Basic Math

Add and subtract decimals | Sixth Grade

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

RuleWhat to Do
Adding/SubtractingLine up decimal points
PlaceholdersAdd zeros as needed
Decimal Point in AnswerBring straight down
MoneyAlways 2 decimal places
EstimatingRound 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!

Shares: