Alternendo and Invertendo
Rearrange a proportion to swap places or flip fractions.
Equation
y = 1*6 - 1*x
Graph
Table
| x | y |
|---|---|
| 0 | 6 |
| 1 | 5 |
| 2 | 4 |
| 3 | 3 |
| 4 | 2 |
| 5 | 1 |
| 6 | 0 |
| 7 | -1 |
| 8 | -2 |
| 9 | -3 |
| 10 | -4 |
What this lesson covers
What you do
You shape the function y = a*d - b*x and watch the graph answer.
Challenges to clear
- Set a = 2 and b = 3 (d stays 6). The curve y = ad − bc hits ZERO at c = 4 — the proportion 2/3 = 4/6 balances.
- Alternendo swaps the means: 2/4 = 3/6 — both are ½, the same zero point proves it.
- A new proportion 3 : b = c : 8. Set a = 3 and d = 8.
- Now slide b until the curve hits zero at c = 6, so ad = bc balances. Swapping the means keeps it balanced — that is alternendo.
Check yourself
If a/b = c/d, what does Invertendo state?
If a/b = c/d, what does Alternendo state?
- b/a = d/c — correct
- a/c = b/d
- (a+b)/b = (c+d)/d
- a/d = b/c
- b/a = d/c
- a/c = b/d — correct
- (a+b)/b = (c+d)/d
- a/d = b/c
Think about it
- a/b = c/d means ad = bc. With a = 2, b = 3, d = 6: what c balances the proportion?