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Within 1,000 Knowledge-Based Study

Math · Number Sense & Operations · Math · Addition & Subtraction

Math topic explanations on Within 1,000.

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  1. Adding Three-Digit Numbers Without Regrouping

    To add numbers within 1,000, align digits according to their place value: hundreds, tens, and ones.

    Always begin adding from the rightmost column (ones) and move leftward:

    • Step 1 (Ones): Add the ones digits together.
    • Step 2 (Tens): Add the tens digits together.
    • Step 3 (Hundreds): Add the hundreds digits together.

    For example, to solve 324 + 153:

    • 4 ones + 3 ones = 7 ones
    • 2 tens + 5 tens = 7 tens
    • 3 hundreds + 1 hundred = 4 hundreds

    The total sum is 477.

    Regrouping Across Tens and Hundreds

    When the sum of digits in any place-value column is 10 or greater, you must regroup (or carry) 10 of that unit into 1 unit of the next column to the left.

    Consider the problem: 468 + 275

    1. Add the ones: 8 + 5 = 13. Write down 3 in the ones place and regroup 1 ten to the tens place.
    2. Add the tens: 1 (regrouped) + 6 + 7 = 14 tens. Write down 4 in the tens place and regroup 1 hundred to the hundreds place.
    3. Add the hundreds: 1 (regrouped) + 4 + 2 = 7 hundreds. Write down 7 in the hundreds place.

    Therefore, 468 + 275 = 743.

    Subtracting Without Regrouping

    Subtraction finds the difference between two quantities. Place the larger number (minuend) on top and line up the smaller number (subtrahend) by place value.

    Work systematically from right to left:

    • Ones column: Subtract the bottom digit from the top digit.
    • Tens column: Subtract the tens.
    • Hundreds column: Subtract the hundreds.

    For example, calculate 685 - 241:

    • 5 ones - 1 one = 4 ones
    • 8 tens - 4 tens = 4 tens
    • 6 hundreds - 2 hundreds = 4 hundreds

    The difference is 444.

    Decomposing Tens and Hundreds

    When a digit in the top number is smaller than the digit directly below it, you must regroup (borrow) from the column to the left.

    Rule: 1 hundred can be traded for 10 tens, and 1 ten can be traded for 10 ones.

    Consider 532 - 178:

    1. Ones place: You cannot subtract 8 from 2. Regroup 1 ten from the 3 tens (leaving 2 tens). The 2 ones become 12 ones. Now, 12 - 8 = 4.
    2. Tens place: You cannot subtract 7 from the remaining 2 tens. Regroup 1 hundred from 5 hundreds (leaving 4 hundreds). The 2 tens become 12 tens. Now, 12 - 7 = 5.
    3. Hundreds place: Subtract 4 hundreds - 1 hundred = 3 hundreds.

    Thus, 532 - 178 = 354.

    Special Cases and Verification

    When subtracting from a number containing zeros (such as 600 - 247), regroup step-by-step from the nearest non-zero place value:

    • Trade 1 hundred from 6 hundreds to make 10 tens (hundreds become 5, tens become 10).
    • Trade 1 ten from 10 tens to make 10 ones (tens become 9, ones become 10).
    • Subtract: 10 - 7 = 3 ones, 9 - 4 = 5 tens, and 5 - 2 = 3 hundreds. The result is 353.

    Checking Your Answer:
    Addition and subtraction are inverse operations. You can verify any subtraction result by adding the difference back to the subtrahend:

    353 + 247 = 600, confirming that the solution is correct.