Decimal Operations
Add, subtract, multiply, and divide decimals with confidence
What You'll Learn
Adding Decimals
Adding decimals is similar to adding whole numbers, but you must keep the decimal points aligned.
Steps for Adding Decimals
- 1 Line up the decimal points vertically
- 2 Add zeros as placeholders if needed
- 3 Add from right to left as usual
- 4 Place decimal point directly below the others
Example: 23.45 + 6.7
23.45 + 6.70 (Added zero) ------- 30.15
Answer: 30.15
Subtracting Decimals
Subtracting decimals follows the same alignment principle as addition.
Example: 45.8 - 12.35
45.80 (Added zero) - 12.35 ------- 33.45
Answer: 33.45
Example: Money Problem
You have $50.00 and buy an item for $23.75. How much change?
$50.00 - $23.75 -------- $26.25
Change: $26.25
Multiplying Decimals
For multiplication, you DON'T need to align decimal points. Instead, count decimal places at the end.
Steps for Multiplying Decimals
- 1 Multiply as if there were no decimal points
- 2 Count total decimal places in BOTH factors
- 3 Place decimal point that many places from right
Example: 3.4 × 2.5
Step 1: Multiply 34 × 25 = 850
Step 2: Count decimals: 3.4 (1) + 2.5 (1) = 2 total
Step 3: Place decimal 2 places from right: 8.50
Answer: 8.5
Dividing Decimals
Dividing by a Whole Number
Place the decimal point in the quotient directly above the decimal in the dividend.
Example: 12.6 ÷ 3
4.2 ----- 3 | 12.6
Answer: 4.2
Dividing by a Decimal
Make the divisor a whole number by moving both decimal points.
Example: 15.6 ÷ 1.2
Step 1: Move decimals → 156 ÷ 12
Step 2: Divide: 156 ÷ 12 = 13
Answer: 13
Word Problems
Problem 1: Shopping
A notebook costs $3.45 and a pen costs $1.78. What is the total cost?
$3.45 + $1.78 = $5.23
Problem 2: Unit Price
A pack of 6 water bottles costs $4.50. What is the cost per bottle?
$4.50 ÷ 6 = $0.75 per bottle
Problem 3: Area
A rectangle is 4.5 meters long and 2.8 meters wide. What is its area?
4.5 × 2.8 = 12.6 square meters
Practice Problems
Test your understanding
Addition & Subtraction
1. 45.67 + 23.8 ▼
69.47
2. 100.5 - 37.82 ▼
62.68
Multiplication & Division
3. 6.5 × 4.2 ▼
27.3
4. 18.9 ÷ 2.7 ▼
7
Common Mistakes to Avoid
- • Misaligned decimals: Always align decimal points for addition/subtraction
- • Counting decimal places: Count places in BOTH factors when multiplying
- • Division by decimals: Move BOTH decimal points the same amount
- • Forgetting zeros: Add placeholder zeros when needed
Key Takeaways
- ✓ Add/Subtract: Align decimal points vertically
- ✓ Multiply: Count total decimal places in factors
- ✓ Divide by decimal: Make divisor a whole number first
- ✓ Always estimate to check if answer is reasonable
Related Lessons
Ready for Fractions?
You've mastered decimal operations! Continue to learn about fractions.
