Why 2½ × 1⅓ is not 2⅙
| ⅔ × ¾ | = ½ |
| ⅗ × ½ | = 3/10 |
| ⅞ × ⅔ | = 7/12 |
Top times top. Bottom times bottom. Simplify.
Two minutes. Everyone writes an answer — a guess counts.
Most of you chose 2⅙. It comes from a sensible idea. We are going to find out whether the idea is sensible or only comfortable. Thank the learner who offered it, by name.
Those pieces are real. They have area.
The two missing pieces are ½ + ⅔ = 7/6. And 2⅙ + 7/6 = 13/6 + 7/6 = 20/6 = 3⅓.
| How many halves in 2½? | 5 — so 2½ = 5/2 |
| How many thirds in 1⅓? | 4 — so 1⅓ = 4/3 |
| Now use last year's rule | 5/2 × 4/3 = 20/6 |
Not two methods that agree — the same four pieces, added by arithmetic instead of by picture.
| Problem | As fractions | Product | Simplest form |
|---|---|---|---|
| 2½ × 1⅓ | 5/2 × 4/3 | 20/6 | 3⅓ |
| 1½ × ⅔ | 3/2 × 2/3 | 6/6 | 1 |
| 3 × ⅔ | 3/1 × 2/3 | 6/3 | 2 |
| 2¼ × 1⅕ | 9/4 × 6/5 | 54/20 | 2 7/10 |
| ⅘ × 2½ | 4/5 × 5/2 | 20/10 | 2 |
If you see an eraser, ask them to explain their working. It will be correct.
↓ crossed out by a learner who voted for it
Tomorrow: 4 × 2⅗. There is no fraction at all in the first number. Does the rule still work?
Quarter sheet. Name at the top. Question 4 is the one that counts.