"So what's 1+2*3?"
She frowned, sticking out her lower lip. "9."
"No, no, you have to do the multiplications first."
"How come?"
"Order of operations. PEMDAS. That's just how math is written."
"PEMDAS?"
"Parentheses, Exponentiation, then Multiplication/Division, then Add/Subtract. You do the first ones first. Multiplication/Division are ranked the same so you do them left to right, and so are Add/Subtract."
"What's exponentiation?"
"That's powers."
"What are powers?"
"Powers are to multiplication as multiplication is to addition."
"Uh"
"Ignore that for now. 1+2*3 again. Do the multiplication first, then what is it?"
"Uh 2*3 is 6, then what?"
"So after you've done the multiplications, 1+2*3 leaves you with 1+6. What's 1+6?"
"7"
"And that's the answer. Type it into your calculator and see what it says."
She did so. "7. Whoa that's freaky. Why'd it do that?"
"PEMDAS. That's always how it's supposed to be done, so that's how they make calculators. Well most calculators. There's some that just do left to right, but they're wrong."
"Does anyone really care?"
I grinned. "Yes. Well, no. Well yes. Nobody wants to care. People hate math. Nobody's good at it. But if you look at the difference between high paid and low paid jobs, the high paid ones all need to you to do algebra. The laws of nature, what makes a car run, it's all algebra. Banks operate on algebra. Money? Algebra. Statistics, chemistry, biology, computers, all of science need you to be able to do algebra. There's really nothing you'll ever learn that's more useful than being able to do algebra."
"But it's no fun."
"Yes! Exactly!"
"You're weird."
"Weird, but highly paid, because I'm willing to do algebra!"
"Definitely weird."
"OK, let me show you powers now. You know how 2*3 is 2+2+2=6, well 23 is 2 to the 3rd power, or 2 exponentiated by 3, that's 2*2*2=8 ..."