**This is Day 26 of 31 Days of Math Learning Success. Follow all the days here and check out others that are writing for 31 days here.**

*Float like a butterfly, sting like a bee.
~Muhammad Ali*

At cocktail parties I usually hear one of two things:

“I’ve never been good at math. I can’t even balance my checkbook.”

Or

“I love math – there’s always one right answer.”

Both of these are wrong.

I’ve attacked the first thing in many posts. But now it’s time for the second one: *There’s always one right answer.*

### There may be no answer.

A lack of answer is sort of an answer, I know. But most people want a **number** as an answer. Not a comment.

But answers to questions like, “At what point does the graph of cross the x-axis?” has just that.

“Well, it doesn’t cross the x-axis at all.”

And how about solutions to problems like the 5 Five Room House Problem? I worked on that one for 15 years before realizing that there really was no solution.

### There may be one PRETTY answer.

Here’s where most people are happy. The solution to is .

But is also an answer. And depending on how you feel about fractions and decimals, you’ll think one of these is prettier than the other.

But is also a solution. And . They’re not pretty. But if you plug in for x, you get a true statement.

Which means is a solution.

So really, you have an infinite number of different-looking solutions (all the same value, but they could look different).

### There may be MANY pretty answers.

How about the fun guys like ?

This one has three distinct values as answers: , , .

Of course, we can write them in many ways – some nicer than others. The fraction can be very nicely written as -2.2.

### There may be one distinct answer that can be written very differently.

I did a trig problem in class many years ago. My answer seemed solid (150 students were checking my work as I did it). But yet the answer in the back of the book was VERY different.

I validated the answer in the back of the book to make sure that one was correct. And I validated mine. A few times.

Oh how I wish I could recall that problem. The result ended up being like when the book showed (a trig identity). I remember it being a far more obscure identity, though.

The point is that I got a perfectly legitimate, valid answer and it took me a while to figure out why it looked so different.

### Float like a butterfly.

When you finish a problem – from the book or life – ask yourself if it’s the only answer. Is it the best answer? Would it be “nicer” written a different way?

Always look for more or less answers than you see.

Stay on your toes.

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