Can you please help solve using the ‘picking numbers’ method? I was trying to use 1/3 and pi
Try watching these videos first:
These will help you understand what type of numbers to choose etc.
If still confused, I can help you out further.
I watched the videos and they recommend which “easy” numbers to pick.
So, if I follow the videos recommendation and apply it to this problem, is my selection of numbers and thought process correct?
- rational x irrational = irrational –> NOT ALWAYS TRUE
if rational is 1/2 or 0 and irrational is 2.75
1/2 x 2.75 = 2.75/2 result is irrational
0 x 2.75 = 0 result is rational
- irrational + irrational = irrational –> NOT ALWAYS TRUE
if irrational is 2.75 or 1.25
2.75 + 2.75 = 5.5 result is irrational
2.75 + 1.25 = 4 (4/1) result is rational
- rational + irrational = irrational –> MUST ALWAYS BE TRUE
if rational is 1/2 or 0 and irrational is 2.75
1/2 + 2.75 = 6.5/2 result is irrational
0 + 2.75 = 2.75 result is irrational
Thank you!
Yes absolutely. It’s the correct approach.
No, none of the numbers you chose were irrational.
Can you explain and solve the problem with examples please?
Do you know what irrational numbers are? That’s a good place to start. Likewise, do you know what rational numbers are?
Yes. Rational numbers can be written as a fraction and irrational numbers cannot be written as a fraction and also any number when written as a decimal is non-terminating and non-repeating (for example pi)
Okay, so that’s mostly right. Just a slight correction regarding “can’t be written as a fraction,” because technically \frac{\pi}{1} is a fraction. Basically, irrational numbers are numbers that can’t be expressed as a ratio of two integers — or, more precisely, they’re real numbers that are not rational.
Anyway, so owing to that, can you pick appropriate irrational and rational numbers to answer the question? The idea is similar to what you had above except this time you’re actually using rational/irrational numbers.
As a reminder, your goal is to pick numbers such that they contradict the claim (if possible). If they do they know that option can’t possibly be true.
Okay, so what if I select the following as rational and irrational?
Rational: 2 (which is 2/1) and 0
Irrational: pi
Sure, go for it
My bad, I missed the irrational part. Focused just on the numbers part. Sorry for the confusion.
1 Like