Arithmetic & equation rearrangement — a+b=c becomes c-b=a

The forgotten algebra you actually need

Quick test. a + b = c. Solve for a.

If you said a = c - b instantly, skip ahead. If you froze for half a second — welcome, you're at the right starting line. Most people think they forgot algebra. They didn't. They forgot the one move behind every equation rearrangement: do the same thing to both sides. That's the entire idea. Pictures help.

The seesaw picture

Imagine an old seesaw. On the left side: a + b. On the right: c. The seesaw is balanced — the equation says they weigh the same.

You want a alone on the left. So you take b off the left side. But the seesaw tips! Right side is heavier now. The fix: take b off the right side too. Same amount, both sides. Balance restored.

Now you read off the seesaw. Left: a. Right: c - b. So a = c - b. Done. That's it. Every equation rearrangement is this one move, repeated.

Multiplication has the same trick

Now: a × b = c. Solve for a. Same idea. a is multiplied by b. To peel off the b, divide both sides by b. Balance preserved.

Result: a = c / b. (Assuming b ≠ 0 — otherwise the seesaw doesn't have a right side to weigh on.)

So: plus comes off with minus, minus comes off with plus, multiply comes off with divide, divide comes off with multiply. Each move is the seesaw, balanced. That's it.

Why this is finance's foundation

Time Value of Money — the very first finance equation you'll meet in Track 2 — looks like this:

F V = P V \times (1 + r)^{n}

That's future value equals present value times one-plus-rate-to-the-n. Don't worry about the exponent yet — we'll get there in Track 1 lesson 5. But notice: this is the same shape as c = a × b, just with longer names.

What if you know FV and want PV? Same trick. Divide both sides by (1+r)^n:

P V = \frac{F V}{( 1 + r ) ^{n}}

Same seesaw. The names got longer; the move didn't.

Negative numbers — same idea, no panic

Subtraction is just adding a negative. a - b is a + (-b). So everything we said about plus also covers minus. No new rule. If you've ever stared at x - 7 = 12 and wondered what to do — just add 7 to both sides. Seesaw move, same as before. x = 19.

The takeaway

One picture. Whatever you do to one side, do to the other. Add, subtract, multiply, divide — all the same idea, applied symmetrically. The Greek letters and ratios coming up later are just longer names on the seesaw. The seesaw doesn't care.

If you can rearrange a + b = c, you can rearrange any finance equation we'll see. Which is most of them.