Math with Mr. J: Adding Decimals

Introduction

• Topic: How to add decimals
• Pre-requisite: Ability to add whole numbers
• Key concept: Proper setup of problems by aligning decimal points

Example 1: Adding 18.4 and 6.72

• Numbers: 18.4 + 6.72
• Alignment:
  • Line decimals vertically to align all place values.
  • Use placeholder zeros to better organize (e.g., 18.40 + 6.72).
  • Placeholder zeros do not change the value as they are equivalent decimals.
• Process:
  • Start adding from the rightmost digit (hundredths).
  • Hundredths: 0 + 2 = 2
  • Tenths: 4 + 7 = 11, carry 1 to the next column.
  • Bring decimal point straight down.
  • Ones: 1 + 8 + 6 (carried over) = 15, carry 1.
  • Tens: 1 + 1 (carried over) = 2
• Result: 25.12

Common Mistake

• Mistake: Lining up digits instead of decimal points.
  • Example of incorrect setup: 18.4 + 6.72 aligned by digits.
• Consequence: Misaligned places result in incorrect answers.
• Solution: Always align decimal points first.

Example 2: Adding 55.909 and 23.3

• Numbers: 55.909 + 23.3
• Alignment:
  • Line decimals up vertically.
  • Use placeholder zeros (55.909 + 23.300).
• Process:
  • Start adding from the rightmost digit.
  • Thousandths: 9 + 0 = 9
  • Hundredths: 0 + 0 = 0
  • Tenths: 9 + 3 = 12, carry 1.
  • Bring decimal point straight down.
  • Ones: 1 + 5 + 3 (carried over) = 9
  • Tens: 5 + 2 = 7
• Result: 79.209

Conclusion

• Summary:
  • Align decimals to ensure place values are correct.
  • Use zeros as placeholders to facilitate neat alignment without altering values.
• Encouragement: Practice to avoid common pitfalls and improve accuracy.