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

Lesson 2: Mental Subtraction Strategies with Decimals

In this Grade 5 lesson from Pengi Math, students learn mental subtraction strategies for decimals, including compensation, place-value decomposition, and number line representation. The lesson builds flexible thinking by connecting place value to step-by-step subtraction and teaches students to estimate differences to check for reasonableness.

Section 1

Using Compensation for Subtraction

Property

To mentally calculate a difference like aba - b, you can change the subtrahend (bb) to a nearby, easier number (cc). Then, subtract cc from aa and adjust the result by adding the difference between cc and bb.

ab=(ac)+(cb)a - b = (a - c) + (c - b)

Examples

Section 2

Using the Partial Differences Method

Property

To subtract using partial differences, break the second number into its place value parts (e.g., ones, tenths, hundredths). Then, subtract each part one at a time from the first number. For a problem like 5.852.415.85 - 2.41, the process is:

(5.852)0.40.01(5.85 - 2) - 0.4 - 0.01

Examples

Section 3

Modeling Decimal Subtraction on a Number Line

Property

To subtract decimals on a number line, start at the minuend (the first number) and move to the left. The total distance moved is the value of the subtrahend (the second number). The final position on the number line is the difference.

Examples

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 2Current

    Lesson 2: Mental Subtraction Strategies with Decimals

  3. Lesson 3

    Lesson 3: Decimal Addition with Regrouping

  4. Lesson 4

    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

Using Compensation for Subtraction

Property

To mentally calculate a difference like aba - b, you can change the subtrahend (bb) to a nearby, easier number (cc). Then, subtract cc from aa and adjust the result by adding the difference between cc and bb.

ab=(ac)+(cb)a - b = (a - c) + (c - b)

Examples

Section 2

Using the Partial Differences Method

Property

To subtract using partial differences, break the second number into its place value parts (e.g., ones, tenths, hundredths). Then, subtract each part one at a time from the first number. For a problem like 5.852.415.85 - 2.41, the process is:

(5.852)0.40.01(5.85 - 2) - 0.4 - 0.01

Examples

Section 3

Modeling Decimal Subtraction on a Number Line

Property

To subtract decimals on a number line, start at the minuend (the first number) and move to the left. The total distance moved is the value of the subtrahend (the second number). The final position on the number line is the difference.

Examples

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 2Current

    Lesson 2: Mental Subtraction Strategies with Decimals

  3. Lesson 3

    Lesson 3: Decimal Addition with Regrouping

  4. Lesson 4

    Lesson 4: Decimal Subtraction with Regrouping

  5. Lesson 5

    Lesson 5: Estimation and Reasonableness Checks

  6. Lesson 6

    Lesson 6: Multi-Step Decimal Problems