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U06 • Lesson 24 of 105

Decimal Operations: Addition & Subtraction

Teaches addition and subtraction of decimal numbers by emphasizing place value alignment. Students use base-ten blocks and hundredths grids to model decimal sums and differences, learn to align decimal points before computing, and estimate to check reasonableness of results.

Upper Elementary • 3-5

Prerequisites: M16, U01

Key Concepts

  • aligning decimal points for addition and subtraction
  • modeling decimal operations with base-ten blocks
  • estimating decimal sums and differences
  • adding and subtracting decimals through hundredths

Decimal Operations: Addition and Subtraction

Decimals are another way to write fractions. The number 0.75 means 75/100, which is the same as 3/4. When we add or subtract decimals, the most important rule is to line up the decimal points.

Decimal Place Value

Ones.TenthsHundredthsThousandths
3.452
3.452 = 3 + 0.4 + 0.05 + 0.002

Key Principle

Just like with whole numbers, we can only add or subtract digits that are in the same place. Tenths with tenths. Hundredths with hundredths. Lining up the decimal points ensures this happens automatically.

Adding Decimals

  1. Write the numbers vertically, lining up the decimal points.
  2. Fill in any empty places with zeros (placeholders).
  3. Add column by column from right to left, just like whole numbers.
  4. Place the decimal point straight down into the answer.

Worked Example 1: Adding Decimals

Find 3.25 + 14.8.

  1. Line up the decimal points. Write 14.8 as 14.80 (add a zero).
  2. Add:
       3.25
    + 14.80
    -------
      18.05
  3. Hundredths: 5+0=5. Tenths: 2+8=10, write 0 carry 1. Ones: 1+3+4=8. Tens: 1.
3.25 + 14.8 = 18.05

Subtracting Decimals

Worked Example 2: Subtracting Decimals

Find 7.4 - 2.65.

  1. Line up decimal points. Write 7.4 as 7.40.
  2. Subtract:
      7.40
    - 2.65
    ------
      4.75
  3. Hundredths: 0-5? Borrow! 10-5=5. Tenths: 3-6? Borrow! 13-6=7. Ones: 6-2=4.
7.4 - 2.65 = 4.75

Modeling with Base-Ten Blocks

We can use the same blocks but give them new values:

BlockWhole Number ValueDecimal Value
Flat (100 square)1001 (one whole)
Rod (10 stick)100.1 (one tenth)
Unit cube10.01 (one hundredth)

Worked Example 3: Estimating Before Computing

Estimate 8.73 + 4.19, then find the exact answer.

  1. Estimate: Round to whole numbers: 9 + 4 = 13.
  2. Exact: 8.73 + 4.19 = 12.92
  3. Our exact answer (12.92) is close to our estimate (13). Makes sense!

Common Mistake

Do NOT line up the last digits -- line up the decimal points. Writing 3.25 + 14.8 so that the 5 and 8 are in the same column is WRONG. The 5 (hundredths) and 8 (tenths) belong in different columns.

Real-World Connection

Money uses decimals! If you buy a book for $7.49 and a pencil for $1.25, your total is $7.49 + $1.25 = $8.74. The decimal point separates dollars from cents.

Practice Problems

1. Add: 5.6 + 3.48

Show Answer

5.60 + 3.48 = 9.08. Hundredths: 0+8=8. Tenths: 6+4=10, write 0 carry 1. Ones: 1+5+3=9.

2. Subtract: 10.00 - 3.75

Show Answer

10.00 - 3.75 = 6.25. This is like making change from a $10 bill.

3. Add: 0.456 + 2.3

Show Answer

0.456 + 2.300 = 2.756.

4. Estimate 12.85 - 7.2, then find the exact answer.

Show Answer

Estimate: 13 - 7 = 6. Exact: 12.85 - 7.20 = 5.65. Close to the estimate.

5. You have $20.00. You spend $8.47 on lunch and $3.29 on a drink. How much do you have left?

Show Answer

Total spent: $8.47 + $3.29 = $11.76. Remaining: $20.00 - $11.76 = $8.24.

Lesson Summary

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