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Tuesday, May 19 — Day 6

Today's new thing: fraction subtraction.

What sub actually is

Subtraction uses the exact same rule as addition. There is no new technique to learn. The only difference is one symbol.

  1. Find a common denominator. (LCM, just like add.)
  2. Rewrite both fractions over it.
  3. Subtract the tops. Keep the bottom. Reduce.

Worked example: 3/4 − 1/6

  1. LCM(4, 6) = 12.
  2. 3/4 = 9/12. 1/6 = 2/12.
  3. 9 − 2 = 7. Answer: 7/12.

Same-denominator case: 3/5 − 1/5 = 2/5. Just subtract the tops.

If the second fraction is bigger than the first, the answer is negative — the minus sign goes on the numerator: 1/4 − 3/4 = −2/4 = −1/2. Today's exam keeps the answer positive in every problem so you don't have to worry about sign yet — we'll get to that another day.

Today's deal

  • Time. 9:00 → 12:30 with two 15-min breaks. 3 hours of work.
  • One new thing. Fraction subtraction.
  • Everything else is review. GCF, LCM, fraction addition, periodic rows 1-2, wars 5-8, plus three new evolution events.

Today's exam (22 questions)

  • 2 GCF + 3 LCM + 3 add review + 3 sub (new)
  • 4 periodic — rows 1-2
  • 4 wars — wars 5-8 (Franco-Prussian, Spanish-American, Russo-Japanese, WWI)
  • 3 evolution — Cambrian, first fish, first land plants

LCM — the move that matters most

Last week you mixed up LCM (least common multiple) and GCF (greatest common factor). One trick that always works:

  • GCF answer is small — it divides into both numbers, so it can't be bigger than either.
  • LCM answer is large — it's a multiple of both, so it can't be smaller than either.

If you find an "LCM" that's smaller than one of the inputs, that's a red flag — go back. (On Day 13 you wrote 5 as LCM(10, 15). 5 is smaller than both, so it can't be a multiple of either. The answer was 30.)

Practice before the exam

Do at least 15 subtractions on /fractions before the exam. Then 5 LCM problems on paper. That's the warm-up.

Help links

A note on the new wars

Five through eight are all in the late 1800s / early 1900s:

  • Franco-Prussian War — 1870
  • Spanish-American War — 1898
  • Russo-Japanese War — 1904
  • World War I — 1914

A clean way to remember: 70 → 98 → 04 → 14. Roughly a generation between each, all leading up to WWI.

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