Say we are dividing out the common factors in
Is an answer of just as valid and correct as ?
When we write a fraction in the simplest form, we cancel out what is common in the numerator and denominator. This is what a teacher tells us in a class. After this the practice problem was given:
Simplify
One student cancelled out the (common in numerator and denominator) and got the answer , which was suprisingly the right answer. How many more fractions are there like this?
KeepSmiling
Malay
Hello, Euclid Alexandria!
Are these all the two-digit fractions that are like this?
Did you know this intuitively or did you use a method to figure it out?
I had seen these listed a book many years ago.
But you can derive your own formula for finding these "jokes".
We want digits so that: .
Solve for
Now try all digits for and which make a digit.
You'll find that the list I gave is complete.
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
One more joke:
Reduce: .
Answer: .
Hello, Euclid Alexandria!
A few really gruesome errors . . .
Can you possibly make any more mistakes?I am having difficulty following the example and reproducing the results. . . . No wonder!
Here are the steps I took to reproduce the example:
Let a = 1, b = 6, and c = 4.
. . . ↑ . ↑? . .↑?
.ten? . ↑ . b = 6
. . . . a = 1
. 10·1·6 = 60
. . . ↓?
. . . ↑?
. 10·6 + 4 = 64
. What is this? . 16 = 2·2·2·2
. . .↓ . ↓ . ↓
It's mathematically incorrect, but I thought she had done it on purpose. If so, I found it rather humerous. Here's why:Originally Posted by Soroban
Well, 10 x 1 = 10 and thus 10 x 1 x 6 = 10 x 6 = 1(0+6)=16.
6 + 4 = 10 so 10 * 6 + 4 = 10 * 10 = (1+1)0 = 20.
Now, 16 = 1 (6) = 1 * (2 * 3)
20 = 5 * 2 * 2
All of the Math mistakes are common (at least I've seen alot of them) mistakes similar to the cancelling joke that started this whole conversation.
(At least I HOPE she was making a joke out of it!!)
-Dan