## What Does the Equals Sign Mean?

When kids are taught arithmetic, they're usually given problems that look like "2 + 3 = __", and they're supposed to write "5" in the blank space. So it's not particularly surprising that many kids (and even some adults) don't actually understand what it means. They think it means something like, "Here's the answer" or "Evaluate this expression".

What it actually means is that whatever is on the left of the equals sign **is the same as** whatever is on the right.

There's some nuance about what exactly it means for something to be the same as something else, which can vary somewhat depending on the context, but generally it just means that the two things have the same value.

So, 2 + 3 = 5 is a true equation because the expression 2 + 3 has the same value as 5.

But that equation could also be written as 5 = 2 + 3. Since thing on the left is the same as the thing on the right, the thing on the right must be the same as the thing on the left too.

You can even write 2 + 3 = 1 + 4. It might not be immediately obvious why you would want to, but being able to manipulate equations like that is the basis of algebra, which is a very useful thing

Sometimes you'll see someone write something like "2 + 3 = 5 + 4 = 9". This is incorrect. What's meant is "2 + 3 = 5 and 5 + 4 = 9", but the correct interpretation is "2 + 3 = 5 + 4 and 5 + 4 = 9". 2 + 3 doesn't have the same value as 5 + 4, so that's false.