Add & Subtract Decimals
How do we add and subtract numbers with decimal points?
📚
Unit
5
📅
Day
1
⏱️
Duration
60m
📋 Standards & Learning Targets
📋Common Core Standard
5.NBT.7
Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
🎯I Will Be Able To...
- Add decimals by lining up place values
- Subtract decimals using regrouping when needed
- Estimate sums and differences to check reasonableness
🚀 Decimals Are Everywhere!
You have $20.00. A book costs $12.75 and a snack costs $3.49. Can you afford both? How much change would you get?
📕
Book
$12.75
🍎
Snack
$3.49
💰
Your Money
$20.00
📖 Key Vocabulary
Decimal Point
The dot that separates whole numbers from parts (e.g., 3.75)
Estimate
A close answer found by rounding before computing
Regroup
To trade 10 of one place value for 1 of the next (like borrowing)
Placeholder Zero
A zero added to give decimals the same number of places (e.g., 5.4 → 5.40)
✨ Adding Decimals: The Big Idea
Line up the decimal points, then add just like whole numbers!
1
Estimate First
Round to the nearest whole number and estimate the sum
2
Line Up Decimals
Write vertically with decimal points aligned — add placeholder zeros
3
Add & Check
Add column by column. Compare your answer to your estimate
📌 Three Steps to Add Decimals
1
Write the problem and line up the decimal points vertically
2
Add placeholder zeros so both numbers have the same number of decimal places
3
Add column by column from right to left, just like whole numbers
Example: 3.28 + 8.4
3.28
+ 8.40
───────
11.68
+ 8.40
───────
11.68
✏️ Problem 1
3.28 + 8.4
Add the decimals
📊
Three-Step Strategy
1
Estimate: Round first — 3 + 8 = about 11
2
Line Up & Add: Write vertically, add a placeholder zero:
3.28
+ 8.40
───────
11.68
3.28
+ 8.40
───────
11.68
3
Check: Is 11.68 close to our estimate of 11? Yes! ✓ Reasonable!
✓ Answer
3.28 + 8.4 = 11.68
✏️ Problem 2
4.7 + 9.53
Add the decimals
📊
Three-Step Strategy
1
Estimate: Round first — 5 + 10 = about 15
2
Line Up & Add: Write vertically, add a placeholder zero:
4.70
+ 9.53
───────
14.23
4.70
+ 9.53
───────
14.23
3
Check: Is 14.23 close to our estimate of 15? Yes! ✓ Reasonable!
✓ Answer
4.7 + 9.53 = 14.23
✏️ Problem 3
16.92 + 5.32
Add the decimals together
📊
Three-Step Strategy
1
Estimate: Round first — 17 + 5 = about 22
2
Line Up & Add: Both numbers already have 2 decimal places:
16.92
+ 5.32
───────
22.24
16.92
+ 5.32
───────
22.24
3
Check: Is 22.24 close to our estimate of 22? Yes! ✓ Reasonable!
✓ Answer
16.92 + 5.32 = 22.24
✏️ Problem 4
6.48 + 18.9
Add the decimals together
📊
Three-Step Strategy
1
Estimate: Round first — 6 + 19 = about 25
2
Line Up & Add: Add a placeholder zero to 18.9:
6.48
+18.90
───────
25.38
6.48
+18.90
───────
25.38
3
Check: Is 25.38 close to our estimate of 25? Yes! ✓ Reasonable!
✓ Answer
6.48 + 18.9 = 25.38
✏️ Problem 5
7.35 + 12.8
Try it on your own!
📊
Three-Step Strategy
1
Estimate: Round first — 7 + 13 = about 20
2
Line Up & Add: Add a placeholder zero to 12.8:
7.35
+12.80
───────
20.15
7.35
+12.80
───────
20.15
3
Check: Is 20.15 close to our estimate of 20? Yes! ✓ Reasonable!
✓ Answer
7.35 + 12.8 = 20.15
✏️ Problem 6
24.06 + 9.7
Try it on your own!
📊
Three-Step Strategy
1
Estimate: Round first — 24 + 10 = about 34
2
Line Up & Add: Add a placeholder zero to 9.7:
24.06
+ 9.70
───────
33.76
24.06
+ 9.70
───────
33.76
3
Check: Is 33.76 close to our estimate of 34? Yes! ✓ Reasonable!
✓ Answer
24.06 + 9.7 = 33.76
✨ Subtracting Decimals: Watch for Regrouping!
Line up decimal points, add placeholder zeros, then subtract — regroup (borrow) when needed!
Addition
Sometimes we regroup by combining tens and ones
vs.
Subtraction
Sometimes we need to borrow from the next place value
📌 Three Steps to Subtract Decimals
1
Write the problem and line up the decimal points vertically
2
Add placeholder zeros so both numbers have the same number of decimal places
3
Subtract column by column from right to left. Regroup (borrow) when needed!
Example: Rewriting a whole number
24 becomes 24.00 (add decimal and placeholder zeros)
✏️ Problem 7
9.4 − 2.34
Subtract the decimals
📊
Three-Step Strategy
1
Estimate: Round first — 9 − 2 = about 7
2
Line Up & Subtract: Add a placeholder zero to 9.4:
9.40
− 2.34
───────
7.06
9.40
− 2.34
───────
7.06
3
Check: Is 7.06 close to our estimate of 7? Yes! ✓ Reasonable!
✓ Answer
9.4 − 2.34 = 7.06
✏️ Problem 8
24 − 12.2
Subtract from a whole number
📊
Three-Step Strategy
1
Estimate: Round first — 24 − 12 = about 12
2
Line Up & Subtract: Rewrite 24 as 24.0, then subtract:
24.0
−12.2
──────
11.8
24.0
−12.2
──────
11.8
3
Check: Is 11.8 close to our estimate of 12? Yes! ✓ Reasonable!
✓ Answer
24 − 12.2 = 11.8
✏️ Problem 9
18.29 − 5.7
Subtract the decimals together
📊
Three-Step Strategy
1
Estimate: Round first — 18 − 6 = about 12
2
Line Up & Subtract: Add a placeholder zero to 5.7:
18.29
− 5.70
───────
12.59
18.29
− 5.70
───────
12.59
3
Check: Is 12.59 close to our estimate of 12? Yes! ✓ Reasonable!
✓ Answer
18.29 − 5.7 = 12.59
✏️ Problem 10
26 − 15.7
Subtract from a whole number together
📊
Three-Step Strategy
1
Estimate: Round first — 26 − 16 = about 10
2
Line Up & Subtract: Rewrite 26 as 26.0, then subtract:
26.0
−15.7
──────
10.3
26.0
−15.7
──────
10.3
3
Check: Is 10.3 close to our estimate of 10? Yes! ✓ Reasonable!
✓ Answer
26 − 15.7 = 10.3
✏️ Problem 11
15.3 − 8.46
Try it on your own!
📊
Three-Step Strategy
1
Estimate: Round first — 15 − 8 = about 7
2
Line Up & Subtract: Add a placeholder zero to 15.3:
15.30
− 8.46
───────
6.84
15.30
− 8.46
───────
6.84
3
Check: Is 6.84 close to our estimate of 7? Yes! ✓ Reasonable!
✓ Answer
15.3 − 8.46 = 6.84
✏️ Problem 12
32 − 17.85
Try it on your own!
📊
Three-Step Strategy
1
Estimate: Round first — 32 − 18 = about 14
2
Line Up & Subtract: Rewrite 32 as 32.00, then subtract:
32.00
−17.85
──────
14.15
32.00
−17.85
──────
14.15
3
Check: Is 14.15 close to our estimate of 14? Yes! ✓ Reasonable!
✓ Answer
32 − 17.85 = 14.15
✨ Mixed Operations: Read Carefully!
The steps are the same — the only thing that changes is the operation. Always read the sign!
Adding (+)
➕
Combine totals
vs.
Subtracting (−)
➖
Take away
✏️ Problem 13
7.3 + 4.26
Add the decimals
📊
Three-Step Strategy
1
Estimate: Round first — 7 + 4 = about 11
2
Line Up & Add: Add a placeholder zero to 7.3:
7.30
+ 4.26
───────
11.56
7.30
+ 4.26
───────
11.56
3
Check: Is 11.56 close to our estimate of 11? Yes! ✓ Reasonable!
✓ Answer
7.3 + 4.26 = 11.56
✏️ Problem 14
18.24 − 9.57
Subtract the decimals
📊
Three-Step Strategy
1
Estimate: Round first — 18 − 10 = about 8
2
Line Up & Subtract: Both numbers have 2 decimal places:
18.24
− 9.57
───────
8.67
18.24
− 9.57
───────
8.67
3
Check: Is 8.67 close to our estimate of 8? Yes! ✓ Reasonable!
✓ Answer
18.24 − 9.57 = 8.67
✏️ Problem 15
10.98 − 5.6
Subtract the decimals together
📊
Three-Step Strategy
1
Estimate: Round first — 11 − 6 = about 5
2
Line Up & Subtract: Add a placeholder zero to 5.6:
10.98
− 5.60
───────
5.38
10.98
− 5.60
───────
5.38
3
Check: Is 5.38 close to our estimate of 5? Yes! ✓ Reasonable!
✓ Answer
10.98 − 5.6 = 5.38
✏️ Problem 16
14.5 + 8.73
Add the decimals together
📊
Three-Step Strategy
1
Estimate: Round first — 15 + 9 = about 24
2
Line Up & Add: Add a placeholder zero to 14.5:
14.50
+ 8.73
───────
23.23
14.50
+ 8.73
───────
23.23
3
Check: Is 23.23 close to our estimate of 24? Yes! ✓ Reasonable!
✓ Answer
14.5 + 8.73 = 23.23
✏️ Problem 17
21.6 − 13.84
Try it on your own!
📊
Three-Step Strategy
1
Estimate: Round first — 22 − 14 = about 8
2
Line Up & Subtract: Add a placeholder zero to 21.6:
21.60
−13.84
───────
7.76
21.60
−13.84
───────
7.76
3
Check: Is 7.76 close to our estimate of 8? Yes! ✓ Reasonable!
✓ Answer
21.6 − 13.84 = 7.76
✏️ Problem 18
9.47 + 15.8
Try it on your own!
📊
Three-Step Strategy
1
Estimate: Round first — 9 + 16 = about 25
2
Line Up & Add: Add a placeholder zero to 15.8:
9.47
+15.80
───────
25.27
9.47
+15.80
───────
25.27
3
Check: Is 25.27 close to our estimate of 25? Yes! ✓ Reasonable!
✓ Answer
9.47 + 15.8 = 25.27
🏆 Challenge: Multi-Step!
Two-Step Problem
Maria has $50.00. She buys a notebook for $8.75 and a pen set for $12.50. How much money does she have left?
📊
Multi-Step Strategy
1
Find Total Cost: Add the two purchases together:
8.75
+12.50
───────
21.25Total cost: $21.25
8.75
+12.50
───────
21.25Total cost: $21.25
2
Find Money Left: Subtract the total cost from $50.00:
50.00
−21.25
───────
28.75Money left: $28.75
50.00
−21.25
───────
28.75Money left: $28.75
3
Check: Does this make sense? She spent about $21, and she had about $50, so about $29 is reasonable. ✓ Reasonable!
✓ Answer
Maria has $28.75 left
📝 Word Problem
Real-World Application
A recipe needs 2.75 cups of flour. Jake already added 1.8 cups. How much more flour does he need?
📊
Word Problem Strategy
1
Identify the Operation: We need to find how much MORE is needed, so we subtract: 2.75 − 1.8 = ?
2
Line Up & Subtract: Add a placeholder zero to 1.8:
2.75
−1.80
──────
0.95Jake needs 0.95 more cups of flour
2.75
−1.80
──────
0.95Jake needs 0.95 more cups of flour
✓ Answer
Jake needs 0.95 cups more flour
💬 Turn & Talk
Question 1: Why is it important to line up decimal points before adding or subtracting? What could go wrong if you don't?
Question 2: When do you need to add placeholder zeros? Give an example.
Talk with a partner for 2 minutes, then share with the class!
📝 Key Takeaways
📊
Estimate First
Always round and estimate before computing to check your answer
📏
Line Up Decimals
The most important step: line up the decimal points vertically
0️⃣
Placeholder Zeros
Add zeros so both numbers have the same number of decimal places
✅
Check Reasonableness
Compare your answer to your estimate. Does it make sense?
🎫 Exit Ticket
7.85 + 3.6 = ?
11.45
15.2 − 8.74 = ?
6.46
20 − 13.25 = ?
6.75
🎯 Great Work Today!
You did an amazing job!
You learned how to:
- Add decimals by lining up place values
- Subtract decimals using regrouping when needed
- Estimate sums and differences to check reasonableness
Remember:
Always line up your decimal points and add placeholder zeros before adding or subtracting!