Add and Subtract Decimals - Sixth Grade
Complete Notes & Formulas
1. Add Decimal Numbers
The Golden Rule
LINE UP THE DECIMAL POINTS!
This keeps place values aligned
Steps for Adding Decimals
Step 1: Write numbers vertically with decimal points lined up
Step 2: Add zeros as placeholders if needed
Step 3: Add as you would with whole numbers
Step 4: Bring the decimal point straight down
Example 1: Same Decimal Places
Problem: 3.45 + 2.78
3.45
+ 2.78
------
6.23
Answer: 6.23
Example 2: Different Decimal Places
Problem: 15.6 + 3.247
Step 1: Line up decimal points and add zeros
15.600
+ 3.247
--------
18.847
Answer: 18.847
Example 3: Adding with Whole Numbers
Problem: 8 + 4.325
Remember: 8 = 8.000
8.000
+4.325
-------
12.325
Answer: 12.325
2. Subtract Decimal Numbers
Steps for Subtracting Decimals
Step 1: Write numbers vertically with decimal points lined up
Step 2: Add zeros as placeholders if needed
Step 3: Subtract as you would with whole numbers (borrow if necessary)
Step 4: Bring the decimal point straight down
Example 1: Simple Subtraction
Problem: 8.76 − 3.42
8.76
− 3.42
------
5.34
Answer: 5.34
Example 2: With Borrowing
Problem: 7.3 − 4.58
Step 1: Add zero: 7.3 = 7.30
Step 2: Borrow as needed
7.30
− 4.58
------
2.72
Answer: 2.72
Example 3: Subtracting from Whole Number
Problem: 10 − 3.764
Remember: 10 = 10.000
10.000
− 3.764
--------
6.236
Answer: 6.236
3. Word Problems with Decimals
Keywords
Addition: Total, Sum, Combined, Altogether, In all
Subtraction: Difference, How much more, Left over, Remaining, Change
Example 1: Addition Word Problem
Problem: Sarah ran 3.75 kilometers on Monday and 4.6 kilometers on Tuesday. How many kilometers did she run in total?
Keyword: "total" → Addition
3.75 + 4.6 = 3.75 + 4.60 = 8.35
Answer: 8.35 kilometers
Example 2: Subtraction Word Problem
Problem: A rope is 12.5 meters long. A piece 3.75 meters is cut off. How much rope is left?
Keyword: "left" → Subtraction
12.5 − 3.75 = 12.50 − 3.75 = 8.75
Answer: 8.75 meters
4. Money Word Problems
Money Rules
✓ Always use 2 decimal places for money
✓ Include the dollar sign ($) in your answer
✓ $3.5 should be written as $3.50
Example 1: Buying Items
Problem: Tom bought a book for $12.75 and a pen for $3.50. How much did he spend in total?
$12.75 + $3.50 = $16.25
Answer: $16.25
Example 2: Making Change
Problem: Lisa paid with a $20 bill for a toy that costs $14.85. How much change does she receive?
$20.00 − $14.85 = $5.15
Answer: $5.15
Example 3: Multi-Step Money Problem
Problem: Mike has $50. He buys lunch for $8.75 and a movie ticket for $12.50. How much money does he have left?
Step 1: Total spent = $8.75 + $12.50 = $21.25
Step 2: Money left = $50.00 − $21.25 = $28.75
Answer: $28.75
5. Complete the Decimal Sentence
Finding Missing Numbers
Use inverse operations to find missing numbers in decimal sentences.
Example 1: Missing Addend
Problem: 3.5 + ___ = 8.2
Strategy: Subtract to find the missing number
8.2 − 3.5 = 4.7
Answer: 4.7
Check: 3.5 + 4.7 = 8.2 ✓
Example 2: Missing Minuend
Problem: ___ − 2.75 = 5.6
Strategy: Add to find the missing number
5.6 + 2.75 = 8.35
Answer: 8.35
Check: 8.35 − 2.75 = 5.6 ✓
6. Estimate Sums and Differences
Why Estimate?
Estimating helps you check if your answer is reasonable and allows for quick mental calculations.
Method 1: Rounding
Steps:
1. Round each decimal to nearest whole number, tenth, etc.
2. Add or subtract the rounded numbers
Example: Estimate 8.7 + 5.2
Round to nearest whole:
8.7 → 9
5.2 → 5
9 + 5 = 14
Estimate: About 14
(Actual: 8.7 + 5.2 = 13.9)
Method 2: Benchmarks
Common Benchmarks: 0, 0.25, 0.5, 0.75, 1
Round to the nearest benchmark
Example: Estimate 0.72 − 0.29
0.72 → 0.75 (nearest benchmark)
0.29 → 0.25 (nearest benchmark)
0.75 − 0.25 = 0.5
Estimate: About 0.5
(Actual: 0.72 − 0.29 = 0.43)
7. Maps with Decimal Distances
Real-World Application
Maps often show distances in decimals (miles or kilometers). You need to add or subtract to find total distances or differences.
Example: Multi-Leg Journey
Problem: On a map:
• Home to Store: 2.3 km
• Store to Park: 1.75 km
• Park to School: 3.6 km
Question: What is the total distance from home to school?
Solution:
2.3 + 1.75 + 3.6 = ?
2.30
1.75
+3.60
-----
7.65
Answer: 7.65 km
Example: Finding Shorter Route
Problem: Route A is 12.8 miles. Route B is 9.65 miles. How much shorter is Route B?
12.8 − 9.65 = 12.80 − 9.65 = 3.15
Answer: 3.15 miles shorter
Quick Reference: Decimal Operations
Rule | What to Do |
---|---|
Adding/Subtracting | Line up decimal points |
Placeholders | Add zeros as needed |
Decimal Point in Answer | Bring straight down |
Money | Always 2 decimal places |
Estimating | Round then calculate |
💡 Important Tips to Remember
✓ ALWAYS line up decimal points vertically
✓ Add zeros as placeholders to match decimal places
✓ Bring the decimal point straight down
✓ For money, always use 2 decimal places
✓ Estimate first to check reasonableness
✓ Remember: 5 = 5.0 = 5.00 = 5.000
✓ Borrow when subtracting (just like whole numbers)
✓ Use inverse operations to find missing numbers
✓ Check your work by estimating
✓ In word problems, look for keywords
🧠 Memory Tricks & Strategies
Line Up Decimals:
"Dots on dots, numbers in slots!"
Adding Zeros:
"When in doubt, zero it out!"
(Add zeros to make decimal places match)
Decimal Point Placement:
"Straight down the line, works every time!"
Money Problems:
"Two decimal places, that's the money way!"
Estimating:
"Round it quick, check your trick!"
Word Problems:
"Read with care, keywords are there!"
Master Decimal Operations! ➕ ➖ 💰 🗺️
Line up those decimal points and practice daily!