To multiply a whole number by a fraction:
1. Multiply the whole number × the numerator
2. Keep the denominator the same
3. Simplify or convert to a mixed number if needed
Example: 6 × 15 = 65 = 115
Whole Number × Fraction
Multiply a whole number by a fraction using models, repeated addition, and the algorithm
📚
Subject
Math
⏱️
Duration
50 min
🎯
Standard
5.NF.B.4a
📋 Standards & Objectives
📜Standards
5.NF.B.4aApply and extend previous understandings of multiplication to multiply a fraction by a whole number.
5.NF.B.5aInterpret multiplication as scaling — comparing the size of a product to the size of one factor.
5.NF.A.1Add and subtract fractions with unlike denominators (spiral review).
🎯SWBAT
- Multiply a whole number by a fraction using visual models (number line, area model, equal groups)
- Apply the algorithm: whole number × numerator ÷ denominator
- Predict whether a product will be greater or less than a factor when multiplying by a fraction
- Solve word problems involving whole number × fraction
📖 Key Vocabulary
📝Numerator
The top number in a fraction — it tells how many parts you have.
In 34, the numerator is 3 — you have 3 out of 4 equal parts.
When we multiply 6 × 15, we multiply 6 × the numerator (1) to get 65.
📝Denominator
The bottom number in a fraction — it tells how many equal parts the whole is divided into.
In 58, the denominator is 8 — the whole is split into 8 equal pieces.
When multiplying a whole number by a fraction, the denominator stays the same!
📝Improper Fraction
A fraction where the numerator is greater than or equal to the denominator. It equals 1 whole or more.
65 is an improper fraction because 6 > 5. It equals 115.
163 is an improper fraction — it means more than 5 wholes!
📝Mixed Number
A number made of a whole number and a fraction together.
115 is a mixed number — it has 1 whole and 15 left over.
513 is a mixed number. It's the same as the improper fraction 163.
📝Scaling
Using multiplication to make a number bigger or smaller. Multiplying by a fraction less than 1 scales down (makes smaller).
40 × 58 = 25. Scaling 40 by 58 made it smaller because 58 < 1.
When you scale a number by a fraction greater than 1, like 53, the product gets bigger.
🔄 Spiral Warm-Up
Fraction addition review (5.NF.A.1)
Find the sum:
23
+
14
=
?
23
+
14
LCD = 12
23 (×4 top & bottom)
= 812
14 (×3 top & bottom)
= 312
812
+
312
=
1112
🔄 Spiral Warm-Up
Fraction subtraction review (5.NF.A.1)
Find the difference:
56
−
13
=
?
56
−
13
LCD = 6
56 (already sixths!)
= 56 ✓
13 (×2 top & bottom)
= 26
56
−
26
=
36
=
12
🚀 You Already Know This!
Connecting whole numbers to fractions
Think about it…
You already know what 6 × 3 means — 6 groups of 3.
Today we'll see that 6 × 15 works the SAME way — 6 groups of 15.
The multiplication sign always means "groups of." That doesn't change when we use fractions!
🚀 Same Idea, Different Numbers
6 × 3 = 18
🍪3
🍪3
🍪3
🍪3
🍪3
🍪3
6 groups of 3 cookies = 18 cookies
6 × 15 = ?
🍕⅕
🍕⅕
🍕⅕
🍕⅕
🍕⅕
🍕⅕
6 groups of 15 of a pizza = ?
💡 Same structure — "groups of" — just with fractions now!
👨🏫 I Do: 6 × 15
Repeated addition on a number line
6
×
15
=
?
"6 groups of 15" = 15 + 15 + 15 + 15 + 15 + 15
Each hop = +15. We hop 6 times.
👨🏫 I Do: 6 × 15 — Solution
1
Multiply the whole number by the numerator: 6 × 1 = 6
2
Keep the denominator the same: 65
3
Convert improper fraction → mixed number: 65 = 115
6
×
15
=
65
=
115
📓 Write This Down
The rule for whole number × fraction
Key Words
Whole × Fraction
Numerator
Denominator
In Your Notebook
👨🏫 I Do: 8 × 23 — Area Model
8
×
23
Count the shaded parts: 8 groups × 2 shaded thirds = 16 thirds total → 163
👨🏫 I Do: 8 × 23 — Algorithm
Step-by-step reveal
1
Multiply whole number × numerator:
8
×
2
=
16
2
Put over the denominator:
163
3
Convert to a mixed number: 16 ÷ 3 = 5 remainder 1
163
=
513
8
×
23
=
163
=
513
✅ Quick Check
When we compute 8 × 23, the denominator …
A) Gets multiplied by 8 too
B) Stays the same
C) Disappears
👍 Hold up A, B, or C
B — The denominator stays the same! We only multiply the whole number × the numerator.
👨🏫 I Do: 40 × 58
Equal groups strategy
Think: "What is 58 of 40?"
1
Divide 40 into 8 equal groups: 40 ÷ 8 = 5 per group
2
Take 5 of those groups: 5 × 5 = 25
40
×
58
=
25
👨🏫 Scaling: Bigger or Smaller?
5.NF.B.5a — Multiplication as scaling
⚡ Key Rule
When you multiply a whole number by a fraction less than 1, the product is LESS than the whole number.
Look at our answer
40 × 58 = 25
25
product
<
40
factor
58 < 1, so the answer shrank!
Why?
Taking 58 of something means you're taking less than all of it.
It's like eating 5 out of 8 slices — you didn't eat the whole pizza!
👨🏫 The Shortcut
Whole number × numerator ÷ denominator
⚡ Shortcut Formula
Whole Number
×
numerator
÷
denominator
Example: 40 × 58
40 × 5 = 200
200 ÷ 8 = 25 ✓
Example: 6 × 15
6 × 1 = 6
6 ÷ 5 = 115 ✓
💡 This works every time — but understanding the model behind it is what matters most!
📓 Write This Down
Algorithm & shortcut
Key Words
Algorithm
Shortcut
Scaling
In Your Notebook
Algorithm: whole × numerator = new numerator, keep the denominator.
Shortcut: whole × numerator ÷ denominator
Scaling rule: Fraction < 1 → product < whole number. Fraction > 1 → product > whole number.
🔄 Bridge
✅ What We Learned
Multiply whole number × numerator, keep the denominator.
If the fraction < 1, the product is smaller than the whole number.
🔜 What's Next
Now you'll try some problems with me. Let's practice together!
👥 We Do: 4 × 34
Try it, then check!
4
×
34
=
?
Work it out on your whiteboard. Use any model you like!
4 × 3 = 12 → 124 = 3
12 shaded fourths = 3 wholes. Makes sense — ¾ of each of 4 wholes = 3!
👥 We Do: 12 × 23
Bar/tape diagram model
12
×
23
=
?
Try it! Then click to see the tape diagram.
12 ÷ 3 = 4 per group → 2 groups = 8
Algorithm check: 12 × 2 = 24, ÷ 3 = 8 ✓
💬 Turn & Talk
🤔Discuss with a Partner
Will 7 × 56 be more or less than 7?
How do you know WITHOUT computing?
Sentence starter: "I think 7 × 56 will be ___ than 7 because ___"
Less than 7! Since 56 < 1, we're taking part of 7, not all of it.
(Scaling down — the product shrinks when you multiply by a fraction less than 1.)
Check: 7 × 5 = 35, ÷ 6 = 556. Yep — 556 < 7 ✓
👥 We Do: Word Problem
Bridges Unit 5 Pre-Assessment
📝The Problem
In Teacher Zach's class, 35 of the 25 students are boys. How many boys are in the class?
Set up the expression, draw a model, then check your answer.
25 ÷ 5 = 5 per group → 3 groups = 15 boys
Algorithm: 25 × 3 = 75, ÷ 5 = 15 ✓
✅ Quick Check #2
Without solving, which is larger?
A) 20 × 34
or
B) 20
👍 Hold up A or B
B is larger! Since 34 < 1, multiplying 20 by it gives a product less than 20. (Scaling down!)
🔄 Bridge
✅ What We Practiced Together
Area models, tape diagrams, the algorithm, and scaling predictions.
🔜 Your Turn — Solo!
Try these 4 problems on your own. Use any strategy. Click to check when you're done!
🔍 You Try #1
5
×
13
=
?
Solve on your whiteboard. Show your work!
1
5 × 1 = 5
2
Keep denominator: 53
3
Convert: 5 ÷ 3 = 1 R2 → 123
🔍 You Try #2
9
×
25
=
?
Before you solve: will the answer be more or less than 9?
9 × 2 = 18 → 185 → 18 ÷ 5 = 3 R3
9
×
25
=
185
=
335
335 < 9 ✓ — scaling down because 25 < 1
🔍 You Try #3
24
×
38
=
?
Try both the algorithm AND the equal-groups strategy!
Algorithm
24 × 3 = 72
72 ÷ 8 = 9
Equal Groups
24 ÷ 8 = 3 per group
3 groups × 3 = 9
Both methods give 9. And 9 < 24 ✓ (scaling down!)
🔍 You Try #4: Word Problem
📝The Problem
A recipe calls for 34 cup of sugar. If you make 6 batches, how many cups of sugar do you need?
Your Turn
- Write the expression.
- Solve using the algorithm or a model.
- Convert to a mixed number if needed.
- Write your answer as a complete sentence.
6 × 34 = 184 = 424 = 412 cups
You need 412 cups of sugar to make 6 batches.
📝 Three Strategies for Whole × Fraction
Your toolkit — pick the one that fits!
🔢Algorithm
Rule: Whole × numerator, keep the denominator
Works every time!
8 × 23 → 163 = 513
📊Equal Groups
Rule: Divide whole by denom, multiply by numer
Best when whole ÷ denom is clean
40 × 58 → 40÷8=5, ×5=25
📐Visual Model
Rule: Draw it — number line, area, or tape diagram
Best for understanding WHY
6 × 15 → 6 hops on a number line
📓 Summary Note
Write 1 Sentence
In the bottom of your notebook page, write one sentence explaining what you learned today about multiplying whole numbers by fractions.
Sentence starter: "Today I learned that when you multiply a whole number by a fraction…"
🎫 Exit Ticket
Show what you know — 4 questions!
1️⃣Compute
10 × 35 = ?
Show your work!
10 × 3 = 30, ÷ 5 = 6
2️⃣Compute
8 × 34 = ?
Show your work!
8 × 3 = 24, ÷ 4 = 6
3️⃣Word Problem
30 students on the playground. 25 are playing basketball. How many?
30 × 25 = 605 = 12 students
4️⃣🔄 Spiral Review
34 + 56 = ?
Unlike denominators!
912 + 1012 = 1912 = 1712