# Thread: Factors and Simplest Form: Concept Check

1. ## Factors and Simplest Form: Concept Check

From the book
"Why is the following way to simplify the fraction 17/75 incorrect?"

$\frac{1\not7}{\not75}=\frac{1}{5}$

This is an incorrect way to simplify the fraction because 17/75 cannot be simplified any further by dividing out digits within whole numbers in the numerator and denominator.

Do you think this clear and correct?

2. Originally Posted by Euclid Alexandria
From the book
"Why is the following way to simplify the fraction 17/75 incorrect?"

$\frac{1\not7}{\not75}=\frac{1}{5}$

This is an incorrect way to simplify the fraction because 17/75 cannot be simplified any further by dividing out digits within whole numbers in the numerator and denominator.

Do you think this clear and correct?
Perhaps something like:

When cancelling you are removing common factors of the numerator and
the denominator. In this case the 7's are not factors of the 17 or 75 but
are digits in their decimal representation. As 7 is not a common factor of
17 and 75 the 7's cannot be cancelled

RonL.

3. Hello, Euclid Alexandria!

Why is the following way to simplify the fraction $\frac{17}{75}$ incorrect?

$\frac{1\!\!\!\not7} {\not75}=\frac{1}{5}$

But it works for these . . . LOL!

. . $\frac{16}{64}\;=\;\frac{1\!\!\!\not6}{\not64}\;=\; \frac{1}{4}$

. . $\frac{19}{95}\;=\;\frac{1\!\!\!\not9}{\not95} \;=\;\frac{1}{5}$

. . $\frac{26}{65}\;=\;\frac{2\!\!\!\not6}{\not65} \;=\;\frac{2}{5}$

. . $\frac{49}{98}\;=\;\frac{4\!\!\!\not9}{\not98} \;=\;\frac{4}{8}\:=\:\frac{1}{2}$

4. Thanks Captain, that explanation is right on the mark (well, except for the first sentence, if you consider Soroban's reply).

5. Originally Posted by Euclid Alexandria
From the book
"Why is the following way to simplify the fraction 17/75 incorrect?"

$\frac{1\not7}{\not75}=\frac{1}{5}$