Learn on PengienVision, Mathematics, Grade 4Chapter 2: Fluently Add and Subtract Multi-Digit Whole Numbers

Lesson 7: Subtract Across Zeros

In this Grade 4 enVision Mathematics lesson from Chapter 2, students learn how to subtract across zeros using the standard algorithm, including regrouping across multiple place values when zeros appear in the minuend. The lesson covers multi-digit subtraction problems such as 6,000 minus 4,678, where students must regroup from the thousands place through hundreds and tens before subtracting. Students also practice using estimation to verify that their differences are reasonable.

Section 1

Regrouping Across Zeros: The Role of 9s

Property

When regrouping across zeros, the first non-zero digit is reduced by 1, the place value you are regrouping to becomes 10 (or 10 + its original value), and all intermediate zeros become 9. This happens because you are borrowing sequentially. For example:

4,000=3 thousands+9 hundreds+9 tens+10 ones4,000 = 3 \text{ thousands} + 9 \text{ hundreds} + 9 \text{ tens} + 10 \text{ ones}

Examples

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Chapter 2: Fluently Add and Subtract Multi-Digit Whole Numbers

  1. Lesson 1

    Lesson 1: Finding Sums and Differences with Mental Math

  2. Lesson 2

    Lesson 2: Estimate Sums and Differences

  3. Lesson 3

    Lesson 3: Add Whole Numbers

  4. Lesson 4

    Lesson 4: Add Greater Numbers

  5. Lesson 5

    Lesson 5: Subtract Whole Numbers

  6. Lesson 6

    Lesson 6: Subtract Greater Numbers

  7. Lesson 7Current

    Lesson 7: Subtract Across Zeros

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Regrouping Across Zeros: The Role of 9s

Property

When regrouping across zeros, the first non-zero digit is reduced by 1, the place value you are regrouping to becomes 10 (or 10 + its original value), and all intermediate zeros become 9. This happens because you are borrowing sequentially. For example:

4,000=3 thousands+9 hundreds+9 tens+10 ones4,000 = 3 \text{ thousands} + 9 \text{ hundreds} + 9 \text{ tens} + 10 \text{ ones}

Examples

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 2: Fluently Add and Subtract Multi-Digit Whole Numbers

  1. Lesson 1

    Lesson 1: Finding Sums and Differences with Mental Math

  2. Lesson 2

    Lesson 2: Estimate Sums and Differences

  3. Lesson 3

    Lesson 3: Add Whole Numbers

  4. Lesson 4

    Lesson 4: Add Greater Numbers

  5. Lesson 5

    Lesson 5: Subtract Whole Numbers

  6. Lesson 6

    Lesson 6: Subtract Greater Numbers

  7. Lesson 7Current

    Lesson 7: Subtract Across Zeros