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Multiply a fraction by a whole number
Learn step-by-step with practice exercises built right in.
Multiplying a fraction by a whole number means adding that fraction multiple times.
Example: 3 × 1/4 means "1/4 + 1/4 + 1/4"
Think of it as: "I want 3 groups of 1/4"
Problem: 4 × 1/5
Picture it as adding: 1/5 + 1/5 + 1/5 + 1/5 = 4/5
[■][□][□][□][□] ← 1/5
[■][□][□][□][□] ← 1/5
[■][□][□][□][□] ← 1/5
[■][□][□][□][□] ← 1/5
─────────────
[■][■][■][■][□] = 4/5 total
Answer: 4 × 1/5 = 4/5 ✓
Rule: Multiply the whole number by the numerator (top number)
Steps:
Example: 5 × 2/3
Multiply: 5 × 2 = 10 Keep denominator: 3 Write answer: 10/3 = 3 1/3
Multiply: 3 × 1/4 = ?
Think: "3 groups of 1/4"
Method 1: Add it 1/4 + 1/4 + 1/4 = 3/4
Method 2: Multiply numerator 3 × 1/4 = (3 × 1)/4 = 3/4
Answer: 3/4 ✓
Imagine: 3 quarter slices of pizza = 3/4 of a pizza!
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Answer: 5 × 2/3 = 10/3 = 3 1/3 ✓
Example 1: 3 × 1/4
Example 2: 6 × 2/5
Example 3: 4 × 3/8
Another way to think about it:
Any whole number can be written as a fraction with denominator 1.
Then multiply numerators and denominators:
Example: 4 × 2/3
(Same answer, different method!)
Recipes: You're making 3 batches of cookies. Each batch needs 2/3 cup of sugar.
Running: You run 3/4 mile each day for 5 days.
Ribbon: You need 4 pieces of ribbon, each 5/8 yard long.
When numerator > denominator:
Example: 7 × 3/4 = 21/4
Convert to mixed number:
Answer: 21/4 = 5 1/4 ✓
Problem: 3 × 2/5
Visual:
Row 1: [■■][□□□] ← 2/5
Row 2: [■■][□□□] ← 2/5
Row 3: [■■][□□□] ← 2/5
────
Total: 6 shaded out of 15 parts
But we're counting fifths!
3 groups of 2/5 = 6/5
Answer: 3 × 2/5 = 6/5 = 1 1/5 ✓
Adding 1/3 four times:
0 ―――⅓―――⅔―――1―――1⅓―――
↑ ↑ ↑ ↑
1st 2nd 3rd 4th
4 × 1/3 = 4/3 = 1 1/3 ✓
Always check if you can simplify:
Example: 6 × 2/4
Or simplify before multiplying:
Pattern to notice:
As the whole number gets bigger, the answer gets bigger!
Commutative property works with fractions:
Same answer either way! ✓
Before solving:
After solving:
❌ Multiplying the denominator too
❌ Forgetting to simplify
❌ Not converting improper fractions
✅ Only multiply the numerator ✅ The denominator stays the same ✅ Always simplify ✅ Convert improper fractions to mixed numbers
Multiplying by small numbers:
Times 2: Double the numerator
Times 3: Triple the numerator
Times 4: Quadruple the numerator
Problem 1: Each person gets 3/4 cup of juice. How much juice for 5 people?
Problem 2: A recipe calls for 2/3 teaspoon of vanilla. You're making 6 batches.
Problem 3: Each book is 5/8 inch thick. How tall is a stack of 8 books?
Method 1: Use repeated addition
Method 2: Draw a picture
Method 3: Does it make sense?
✅ Whole number × numerator ✅ Denominator stays the same ✅ Simplify when possible ✅ Convert improper fractions to mixed numbers ✅ Think of it as repeated addition
Remember: Multiplying by a whole number makes the fraction bigger (you're adding it that many times)!
Multiply: 2/5 × 4 = ?
Multiply the numerator by the whole number:
2/5 × 4 = (2 × 4)/5 = 8/5
This is an improper fraction!
Convert to mixed number: 8 ÷ 5 = 1 R3 8/5 = 1 3/5
Answer: 1 3/5 ✓
Or as improper fraction: 8/5 ✓
A recipe calls for 2/3 cup of sugar. If you make the recipe 5 times, how much sugar do you need?
Multiply: 5 × 2/3
5 × 2/3 = (5 × 2)/3 = 10/3
Convert to mixed number: 10 ÷ 3 = 3 R1 10/3 = 3 1/3
Answer: 3 1/3 cups of sugar ✓
You need 3 full cups plus 1/3 cup more!
Multiply and simplify: 6 × 3/8 = ?
Step 1: Multiply 6 × 3/8 = (6 × 3)/8 = 18/8
Step 2: Simplify (both divisible by 2) 18/8 = 9/4
Step 3: Convert to mixed number 9 ÷ 4 = 2 R1 9/4 = 2 1/4
Answer: 2 1/4 ✓
Or as improper fraction: 9/4 ✓
Multiply: 4/7 × 3 = ? Then find what fraction this is of a whole.
Step 1: Multiply 4/7 × 3 = (4 × 3)/7 = 12/7
Step 2: Convert to mixed number 12 ÷ 7 = 1 R5 12/7 = 1 5/7
Answer: 1 5/7 ✓
This means: