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
  • 204.5−67.123=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.

Lesson overview

Expand to review the lesson summary and core properties.

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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
  • 204.5−67.123=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.