds | Tens | Ones |
|---|---|---|
6 | 5 | 2 |
3 | 4 | 6 |
Now, find the partial sums.
After adding the partial sums, the total sum is 998.
Example 2: Find the sum of 362 and 453 using the partial sum method.
Solution: Let us first arrange the numbers as per their place values.
Hundreds | Tens | Ones |
|---|---|---|
3 | 6 | 2 |
4 | 5 | 3 |
Next, we will find the partial sums.
Once the partial sums are added together to get the total sum, the answer will be 815.
Example 3: What is the sum of 442 and 216?
Solution: To find the sum of the above problem, first arrange the numbers as per their place values.
Hundreds | Tens | Ones |
|---|---|---|
4 | 4 | 2 |
2 | 1 | 6 |
Let us now add the partial sums.
Once the partial sums are found, add them up to find the total sum.
The answer is 658
Example 4: There are 266 books in a library. After a week, another 156 books were added to the library. Find the total number of books in the library.
Solution: Let us arrange the numbers according to their place values.
Hundreds | Tens | Ones |
|---|---|---|
2 | 6 | 6 |
1 | 5 | 6 |
Now, we will add the partial sums.
The sum is 422.
Hence, the total number of books in the library is 422.
Example 5: Jim bought 34 comic books. His mother gifted him 28 more. How many comic books does Jim have in total?
Solution: Let us first arrange the numbers according to their place values.
Tens | Ones |
|---|---|
3 | 4 |
2 | 8 |
Now, we will add the partial sums.
The sum is 62.
Jim has a total of 62 comic books.
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When children use the partial sum method, they develop a diverse range of skills related to number sense and algebraic reasoning. They learn about the place value of digits as well. They can write numbers in expanded form and solve sums for large numbers.
Place value can be defined as the value of a digit in a number as per its position, such as ones, tens, hundreds, and so on. For example, in the number 639, the place value of 6 is 6 hundreds, or 600, because 6 is in the hundreds place.