What kind of problem is this?

[scomorga]

Hello,

I ran into a problem that is giving me a problem. What kind of problem is this and what is the best way to solve a problem of this type?

If P divided by 5 = Q then P divided by 10 = ?


I know the answer is Q divided by 2...but how does one get to that answer? Also, what kind of problem is this, is it probability, ratio, ?????

Thanks for your help!

[galactus]

\frac{P}{5}=Q

Multiply both sides by 1/2:

\frac{1}{2}\cdot\frac{P}{5}=\frac{1}{2}\cdot Q=\frac{Q}{2}

\frac{P}{10}=\frac{Q}{2}

[scomorga]

Thank you,

But how do you know to use 1/2? How did you get to that?

Sorry to be so thick.

Thanks!

[galactus]

What do we have to do to make k\frac{P}{5}=\frac{P}{10}?.

Multiply \frac{P}{5} by k=1/2. That's it. Just like multiplying a fraction.

When we multiply, we have to do it to both sides. So we multiply Q by 1/2 as well.

Think of it as a proportion.

P=5Q

Therefore, \frac{P}{10}=\frac{5Q}{10}=\frac{Q}{2}

[DrMike]

Thank you,

But how do you know to use 1/2? How did you get to that?

Thanks!

It often helps to make the problem more concrete, ie, to invent some story around it. For example....

"If P divided by 5 = Q..."

I'll invent this story - I have box of P peanuts, to share between 5 people. Each person gets Q, because P divided by 5 is Q. Try to imagine this in your head. Now for the next part of the story.

"P divided by 10 = ?"

Suddenly, some extra people turn up. Now I have to divide the P peanuts amongst 10 people, instead of 5. Now how many does each person get??

If it's still not clear, can you solve the problem for a few different actual values of Q, and spot the pattern?

[scomorga]

Thank you galactus and DrMike!

Now I understand completely!

I can't tell you how much this helps :)

[DrMike]

You're welcome.. :-)