Wednesday, May 20 — Day 7
Today's new thing: fraction multiplication.
This one is easier than add and sub. No LCM needed. Promise.
The rule
For multiplying fractions, just:
- Multiply the tops. Numerator times numerator.
- Multiply the bottoms. Denominator times denominator.
- Reduce.
Worked example: 2/3 × 3/4
- Top: 2 × 3 = 6.
- Bottom: 3 × 4 = 12.
- 6/12 = 1/2.
That's it. No common denominator. No "rewrite each fraction".
Pro move: cancel before you multiply
You can cancel a top with a bottom before multiplying, to keep the numbers small. 3/4 × 4/9 — the 4 on top of the second cancels with the 4 on the bottom of the first → 3/1 × 1/9 = 3/9 = 1/3. Same answer either way; the canceling version just keeps you out of big-number territory.
You don't have to cancel early — it's fine to multiply first and reduce at the end. Pick whichever feels safer.
Today's deal
- Time. 9:00 → 12:30, 2×15-min breaks. 3 hours of work.
- One new thing. Fraction multiplication.
- New on the side. First half of row 3 of the periodic table — Na, Mg, Al, Si.
- Everything else is review. Add, sub, LCM, periodic rows 1-2, wars 9-12, dinosaurs, KT extinction.
Today's exam (22 questions)
- 2 LCM + 3 add + 3 sub + 3 mul (new)
- 4 periodic — 2 from new row-3 elements (Na, Mg, Al, Si) + 2 review
- 4 wars — wars 9-12 (Russian Civil, Spanish Civil, WWII, Korean)
- 3 evolution — first dinosaurs, KT extinction, plus a Cambrian review
Periodic — row 3 starts
The four new elements of the day:
| Z | Symbol | Element | Most common N | Electrons (neutral) |
|---|---|---|---|---|
| 11 | Na | Sodium | 12 | 11 |
| 12 | Mg | Magnesium | 12 | 12 |
| 13 | Al | Aluminum | 14 | 13 |
| 14 | Si | Silicon | 14 | 14 |
Pattern: protons go 11, 12, 13, 14 (just count along the row). Electrons of a neutral atom always equal protons. Neutrons jump around — memorize them.
Wars 9-12
| War | Year |
|---|---|
| Russian Civil | 1917 |
| Spanish Civil | 1936 |
| World War II | 1939 |
| Korean War | 1950 |
WWII (1939) and Spanish Civil (1936) are close — Spain came first.
Practice before the exam
Do 10 fraction multiplications before the exam. Mix easy ones (2/3 × 3/4) with cancel-friendly ones (3/8 × 4/9). Then drill the four new elements until you can rattle off Na/Mg/Al/Si without looking.