Operations with Decimals - Seventh Grade
Addition, Subtraction, Multiplication & Division
1. Adding and Subtracting Decimals
Rules for Adding and Subtracting
The Golden Rule: ALIGN THE DECIMAL POINTS!
Step 1: Write numbers vertically, lining up decimal points
Step 2: Add ZEROS to make equal decimal places (if needed)
Step 3: Add or subtract as with whole numbers
Step 4: Bring the decimal point STRAIGHT DOWN
Example 1: Addition
Problem: 25.7 + 3.48
Step 1: Align decimal points:
25.7 + 3.48 -------
Step 2: Add zeros:
25.70 + 3.48 -------
Step 3: Add:
25.70 + 3.48 ------- 29.18
Answer: 29.18
Example 2: Subtraction
Problem: 42.5 − 18.67
Align and add zeros:
42.50 - 18.67 ------- 23.83
Answer: 23.83
2. Multiplying Decimals
Rules for Multiplying
Don't worry about decimal points at first!
Step 1: IGNORE decimal points and multiply as whole numbers
Step 2: COUNT total decimal places in BOTH numbers
Step 3: PUT decimal point in answer (same total places)
Formula
Decimal places in answer =
Decimal places in 1st number + Decimal places in 2nd number
Example 1: Multiply 3.4 × 2.5
Step 1: Multiply ignoring decimals:
34 × 25 = 850
Step 2: Count decimal places:
3.4 has 1 decimal place
2.5 has 1 decimal place
Total: 1 + 1 = 2 decimal places
Step 3: Place decimal point:
850 → 8.50 = 8.5
Answer: 8.5
Example 2: Multiply 0.25 × 0.4
Multiply: 25 × 4 = 100
Decimal places: 2 + 1 = 3
Result: 0.100 = 0.1
Answer: 0.1
3. Dividing Decimals
Rules for Dividing
Make the divisor a WHOLE NUMBER!
Step 1: MOVE decimal point in divisor to the RIGHT (make it whole)
Step 2: MOVE decimal point in dividend the SAME number of places
Step 3: DIVIDE as with whole numbers
Step 4: Place decimal point in quotient directly above
Example 1: Divide 6.4 ÷ 0.8
Step 1: Move decimal in divisor:
0.8 → 8 (moved 1 place right)
Step 2: Move decimal in dividend:
6.4 → 64 (moved 1 place right)
Step 3: Divide:
64 ÷ 8 = 8
Answer: 8
Example 2: Divide 12.6 ÷ 0.03
Move decimal 2 places right in both:
0.03 → 3
12.6 → 1260
Divide: 1260 ÷ 3 = 420
Answer: 420
Dividing by 10, 100, 1000
÷ 10: Move decimal point 1 place LEFT
Example: 45.6 ÷ 10 = 4.56
÷ 100: Move decimal point 2 places LEFT
Example: 234.5 ÷ 100 = 2.345
÷ 1000: Move decimal point 3 places LEFT
Example: 678.9 ÷ 1000 = 0.6789
4. Estimating with Decimals
How to Estimate
ROUND first, then calculate!
Step 1: ROUND each decimal to a convenient place
Step 2: PERFORM the operation with rounded numbers
Step 3: Your result is the ESTIMATE
Examples
Estimate: 24.7 + 38.2
Round: 25 + 38 ≈ 63
Estimate: 63
Estimate: 8.9 × 3.1
Round: 9 × 3 ≈ 27
Estimate: 27
Estimate: 47.8 ÷ 5.9
Round: 48 ÷ 6 ≈ 8
Estimate: 8
5. Word Problems with Decimals
Keywords to Look For
Addition (+): total, sum, combined, altogether, in all
Subtraction (−): difference, how much more, left, remaining, change
Multiplication (×): times, product, of, each, per, total for multiple
Division (÷): split, share, each, per, average, quotient
Example Problems
Problem 1: Sarah bought 2.5 pounds of apples at $1.80 per pound. How much did she pay?
Operation: Multiplication (per means ×)
2.5 × 1.80 = 4.50
Answer: $4.50
Problem 2: A rope is 15.6 meters long. If you cut off 8.75 meters, how much is left?
Operation: Subtraction (left means −)
15.6 − 8.75 = 6.85
Answer: 6.85 meters
Problem 3: Four friends split a bill of $85.20 equally. How much does each person pay?
Operation: Division (split equally means ÷)
85.20 ÷ 4 = 21.30
Answer: $21.30 each
6. Evaluating Expressions with Decimals
Order of Operations (PEMDAS)
Remember: PEMDAS
Parentheses ( )
Exponents
Multiplication and Division (left to right)
Addition and Subtraction (left to right)
Example: Complex Expression
Evaluate: 5.2 + 3.6 × 2 − 4.8 ÷ 1.2
Step 1: Multiply first (3.6 × 2 = 7.2)
5.2 + 7.2 − 4.8 ÷ 1.2
Step 2: Divide (4.8 ÷ 1.2 = 4)
5.2 + 7.2 − 4
Step 3: Add (5.2 + 7.2 = 12.4)
12.4 − 4
Step 4: Subtract (12.4 − 4 = 8.4)
Answer: 8.4
Quick Reference: Decimal Operations
| Operation | Key Rule |
|---|---|
| Addition | Align decimal points, add zeros, bring point down |
| Subtraction | Align decimal points, add zeros, bring point down |
| Multiplication | Multiply as whole, count total decimal places |
| Division | Move decimal in divisor & dividend same amount |
| ÷ by 10, 100, 1000 | Move decimal left 1, 2, or 3 places |
💡 Important Tips to Remember
✓ Adding/Subtracting: Always align decimal points first!
✓ Adding zeros doesn't change value (25.7 = 25.70)
✓ Multiplying: Don't align - count decimal places instead
✓ Total decimal places in product = sum of places in factors
✓ Dividing: Make divisor whole by moving decimal right
✓ Move decimal same places in both divisor and dividend
✓ Estimating: Round first, then calculate
✓ Use PEMDAS for order of operations
✓ Check reasonableness - does your answer make sense?
✓ Word problems: Identify operation first, then solve
🧠 Memory Tricks & Strategies
Adding/Subtracting:
"Line up the dots before you add or subtract - that's where it's at!"
Multiplying:
"Multiply as whole, then count the places - put the point in the right spaces!"
Dividing:
"Move the point to make divisor whole, then move dividend the same - that's the goal!"
Dividing by Powers of 10:
"When dividing by 10, 100, or more - move decimal LEFT, that's what it's for!"
Estimating:
"Round them up or round them down, then calculate to get close to the right amount!"
PEMDAS:
"Please Excuse My Dear Aunt Sally - operations in order, don't be silly!"
Master Decimal Operations! ➕ ➖ ✖️ ➗
Remember: Decimals are just like whole numbers with a point!