Fractions – Multiplying & Dividing

Why This Matters for Nursing: Drug calculations often require multiplying fractions. "Give ½ of a ¾ mg dose" means ½ × ¾ = ⅜ mg. Dividing fractions helps when splitting doses among patients or time intervals.

What You Need to Know

Great news: Multiplying and dividing fractions is actually EASIER than adding them—no common denominators needed!

Multiplication Rule

Multiply straight across: top × top, bottom × bottom

2/3 × 4/5 = (2×4)/(3×5) = 8/15

Division Rule

Keep, Change, Flip (KCF): Keep the first fraction, Change ÷ to ×, Flip the second fraction

2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6

🧠 Memory Trick

For division, remember "KCF" — Keep, Change, Flip

Or think: "Dividing by a fraction? Multiply by its flip!"

Some people say "invert and multiply" — same thing!

Step-by-Step: Multiplication

Multiply: 2/3 × 3/4

1. Multiply numerators: 2 × 3 = 6
2. Multiply denominators: 3 × 4 = 12
3. Write the result: 6/12
4. Simplify: 6/12 = 1/2

Pro Move: Cross-Cancel First

Before multiplying, you can simplify diagonally to make numbers smaller:

2/3 × 3/4 → The 3s cancel! → 2/1 × 1/4 = 2/4 = 1/2

Step-by-Step: Division

Divide: 3/4 ÷ 1/2

1. Keep the first fraction: 3/4
2. Change ÷ to ×
3. Flip the second fraction: 1/2 becomes 2/1
4. Multiply: 3/4 × 2/1 = 6/4
5. Simplify: 6/4 = 3/2 = 1 1/2

✏️ Worked Examples

Example 1: Simple Multiplication

Problem: 1/2 × 4/5

Step 1 — Multiply the top numbers (numerators) together. 1 × 4 = 4. That's your new top number.

Step 2 — Multiply the bottom numbers (denominators) together. 2 × 5 = 10. That's your new bottom number.

Step 3 — Write the result. 4/10.

Step 4 — Simplify. Both 4 and 10 are divisible by 2: 4÷2 = 2, 10÷2 = 5.

Answer: 2/5