A partial sum in decimals refers to a method of addition where you break down each decimal number into its place values (ones, tenths, hundredths, etc.), add the corresponding place values separately, and then add those partial sums together to find the final sum.
Here's a breakdown of how it works:
-
Write the numbers vertically, aligning the decimal points. This ensures you're adding the correct place values together.
-
Add the largest place value first (left to right). For example, if you're adding 12.34 and 5.67, you would first add the 'ones' places: 12 + 5 = 17. Write this partial sum down.
-
Add the next place value. Now add the tenths: 0.3 + 0.6 = 0.9. Write this partial sum below the previous one.
-
Continue adding each place value. Add the hundredths: 0.04 + 0.07 = 0.11. Write this partial sum below the others.
-
Add the partial sums together. Add 17 + 0.9 + 0.11 to get the final sum: 18.01
Example:
Let's add 23.5 and 8.25 using the partial sums method:
| Place Value | Number 1 (23.5) | Number 2 (8.25) | Partial Sum |
|---|---|---|---|
| Tens | 20 | 0 | 20 |
| Ones | 3 | 8 | 11 |
| Tenths | 0.5 | 0.2 | 0.7 |
| Hundredths | 0 | 0.05 | 0.05 |
| Total: 31.75 |
Therefore, 23.5 + 8.25 = 31.75
Why Use Partial Sums?
- Conceptual Understanding: It helps students understand place value and how it relates to addition.
- Flexibility: It allows for different approaches. Students can add in any order.
- Mental Math: It supports the development of mental math skills.
