Learn on PengiPengi Math (Grade 5)Chapter 3: Decimal Operations and Estimation

Lesson 4: Decimal Subtraction with Regrouping

In this Grade 5 Pengi Math lesson, students learn to subtract decimals through the thousandths place using the standard algorithm, including how to regroup when the top digit is smaller and annex zeros to create like units. Lessons build on place-value understanding and require aligning decimal points to subtract accurately and efficiently across decimals of different lengths.

Section 1

Modeling Decimal Subtraction

Property

To model subtraction, you start with the total amount (the minuend) and take away a part (the subtrahend) to find what is left (the difference).

MinuendSubtrahend=DifferenceMinuend - Subtrahend = Difference

Examples

Section 2

Subtracting Decimals Using the Standard Algorithm

Property

To subtract decimals using the standard algorithm, align the numbers vertically by their decimal points. Subtract each column from right to left, regrouping from the place value to the left when a top digit is smaller than the bottom digit. Place the decimal point in the answer directly below the decimal points in the problem.

Examples

Section 3

Annexing Zeros to Subtract Decimals

Property

To subtract decimals with a different number of decimal places, annex (add) zeros to the right of the number with fewer decimal places until both numbers have the same number of places. This does not change the number's value (e.g., 5.2=5.205.2 = 5.20).

Examples

Section 4

Subtracting Decimals to the Thousandths

Property

To subtract decimals, align the numbers by their decimal points. Subtract as you would with whole numbers, starting from the rightmost place value, and regroup (borrow) when necessary. Place the decimal point in the difference directly below the decimal points in the numbers being subtracted.

Examples

  • 5.4322.1565.432 - 2.156
5.433122122.1563.276\begin{array}{rcccccc} & 5 & . & \overset{3}{\cancel{4}} & \overset{12}{\cancel{3}} & \overset{12}{\cancel{2}} \\ -& 2 & . & 1 & 5 & 6 \\ \hline & 3 & . & 2 & 7 & 6 \\ \end{array}
  • 12.53.48112.5 - 3.481
10212.54090103.4819.019\begin{array}{rccccccc} & \overset{0}{\cancel{1}} & \overset{12}{\cancel{2}} & . & \overset{4}{\cancel{5}} & \overset{9}{\cancel{0}} & \overset{10}{\cancel{0}} \\ -& & 3 & . & 4 & 8 & 1 \\ \hline & & 9 & . & 0 & 1 & 9 \\ \end{array}

Book overview

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Chapter 3: Decimal Operations and Estimation

  1. Lesson 1

    Lesson 1: Mental Addition Strategies with Decimals

  2. Lesson 2

    Lesson 2: Mental Subtraction Strategies with Decimals

  3. Lesson 3

    Lesson 3: Decimal Addition with Regrouping

  4. Lesson 4Current

    Lesson 4: Decimal Subtraction with Regrouping

  5. Lesson 5

    Lesson 5: Estimation and Reasonableness Checks

  6. Lesson 6

    Lesson 6: Multi-Step Decimal Problems

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Modeling Decimal Subtraction

Property

To model subtraction, you start with the total amount (the minuend) and take away a part (the subtrahend) to find what is left (the difference).

MinuendSubtrahend=DifferenceMinuend - Subtrahend = Difference

Examples

Section 2

Subtracting Decimals Using the Standard Algorithm

Property

To subtract decimals using the standard algorithm, align the numbers vertically by their decimal points. Subtract each column from right to left, regrouping from the place value to the left when a top digit is smaller than the bottom digit. Place the decimal point in the answer directly below the decimal points in the problem.

Examples

Section 3

Annexing Zeros to Subtract Decimals

Property

To subtract decimals with a different number of decimal places, annex (add) zeros to the right of the number with fewer decimal places until both numbers have the same number of places. This does not change the number's value (e.g., 5.2=5.205.2 = 5.20).

Examples

Section 4

Subtracting Decimals to the Thousandths

Property

To subtract decimals, align the numbers by their decimal points. Subtract as you would with whole numbers, starting from the rightmost place value, and regroup (borrow) when necessary. Place the decimal point in the difference directly below the decimal points in the numbers being subtracted.

Examples

  • 5.4322.1565.432 - 2.156
5.433122122.1563.276\begin{array}{rcccccc} & 5 & . & \overset{3}{\cancel{4}} & \overset{12}{\cancel{3}} & \overset{12}{\cancel{2}} \\ -& 2 & . & 1 & 5 & 6 \\ \hline & 3 & . & 2 & 7 & 6 \\ \end{array}
  • 12.53.48112.5 - 3.481
10212.54090103.4819.019\begin{array}{rccccccc} & \overset{0}{\cancel{1}} & \overset{12}{\cancel{2}} & . & \overset{4}{\cancel{5}} & \overset{9}{\cancel{0}} & \overset{10}{\cancel{0}} \\ -& & 3 & . & 4 & 8 & 1 \\ \hline & & 9 & . & 0 & 1 & 9 \\ \end{array}

Book overview

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

Continue this chapter

Chapter 3: Decimal Operations and Estimation

  1. Lesson 1

    Lesson 1: Mental Addition Strategies with Decimals

  2. Lesson 2

    Lesson 2: Mental Subtraction Strategies with Decimals

  3. Lesson 3

    Lesson 3: Decimal Addition with Regrouping

  4. Lesson 4Current

    Lesson 4: Decimal Subtraction with Regrouping

  5. Lesson 5

    Lesson 5: Estimation and Reasonableness Checks

  6. Lesson 6

    Lesson 6: Multi-Step Decimal Problems