Definition
Partial sums
Partial sums add matching place-value parts separately, then combine those sums.
What it means
Add hundreds with hundreds, tens with tens, and ones with ones. Keep each result as a partial sum, then add the partial sums. For 47 + 35, the tens give 40 + 30 = 70 and the ones give 7 + 5 = 12; then 70 + 12 = 82.
Remember it
Find a sum in each place, then sum the sums.
Example
Find 368 + 247. Hundreds: 300 + 200 = 500. Tens: 60 + 40 = 100. Ones: 8 + 7 = 15. Combine the partial sums: 500 + 100 + 15 = 615.
Watch for
In this elementary place-value sense, partial sums are the intermediate sums in an addition method, not the running totals of a sequence or infinite series.
Common mix-up
A partial sum is one intermediate result. The final total comes from combining every partial sum.
Exact meaning
Partial sums is a place-value addition method. Addends are decomposed by place, corresponding place-value parts are added to make partial sums, and those partial sums are combined to obtain the total.