Say we are dividing out the common factors in

Is an answer of just as valid and correct as ?

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- Jun 22nd 2006, 08:00 PMEuclid AlexandriaWriting a Fraction in Simplest Form
Say we are dividing out the common factors in

Is an answer of just as valid and correct as ? - Jun 22nd 2006, 08:58 PMSoroban
Hello, Euclid Alexandria!

Quote:

Say we are dividing out the common factors in

Is an answer of just as valid and correct as ?

Similarly: . is equal to ,

. . but a denominator of is usually omitted. - Jun 23rd 2006, 04:33 AMQuickQuote:

Originally Posted by**Euclid Alexandria**

- Jun 23rd 2006, 06:51 PMEuclid Alexandria
Thanks guys, I'll get in the habit of omitting the 1 just in case.

Oh hey look, I just became a senior member. - Jun 23rd 2006, 08:44 PMticbolQuote:

Originally Posted by**Euclid Alexandria**

- Jun 24th 2006, 01:59 PMEuclid AlexandriaQuote:

Originally Posted by**ticbol**

- Jun 24th 2006, 07:01 PMmalaygoelWriting fraction in simplest form
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 - Jun 24th 2006, 10:21 PMSoroban
Hello, Malay!

Besides , we have:

. .

. .

. . - Jun 26th 2006, 07:41 PMEuclid AlexandriaQuote:

Originally Posted by**Soroban**

- Jun 26th 2006, 10:11 PMSoroban
Hello, Euclid Alexandria!

Quote:

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: .

- Jun 27th 2006, 07:43 PMEuclid AlexandriaQuote:

Originally Posted by**Soroban**

**Let a = 1, b = 6, and c = 4.**

- Jun 28th 2006, 05:59 AMSoroban
Hello, Euclid Alexandria!

A few reallyerrors . . .*gruesome*

Quote:

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**

. . .**↓****. ↓ . ↓**

- Jun 28th 2006, 09:51 AMtopsquarkQuote:

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 - Jun 28th 2006, 07:53 PMEuclid Alexandria
Yes, it is possible to make more mistakes in this instance. :eek:

:)*Thoughtful pause*:)

Here we are attempting to reproduce as before, except with a.*newly revised method*

**Let a = 1, b = 6, and c = 4**

. . ↑ .. ↑ ...↑

.**nine!**↑ .**b = 6**

. . . .**a = 1**

- Jun 30th 2006, 07:44 PMEuclid Alexandria
Here's another try at using that formula (if that's the correct terminology) to reproduce

**Let a = 1, b = 6, and c = 4**

**(Now it appears that a = 16 and c = 64)**