Learn on PengiIllustrative Mathematics, Grade 5Chapter 5: Place Value Patterns and Decimal Operations

Lesson 9: Addition and Subtraction

In this Grade 5 lesson from Illustrative Mathematics Chapter 5, students add and subtract decimals to the hundredths using place value strategies, including adding on, compensation, and the standard algorithm. Students practice choosing and applying the most efficient method for expressions like 75.2 − 4.37 and 236.87 + 5.15, reinforcing standard 5.NBT.B.7. The lesson builds fluency with decimal operations by encouraging students to think strategically rather than relying on a single prescribed approach.

Section 1

Adding and Subtracting Decimals with More Digits

Property

To add or subtract decimals, align the numbers by their decimal points. Add or subtract as you would with whole numbers, starting from the rightmost digit. Place the decimal point in the answer directly below the decimal points in the numbers above.

Examples

  • 145.78+92.3=238.08145.78 + 92.3 = 238.08
  • 204.567.123=137.377204.5 - 67.123 = 137.377
  • 89.654+11.47=101.12489.654 + 11.47 = 101.124

Explanation

When adding or subtracting larger decimal numbers, the process remains the same. The key is to carefully align the decimal points to ensure you are adding or subtracting corresponding place values. You can add trailing zeros to numbers to make them the same length after the decimal point, which can help with alignment. Then, simply perform the operation as if they were whole numbers and bring the decimal point straight down into your answer.

Book overview

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Chapter 5: Place Value Patterns and Decimal Operations

  1. Lesson 1

    Lesson 1: Thousandths: Introduction and Representation

  2. Lesson 2

    Lesson 2: Thousandths and Place Value Relationships

  3. Lesson 3

    Lesson 3: Compare Decimals

  4. Lesson 4

    Lesson 4: Round Decimals

  5. Lesson 5

    Lesson 5: Order and Solve Problems with Decimals

  6. Lesson 6

    Lesson 6: Decimal Addition: Sense Making and Estimation

  7. Lesson 7

    Lesson 7: Analyze Addition Mistakes

  8. Lesson 8

    Lesson 8: Decimal Subtraction: Sense Making and Estimation

  9. Lesson 9Current

    Lesson 9: Addition and Subtraction

  10. Lesson 10

    Lesson 10: Multiply Decimals by Whole Numbers

  11. Lesson 11

    Lesson 11: Multiply Decimals: Properties and Hundredths

  12. Lesson 12

    Lesson 12: Multiply More Decimals

  13. Lesson 13

    Lesson 13: Divide by Decimals

  14. Lesson 14

    Lesson 14: Divide Decimals

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Adding and Subtracting Decimals with More Digits

Property

To add or subtract decimals, align the numbers by their decimal points. Add or subtract as you would with whole numbers, starting from the rightmost digit. Place the decimal point in the answer directly below the decimal points in the numbers above.

Examples

  • 145.78+92.3=238.08145.78 + 92.3 = 238.08
  • 204.567.123=137.377204.5 - 67.123 = 137.377
  • 89.654+11.47=101.12489.654 + 11.47 = 101.124

Explanation

When adding or subtracting larger decimal numbers, the process remains the same. The key is to carefully align the decimal points to ensure you are adding or subtracting corresponding place values. You can add trailing zeros to numbers to make them the same length after the decimal point, which can help with alignment. Then, simply perform the operation as if they were whole numbers and bring the decimal point straight down into your answer.

Book overview

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

Continue this chapter

Chapter 5: Place Value Patterns and Decimal Operations

  1. Lesson 1

    Lesson 1: Thousandths: Introduction and Representation

  2. Lesson 2

    Lesson 2: Thousandths and Place Value Relationships

  3. Lesson 3

    Lesson 3: Compare Decimals

  4. Lesson 4

    Lesson 4: Round Decimals

  5. Lesson 5

    Lesson 5: Order and Solve Problems with Decimals

  6. Lesson 6

    Lesson 6: Decimal Addition: Sense Making and Estimation

  7. Lesson 7

    Lesson 7: Analyze Addition Mistakes

  8. Lesson 8

    Lesson 8: Decimal Subtraction: Sense Making and Estimation

  9. Lesson 9Current

    Lesson 9: Addition and Subtraction

  10. Lesson 10

    Lesson 10: Multiply Decimals by Whole Numbers

  11. Lesson 11

    Lesson 11: Multiply Decimals: Properties and Hundredths

  12. Lesson 12

    Lesson 12: Multiply More Decimals

  13. Lesson 13

    Lesson 13: Divide by Decimals

  14. Lesson 14

    Lesson 14: Divide Decimals