Simply simple???!

[MeSebtimar]

How do I express ratio 115:37, 92:68 in simplest form?

Also, how do I find a product of two fractions that is between 10 and 11?

 

[MarkFL]

37 is prime, so the ratio 115:37 is in simplest form. 92 and 68 have 4 as their GCD, so divide both by 4 to get the ratio in simplest form.

To find the product of two factions, use:

\(\displaystyle \displaystyle \frac{a}{b}\cdot\frac{c}{d}=\frac{ac}{bd}\) then reduce if possible.

 

[JeffM]

How do I express ratio 115:37, 92:68 in simplest form?

Also, how do I find a product of two fractions that is between 10 and 11?

The ratio 115:37 is in its simplest form because 115 is not an even multiple of 37, which is a prime number: no number larger than 1 or smaller than itself divides it evenly.

92:68 can be expressed more simply as 23:17. The latter is the simplest form possible for that ratio because both 23 and 17 are prime numbers.

I may not understand your last question. There are an infinite number of fractions between 10 and 11 and for each one there may be many ways to factor it. For example:

\(\displaystyle \dfrac{2048}{200} = 10.24 \implies 10 < \dfrac{2048}{200} < 11\ and\ \dfrac{512}{25} * \dfrac{4}{8} = \dfrac{2064}{200} = \dfrac{128}{50} * \dfrac{16}{4}.\)

 

[JeffM]

That statement needs to be "edited". We can reduce (n*37):37 to n:1

Done. Thanks Subhotosh. Maybe I should take the day, maybe the week, off.