Examples of fallacies in arithmetic and/or algebra [closed]

I'm currently preparing for a talk to be delivered to a general audience, consisting primarily of undergraduate students from diverse majors. My proposed topic would be Examples of fallacies in arithmetic and/or algebra.

So my question would be:

What are some examples of arithmetic/algebraic fallacies that you know of?

One example per answer please.

Let me give my own example, which is one of my personal favorites:

Let $$a = b.$$ Multiplying both sides by $a$, we get $$a^2 = ab.$$ Subtracting $b^2$ from both sides, we obtain $$a^2 - b^2 = ab - b^2.$$ Factoring both sides, we have $$(a + b)(a - b) = b(a - b).$$ Dividing both sides by $(a - b)$, $$a + b = b.$$ Substituting $a = b$ and simplifying, $$b + b = b,$$ and $$2b = b.$$ Dividing both sides by $b$, $$2 = 1.$$

Of course, this fallacious argument breaks down because we divided by $a - b = 0$, since $a = b$ by assumption, and division by zero is not allowed.

I like the following one. It's kinda silly, but still interesting.

We know $1\$=100c$. But then:

$$\begin{align}1\$&=100c\\ &=10c\times 10c\\ &=0.1\$\times 0.1\$\\ &=0.01\$\\ &=1c\end{align}$$

So a dollar is worth just a penny!

$$1 = \sqrt{1} = \sqrt{(-1)(-1)} = \sqrt{-1}\sqrt{-1} = i\cdot i = -1$$

You might want to look at Edward J. Barbeau's books "Mathematical Fallacies, Flaws, and Flimflam" (MAA, 2000) and "More Fallacies, Flaws and Flimflam" (MAA, 2013).

Without resorting to $i$:

$$1-3=4-6\\ 1-3+\frac94=4-6+\frac94\\ 1-2\cdot1\cdot\frac32+\left(\frac32\right)^2=4-2\cdot2\cdot\frac32+\left(\frac32\right)^2\\ \left(1-\frac32\right)^2=\left(2-\frac32\right)^2\\ 1-\frac32=2-\frac32\\ 1=2$$