The Math Forum's Ask Dr. Math service provides a place for people who
want to share their knowledge of math with people who need help
learning math.

It is not a 'homework help' service. As a general rule, we don't
provide 'answers' to the questions that we get. Rather, we try to help
our 'patients' get the insight they need to answer their own questions.

The first step toward becoming a 'math doctor' is to try your hand at
answering a typical question, assisted by an online 'guide' that we've
put together to help you evaluate (and possibly revise) your answer as
you write it, as well as to explain some of the philosophy behind our
approach to answering questions. This will give you a feel for what
it's like to try to mentor someone via email, and help you decide
whether this is something you think you'd enjoy doing.

If that works out, we'll set you up with an account,
and you'll start answering live questions as they come in.
Your answers will be reviewed, and you may be required to revise them
one or more times before they can be sent out. When we get to
the point where we're routinely sending your answers without
comment, you'll be cleared to send them directly to the patients.

Does this sound like something you'd like to try? If so, scroll down
to the form, choose a question to answer, provide your name and email
address, and click the button to get started!

Which question would you like to answer?

From Kay (age 11)

Why do we have to line up decimals when we add and
subtract, but not when we multiply and divide?

Important: Assume that Kay already knows how to work with decimals, so
you don't need to focus on what to do. Focus instead on how the
rules she already knows can be understood in terms of how we define
decimal notation.

From Curtis (age 16)

we r doing 2 equations, like
2x - 3y = 12
5x + 4y = 7
but i can't even solve 1 of them. how am i supposed
to solve 2 at once?
thank u, curtis

Important: If you're thinking about
demonstrating a particular technique,
like substitution or elimination, consider this: It's almost certain
that the technique has already been demonstrated
for Curtis, by his math teacher and in his textbook.

The question we want to address is this: Why haven't
those demonstrations been sinking in? Until we clear that up, our
own demonstrations aren't likely to be any more successful than the
ones he's already seen.

For example, you might start discussing the difference between how we
use 'solve' when talking about an equation like
3x + 2 = 7
and how we use it when talking about an equation like
2x + 3y = 10.
In other words, help him get to the point where he can 'solve 1 of
them', and understands what that implies.

From Brent (age 24)

One of my students asked me why, when adding fractions, we can't
just add the numerators and denominators, and he used this as his
example: "In the first game of a double-header, Joe gets 1 hit
in 3 at bats. In the second game, he gets 2 hits in 5 at bats.
That's 3 hits in 8 at bats, and 1/3 + 2/5 = 3/8."
I know this isn't right, but I'm not sure how to explain why.
Help!

Important: Just explaining how to add 1/3 to 2/5 using the 'correct' rule
misses the point of the question. Brent already knows how to add
two fractions. What's confusing him is that in this situation, doing
the 'right' thing gives a result that doesn't make sense, while doing the
'wrong' thing seems to give a perfectly reasonable result. This
questions isn't so much about how to add fractions, as about
when to add them.