Homeschool Math

Fractions Guide

How to Multiply Fractions

Step-by-Step Visual Guide

Multiplying fractions is actually the easiest fraction operation — no common denominator needed. Multiply the tops, multiply the bottoms, simplify. That's the whole method.

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The Rule:

Multiply numerator × numerator → new numerator

Multiply denominator × denominator → new denominator

Then simplify if possible. No common denominator needed — ever.

How to Multiply Fractions — Step by Step

Let's use ⅔ × ¾ as our example

⅔ × ¾ = ?
Start with the problem
⅔ × ¾

Multiplying fractions is simpler than adding them — no common denominator needed.

Step 1: Multiply the numerators
2 × 3 = 6
2 × 3 = 6 (top)

Multiply the top numbers together. This becomes the numerator of your answer.

Step 2: Multiply the denominators
3 × 4 = 12
3 × 4 = 12 (bottom)

Multiply the bottom numbers together. This becomes the denominator of your answer.

Step 3: Write the new fraction
6/12
6 / 12

Put the new numerator over the new denominator. Now check if you can simplify.

Step 4: Simplify if possible
6/12 = ½
6 ÷ 6 = 1 / 12 ÷ 6 = 2

Both 6 and 12 divide by 6. So 6/12 simplifies to ½.

⅔ × ¾ = ½ ✓
That's the answer
✅

Multiply tops, multiply bottoms, simplify. That's the whole method.

Why Multiplying Fractions Works This Way

"½ of ½" means you take half of something that is already half — which gives you a quarter. Fraction multiplication is always asking "what fraction of this fraction do I have?"

⅔ × ¾ means "two thirds OF three quarters"
= take ⅔ of ¾
= (2 × 3) / (3 × 4)
= 6/12
= ½ ✓

Try These Examples

Multiply across, then simplify — same method every time

½ × ½
1×1=1
2×2=4
= ¼ ✓
⅔ × ⅗
2×3=6
3×5=15
÷3 = ⅖
= ⅖ ✓
¾ × ⅔
3×2=6
4×3=12
÷6 = ½
= ½ ✓
⅘ × ½
4×1=4
5×2=10
÷2 = ⅖
= ⅖ ✓
⅓ × ¾
1×3=3
3×4=12
÷3 = ¼
= ¼ ✓
⅝ × ⅔
5×2=10
8×3=24
÷2 = 5/12
= 5/12 ✓

Common Mistakes (And How to Fix Them)

❌ Adding denominators instead of multiplying them
✓ When multiplying fractions, multiply BOTH the top and bottom. Never add the denominators — that's only needed when adding fractions.
❌ Forgetting to simplify the answer
✓ Always check if the numerator and denominator share a common factor. Divide both by the GCF to get the simplest form.
❌ Thinking you need a common denominator
✓ Common denominators are only needed for addition and subtraction. For multiplication, just multiply straight across.

Make sure you can simplify fractions confidently — it's the final step in most multiplication problems.

Number Sense Foundations

GRADES K–2

$57

Fraction operations make sense when children genuinely understand what a fraction represents — equal parts of a whole, part of a group, a point on a number line. This course builds that conceptual foundation in the early years so that multiplying and dividing fractions later on feels logical rather than like rules to memorise.

Get Number Sense Foundations on Gumroad →

More Math Tricks & Guides

What Is a Numerator?
Understand the top number first
What Is a Denominator?
Understand the bottom number
How to Simplify Fractions
Reducing fractions step by step
Fractions Worksheets
Practice what you learned

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