Two Types of Division: Whole ÷ Unit Fraction · Unit Fraction ÷ Whole
A fraction with a numerator of 1 — it represents one equal part of a whole.
The number being divided — it's the amount you start with.
The number you are dividing by — the size of each group OR the number of groups.
Operations that undo each other. Multiplication and division are inverse operations.
The Pizza Question 🍕
You have 5 whole pizzas. You're going to cut each pizza into 14-sized slices.
👉 How many slices will you have in total?
This is a division problem!
We're asking: 5 ÷ 14 = ?
👁️ By the end of today, you'll solve this in your head!
Question: How many 14-pieces fit in 5?
Answer gets BIGGER ⬆️
Question: Cut 14 into 5 equal pieces — how big is each?
Answer gets SMALLER ⬇️
💡 Same numbers, different answers — the ORDER matters!
Before you calculate, ask yourself: "Should my answer be bigger or smaller than the dividend?"
⬆️ BIGGER
If the divisor is a unit fraction (less than 1)
"I'm cutting something into tiny pieces — there will be MORE of them."
⬇️ SMALLER
If the divisor is a whole number (bigger than 1)
"I'm splitting a tiny piece even more — each part is TINIER."
🎯 This single habit will catch MOST of your mistakes.
Question to ask: "How many 13-sized pieces fit in 4 wholes?"
4 wholes × 3 pieces-per-whole = 12 pieces
4 whole rectangles
Each cut into 3 equal pieces
12 pieces total ✓
Multiply 4 × 3
(the whole number × the denominator)
= 12 ✓
🔑 Pattern: whole ÷ ¹⁄denominator = whole × denominator
Question: "How many 12-pieces fit in 3 wholes?"
3 wholes × 2 halves-each = 6 halves
3 ÷ 12 = 6 ✓ (bigger than 3 — as predicted!)
Story: Mrs. Minnerly has 2 granola bars. She cuts each into 15-size pieces. How many pieces total?
2 × 5 = 10 pieces
2 ÷ 15 = 10 ✓
4 ÷ 13 = 12
4 × 3 = 12
3 ÷ 12 = 6
3 × 2 = 6
2 ÷ 15 = 10
2 × 5 = 10
🤯 Lightbulb Moment!
Dividing by ¹⁄ₙ is the SAME as multiplying by n.
Because multiplication and division are inverse operations!
Whole ÷ Unit Fraction
1 Keep the whole number
2 Change ÷ to ×
3 FLIP the unit fraction → becomes n
💬 "Keep · Change · Flip" — remember those 3 words!
6 ÷ 15 = 30
🧠 Predict: Will 7 ÷ 16 be bigger or smaller than 7?
BIGGER — dividing by 16 gives more pieces.
🧮 Solve: Apply Keep · Change · Flip
7 × 6 = 42
💡 Real-world: Mrs. Minnerly has 7 cups of sugar. Each cookie needs 16 cup. How many cookies? 42!
Why does 6 ÷ 12 = 12?
You divided — but the answer got bigger! Weird, right? Explain to your partner WHY it works using a real-world situation (pizzas, granola bars, pancakes, apples — you pick!).
Sentence starter: "Dividing 6 by 12 is like asking ___. We get 12 because ___."
A chef has 8 pounds of cheese. She uses 14 pound on each pizza. How many pizzas can she make?
Ⓐ 2 pizzas Ⓑ 4 pizzas Ⓒ 12 pizzas Ⓓ 32 pizzas
✓ Correct: Ⓓ 32 pizzas. 8 ÷ 14 = 8 × 4 = 32.
❌ Trap Ⓐ (2): Students who did 8 ÷ 4 instead of 8 ÷ 14.
❌ Trap Ⓑ (4): Students who confused this with multiplication: 8 × 12 = 4.
🔑 SBA LOVES this question type. Always predict the size first!
Answer gets bigger ⬆️
Answer gets smaller ⬇️
The question changes: Now we're asking "If I split this unit fraction into __ equal pieces, how big is each piece?"
Story: Mrs. Minnerly has half a pizza left. She wants to share it equally among 3 students. How much does each student get?
Each student gets 16 of a pizza.
12 pizza split among 3 people
Each piece = 16 of a pizza
🔑 Pattern: ¹⁄a ÷ b = ¹⁄a × ¹⁄b = ¹⁄(a × b)
To divide by a whole number, multiply by its reciprocal (flip to ¹⁄whole).
Story: 13 of a kiwi is left. We split it among 4 friends. Each friend gets… how much?
13 ÷ 4 = 112
Story: Only 14 of a cupcake is left. Two kids want to split it fairly.
🧠 Predict: Bigger or smaller than 14?
SMALLER — we're splitting a small piece in half.
🧮 Solve: Keep · Change · Flip the whole
14 × 12 = 18
Each kid gets 18 of the cupcake 🧁
6 ÷ 12 = 6 × 2 = 12
"How many 12-pieces fit in 6?" → More pieces = BIGGER answer
12 ÷ 6 = 12 × 16 = 112
"Split 12 into 6 equal parts" → Tinier pieces = SMALLER answer
💡 Click the buttons to highlight the dividend and divisor in each problem
Problem: Solve 15 ÷ 2
Student wrote: 15 ÷ 2 = 15 × 2 = 25
🧠 Think: What mistake did the student make?
They didn't flip the whole number. When you do "Keep · Change · Flip," you have to flip the divisor. Dividing by 2 means multiplying by 12, not by 2.
✅ Correct Work:
15 ÷ 2 = 15 × 12 = 110
And 110 is smaller than 15 ✓ (makes sense!)
A painter has 14 of a gallon of paint. She needs to pour it equally into 3 small cups. How much paint is in each cup?
Ⓐ 34 gallon Ⓑ 12 gallons Ⓒ 112 gallon Ⓓ 17 gallon
✓ Correct: Ⓒ 112 gallon. 14 ÷ 3 = 14 × 13 = 112
❌ Trap Ⓑ (12): Students who got the TYPE wrong — they did 3 ÷ 14 = 12.
❌ Trap Ⓓ (17): Students who ADDED the denominators (4 + 3) instead of multiplying.
🎯 Ask yourself: "Am I dividing a whole by a fraction, or a fraction by a whole?"
① Whole ÷ Unit Fraction
Example: 5 ÷ 14 = 20
BIGGER ⬆️
② Unit Fraction ÷ Whole
Example: 15 ÷ 4 = 120
SMALLER ⬇️
🔑 Both rules use Keep · Change · Flip — you always flip the divisor (the second number).
8 ÷ 13 = ?
Type ①: 8 × 3 = 24
14 ÷ 3 = ?
Type ②: 14 × 13 = 112
9 ÷ 12 = ?
Type ①: 9 × 2 = 18
16 ÷ 2 = ?
Type ②: 16 × 12 = 112
🕵️ Detective steps:
💡 Look for clue words like "each", "how many ___ fit in", "split equally".
The Problem:
Mrs. Minnerly has 4 birthday cakes for the class. She wants to cut each cake so every student gets a 18-sized slice. How many slices can she make in total?
Step 1: Which type?
Starting with 4 wholes, dividing into 18-pieces → Type ①
Answer will get BIGGER.
Step 2: Solve!
4 ÷ 18 = 4 × 8 = 32 slices
The Problem:
A squirrel has 12 pound of acorns. He wants to pack them equally into 5 little bags to hide for winter. How many pounds of acorns go in each bag?
Step 1: Which type?
Starting with 12 (unit fraction), splitting into 5 equal groups → Type ②
Answer will get SMALLER.
Step 2: Solve!
12 ÷ 5 = 12 × 15 = 110 pound
Each bag: 110 pound of acorns 🌰
The Problem:
Grandma baked 6 pumpkin pies. She's cutting them into 16-sized slices for the Thanksgiving family reunion. How many slices will there be?
Think before you solve:
• What are we starting with?
• What are we dividing by?
• Bigger or smaller?
Your Answer:
Type ①: 6 ÷ 16 = 6 × 6 = 36 slices
That's a LOT of pie! 🥧
① Whole ÷ Unit Fraction = Whole × denominator
Example: 4 ÷ 13 = 4 × 3 = 12 (bigger ⬆️)
Ask: "How many ¹⁄ₙ-pieces fit in the whole?"
② Unit Fraction ÷ Whole = Unit Fraction × ¹⁄whole
Example: 12 ÷ 4 = 12 × 14 = 18 (smaller ⬇️)
Ask: "Split the unit fraction into how many equal pieces?"
🔑 Big Idea: Always Keep · Change · Flip — flip the divisor (2nd number). Predict bigger or smaller BEFORE solving!
5 ÷ 14 = ?
Show your work!
5 ÷ 14 = 5 × 4 = 20
(How many 14-pieces fit in 5? Twenty.)
13 ÷ 5 = ?
Show your work!
13 ÷ 5 = 13 × 15 = 115
(Split 13 into 5 equal pieces — each is 115.)
Mr. Minnerly has 3 yards of ribbon. He cuts it into pieces that are each 16 of a yard long. How many ribbon pieces does he have?
3 ÷ 16 = 3 × 6 = 18 pieces
Multiply: 23 × 45 = ?
(From 5.NF.B.4 — multiplying fractions)
23 × 45 = (2×4)/(3×5) = 815
✅ You Can Now:
• Divide a whole by a unit fraction
• Divide a unit fraction by a whole
• Use "Keep · Change · Flip"
• Solve real-world word problems!
🧠 Remember:
Before solving, PREDICT the size!
Bigger (÷ unit fraction) or smaller (÷ whole number)?
This one habit catches most mistakes.
🌟 Next up: Homework practice — you've got this!