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Add using partial sums

Partial-sums addition represents multi-digit whole numbers as sums of their place-value parts, adds corresponding thousands, hundreds, tens, and ones, and then combines those partial results to find the total. The reasoning preserves the addends’ value while making regrouping explicit when a partial sum reaches ten units of a place; it supports efficient computation and connects place-value understanding to the standard algorithm, without extending to decimals, fractions, or more advanced generalizations.

Detailed Explanation: Add using partial sums

To add with partial sums, break each number into its place-value parts. Add the thousands, hundreds, tens, and ones separately, then combine the results.

Example: Find 3,482+2,7593{,}482+2{,}759.

  1. Break apart both numbers:

3,482=3,000+400+80+23{,}482=3{,}000+400+80+2 2,759=2,000+700+50+92{,}759=2{,}000+700+50+9

  1. Add matching place values:

    • Thousands: 3,000+2,000=5,0003{,}000+2{,}000=5{,}000
    • Hundreds: 400+700=1,100400+700=1{,}100
    • Tens: 80+50=13080+50=130
    • Ones: 2+9=112+9=11

    The sums of 1,1001{,}100, 130130, and 1111 show regrouping: 1,1001{,}100 includes a thousand, 130130 includes a hundred, and 1111 includes a ten.

  2. Combine the partial sums:

5,000+1,100+130+11=6,2415{,}000+1{,}100+130+11=6{,}241

Therefore,

3,482+2,759=6,241\boxed{3{,}482+2{,}759=6{,}241}

Learn by doing: Add using partial sums

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    Addition - Whole Number 4 digit + 4 digit, With Carry

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