🧱 See It
Recall multiplying fractions — numerator × numerator, denominator × denominator — and dividing fractions by flipping and multiplying. Recall also the same-sign/different-sign rule from integers. Those two rules combine directly here: figure out the sign, then multiply or divide as usual. A decimal can always be converted to a fraction first if that makes the multiplication easier.
✏️ Draw It
Convert a decimal to a fraction before multiplying, if that helps:
| Decimal | As a fraction |
|---|---|
0.6 | 3/5 |
0.6 means "6 tenths," which simplifies to 3/5.
🔢 Write It
−2/3 × 0.6 = −2/3 × 3/5 = −6/15 = −2/5
(6/15 simplifies using GCF(6, 15) = 3: divide top and bottom by 3.)
Unlike adding or subtracting, multiplying and dividing rational numbers need NO common denominator — same rule as Level 3's fraction multiplication, just with a sign to track now.
💡 Worked Examples
Example 1: −1/2 × −4/5
- Same signs (both negative) → answer is positive
- Multiply straight across:
1/2 × 4/5 = 4/10 - Simplify using
GCF(4, 10) = 2:4/10 = 2/5 - Answer:
2/5
Example 2: −0.8 ÷ 0.2
- Different signs (negative, positive) → answer is negative
- Divide the magnitudes:
0.8 ÷ 0.2 = 4 - Answer:
−4
🧠 Quick Reference
Multiplying/dividing rational numbers: figure out the sign first (same signs → positive, different signs → negative), then do the arithmetic — no common denominator needed, unlike adding or subtracting.