Step 1: Place the decimal point in the quotient straight above the decimal in the dividend.
Step 2: Divide digit by digit, just like whole numbers.
Step 3: Bring down the next digit after each subtraction.
Step 4: Keep going until the remainder is 0.
Dividing Decimals
Using Models, Algorithms & Real-World Problems
📚
Subject
Math
⏱️
Duration
45 min
🎯
Standard
5.NBT.B.7
📋 Standards & Objectives
📜Standards
5.NBT.B.7Add, subtract, multiply, and divide decimals to hundredths.
5.NBT.A.1Recognize that in a multi-digit number, a digit in one place represents 10× as much as the place to its right and 1/10 of the place to its left.
🎯SWBAT
- Divide decimals by whole numbers using the standard algorithm
- Divide decimals by whole numbers when there is a remainder (add zeros)
- Divide decimals by decimal divisors by making the divisor a whole number
- Solve real-world word problems involving dividing decimals
📖 Key Vocabulary
📝Dividend
The number being divided — the total you are splitting into equal groups.
In 9.36 ÷ 4, the dividend is 9.36 — it’s the number inside the division bracket.
If you split $7.50 evenly among 3 friends, the dividend is $7.50.
📝Divisor
The number you divide by — how many equal groups you’re making.
In 9.36 ÷ 4, the divisor is 4 — you’re splitting into 4 groups.
When the divisor is a decimal like 0.5, you’ll need to make it a whole number first!
📝Quotient
The answer to a division problem — how much is in each group.
In 9.36 ÷ 4 = 2.34, the quotient is 2.34.
The quotient goes on top of the division bracket, right above the dividend.
📝Placeholder Zero
A zero added to the end of a decimal so you can keep dividing when there’s a remainder.
7.23 ÷ 5 — after you get past 7.23, you add a zero to make it 7.230 and keep going. That extra 0 is a placeholder zero.
Adding a placeholder zero doesn’t change the value — 7.23 = 7.230 — it just lets you finish dividing.
🚀 The Big Question
🍕 Pizza Party Problem
You and 3 friends order a pizza that costs $12.84. You split the bill equally. How much does each person pay?
You already know how to divide whole numbers. Today, we’ll learn how dividing decimals works the same way — with one extra step: placing the decimal point.
💬 Turn & Talk
🤔Discuss with a Partner
When you divide $12.84 ÷ 4, where do you think the decimal point goes in your answer? Why?
Sentence starter: "I think the decimal goes ___ because ___"
⭐ The #1 Rule for Dividing Decimals
Bring the decimal straight up!
Before you start dividing, place the decimal point in the quotient directly above where it sits in the dividend. Then divide normally — just like whole numbers.
_.__
49.36
The decimal in the answer lines up with the decimal in 9.36 ↑
👨🏫 I Do: 9.36 ÷ 4
Watch me solve this step by step
Let’s divide a decimal by a whole number. Follow along — don’t write yet!
Step 1: Place the decimal
Write the decimal point in the quotient directly above where it appears in the dividend.
_.__
49.36
👨🏫 I Do: 9.36 ÷ 4 — Solve
2.34
49.36
1
9 ÷ 4 = 2 r 1
Write 2 above the 9. Subtract: 9 − 8 = 1.
2
Bring down 3 → 13 ÷ 4 = 3 r 1
Write 3 above the 3. Subtract: 13 − 12 = 1.
3
Bring down 6 → 16 ÷ 4 = 4 r 0
Write 4 above the 6. Remainder is 0 — done! ✅
The quotient is 2.34
📓 Write This Down
Write this in your notebook!
Key Words
Decimal Up
Divide
Bring Down
Dividing Decimals by Whole Numbers
👨🏫 I Do: 303.5 ÷ 5
A bigger number — same process!
60.7
5303.5
1
30 ÷ 5 = 6 r 0
Write 6. Subtract: 30 − 30 = 0.
2
Bring down 3 → 3 ÷ 5 = 0 r 3
Write 0 — don’t skip it! Then bring down 5.
3
35 ÷ 5 = 7 r 0 ✅
Write 7. Done! Quotient = 60.7
⚠️ Don’t forget the zero! When a digit of the dividend is too small to divide, write 0 in the quotient.
✅ Quick Check
True or False?
When dividing a decimal by a whole number, the decimal in the quotient goes in a different place than in the dividend.
FALSE! The decimal goes straight up — directly above where it is in the dividend.
🔄 What’s Next?
✅ What we learned: Place the decimal straight up, then divide normally.
🚨 But what happens when there’s a remainder? You can’t write a remainder with a decimal answer. Instead, you add placeholder zeros and keep dividing!
👨🏫 I Do: 7.23 ÷ 5 (with remainder)
This one doesn’t come out evenly. Watch what happens when we get a remainder.
1.446
57.230
1
7 ÷ 5 = 1 r 2
Write 1. Bring down 2 → 22.
2
22 ÷ 5 = 4 r 2
Write 4. Bring down 3 → 23.
3
23 ÷ 5 = 4 r 3
Still a remainder! Add a placeholder zero. 30 ÷ 5 = 6. Done!
🌟 Quotient = 1.446
📓 Write This Down
Write this in your notebook!
Key Word
Placeholder Zero
When There’s a Remainder
A decimal answer cannot have a remainder.
If you still have a remainder after dividing all digits, add a zero to the end of the dividend and keep dividing.
Adding zeros doesn’t change the value: 7.23 = 7.230 = 7.2300
Keep adding zeros until the remainder is 0!
If you still have a remainder after dividing all digits, add a zero to the end of the dividend and keep dividing.
Adding zeros doesn’t change the value: 7.23 = 7.230 = 7.2300
Keep adding zeros until the remainder is 0!
💬 Turn & Talk
🤔Discuss with a Partner
Why can’t a decimal answer have a remainder? Think about money — if you split $7.23 among 5 people, does a “remainder of 3” make sense?
Sentence starter: "A remainder doesn’t make sense because ___"
🔄 Level Up!
✅ So far: We can divide decimals by whole numbers and handle remainders with placeholder zeros.
🚀 New challenge: What if the divisor is also a decimal? Like 17.64 ÷ 1.4?
You cannot divide by a decimal directly. First, you must turn the divisor into a whole number.
⭐ The Rule for Decimal Divisors
Multiply both numbers by the same power of 10!
Move the decimal in the divisor to make it a whole number. Then move the decimal in the dividend the same number of places.
1 decimal place
17.64 ÷ 1.4
× 10 → × 10
176.4 ÷ 14
2 decimal places
3.752 ÷ 0.05
× 100 → × 100
375.2 ÷ 5
👨🏫 I Do: 17.64 ÷ 1.4
Step 1: Make the divisor a whole number. 1.4 × 10 = 14. Also 17.64 × 10 = 176.4.
12.6
14176.4
1
17 ÷ 14 = 1 r 3
Write 1. Bring down 6 → 36.
2
36 ÷ 14 = 2 r 8
Write 2. Bring down 4 → 84.
3
84 ÷ 14 = 6 r 0 ✅
Write 6. Remainder 0 — done! Quotient = 12.6
📓 Write This Down
Write this in your notebook!
Key Words
Decimal Divisor
Power of 10
Dividing by a Decimal
You can’t divide by a decimal. First, make the divisor a whole number:
• Count the decimal places in the divisor
• Multiply BOTH the divisor and dividend by that power of 10
• 1 decimal place → × 10
• 2 decimal places → × 100
Then divide normally!
• Count the decimal places in the divisor
• Multiply BOTH the divisor and dividend by that power of 10
• 1 decimal place → × 10
• 2 decimal places → × 100
Then divide normally!
✅ Quick Check
Rewrite with a whole number divisor:
5.6 ÷ 0.8 = ?
Multiply both by 10: 56 ÷ 8 = 7
🔄 Your Turn to Help!
✅ What we covered: Dividing by whole numbers, handling remainders, and converting decimal divisors.
👥 Now let’s solve some together! I’ll start, you help me finish.
👥 We Do: 15.75 ÷ 3
Decimal ÷ whole number
15.75 ÷ 3 = ?
🧠Think About It
Where does the decimal go first? What is 15 ÷ 3?
🎯Answer
15 ÷ 3 = 5 | 7 ÷ 3 = 2 r 1 | 15 ÷ 3 = 5
Quotient = 5.25
👥 We Do: 42.6 ÷ 8
This one has a remainder — what do we do?
42.6 ÷ 8 = ?
💡Hint
After you bring down the 6, you’ll have a remainder. What should you do?
Remember: add a placeholder zero!
🎯Answer
42 ÷ 8 = 5 r 2 | 26 ÷ 8 = 3 r 2 | Add zero: 20 ÷ 8 = 2 r 4 | 40 ÷ 8 = 5
Quotient = 5.325
👥 We Do: 9.66 ÷ 0.3
Decimal divisor — what’s our first step?
9.66 ÷ 0.3 = ?
💡Step 1: Convert
Multiply both by 10:
0.3 × 10 = 3 and 9.66 × 10 = 96.6
Now solve: 96.6 ÷ 3
🎯Answer
96.6 ÷ 3: 9 ÷ 3 = 3 | 6 ÷ 3 = 2 | 6 ÷ 3 = 2
Quotient = 32.2
💬 Turn & Talk
🤔Discuss with a Partner
Which type of dividing decimals problem do you find the trickiest — regular division, remainders, or decimal divisors? Why?
Sentence starter: "I think ___ is trickiest because ___"
📓 Quick Review
Make sure this is in your notebook!
3 Types
Whole # Divisor
Remainders
Decimal Divisor
What to Remember
Type 1 — Whole number divisor: Decimal straight up, divide normally.
Type 2 — Remainder: Add placeholder zeros, keep dividing until remainder = 0.
Type 3 — Decimal divisor: Multiply both numbers by a power of 10 to make the divisor whole, then divide.
Type 2 — Remainder: Add placeholder zeros, keep dividing until remainder = 0.
Type 3 — Decimal divisor: Multiply both numbers by a power of 10 to make the divisor whole, then divide.
🔍 You Try #1
Solve on your whiteboard
23.52 ÷ 6 = ?
Steps
- Place the decimal straight up
- Divide digit by digit
- Show your answer on your whiteboard
3.92
🔍 You Try #2
This one needs placeholder zeros!
31.5 ÷ 4 = ?
Steps
- Place the decimal straight up
- Divide — if you get a remainder, add a zero and keep going
- Show your answer on your whiteboard
7.875
🔍 You Try #3
Decimal divisor — convert first!
6.84 ÷ 0.4 = ?
Steps
- Multiply both by 10 to get a whole number divisor
- Now divide 68.4 ÷ 4
- Show your answer on your whiteboard
17.1
🌍 Word Problem
Use what you’ve learned!
🚌 A school bus driver drove the same number of miles each day for 6 days. If the bus driver drove 148.38 miles total, how many miles were driven each day?
Solve
- Identify the dividend and divisor
- Set up the long division: 148.38 ÷ 6
- Place decimal, divide, find the quotient
- Write a sentence answering the question
148.38 ÷ 6 = 24.73 miles per day
🌍 Word Problem Challenge
🥕 A farmer has 9.36 pounds of carrots to pack equally into bags that hold 0.6 pounds each. How many bags can the farmer fill?
💡Think First
This has a decimal divisor. What’s your first step?
Convert: 9.36 ÷ 0.6 → 93.6 ÷ 6 = 15.6 bags
The farmer can fill 15 full bags with some carrots left over.
📝 Summary: 3 Ways to Divide Decimals
1️⃣Whole Number Divisor
Decimal straight up → divide normally
Ex: 9.36 ÷ 4 = 2.34
2️⃣With Remainders
Add placeholder zeros, keep dividing
Ex: 7.23 ÷ 5 = 1.446
3️⃣Decimal Divisor
Multiply both by power of 10 first
Ex: 17.64 ÷ 1.4 → 176.4 ÷ 14 = 12.6
📓 Summary Note
Write 1 Sentence
In the bottom of your notebook page, write one sentence explaining what you learned today about dividing decimals. Try to use at least TWO vocabulary words (dividend, divisor, quotient, or placeholder zero).
🍕 Let’s Solve the Pizza Problem!
Remember? You and 3 friends split a $12.84 pizza bill equally.
$12.84 ÷ 4 = ?
Each person pays $3.21
12 ÷ 4 = 3 | 8 ÷ 4 = 2 | 4 ÷ 4 = 1
🎫 Exit Ticket
Show what you know!
1️⃣Whole Number Divisor
45.36 ÷ 8
5.67
2️⃣With Remainder
9.7 ÷ 4
2.425
3️⃣Decimal Divisor
7.56 ÷ 0.9
Convert: 75.6 ÷ 9 = 8.4