problem solving, which includes fractions

okay so im having some trouble here, the problem is

the fraction halfway between two other fractions has a decimal equivalent of 0.190476 ( which is a recurring decimal). the smaller of the two fractions is 1/7 (which is a fraction). Which is the larger fraction?

thanks for any help (Happy)

finally understood the question

Quote:

Originally Posted by

**coldplayroxs** okay so im having some trouble here, the problem is

the fraction halfway between two other fractions has a decimal equivalent of 0.190476 ( which is a recurring decimal). the smaller of the two fractions is 1/7 (which is a fraction). Which is the larger fraction?

thanks for any help (Happy)

*the fraction halfway between two other fractions* is the average value or mean value of two given numbers. Let x and y denote the given two numbers then the mean value is calculated by:

$\displaystyle m=\dfrac{x+y}2 = \dfrac x2 + \dfrac y2$

Let x < y then $\displaystyle x = \frac17$ according to your question.

Plug in the values you already know into the formula calculating the mean value:

$\displaystyle 0.190476 = \dfrac{\frac17}2 + \dfrac y2$

Solve this equation for y.

EDIT: Do you mean by *0.190476 ( which is a recurring decimal)* that the given value is:

$\displaystyle 0.\overline{190476} = \dfrac{190476}{999999} = \dfrac4{21}$

If so:

$\displaystyle 0.\overline{190476} = \dfrac4{21} = \dfrac{\frac17}2 + \dfrac y2 ~\implies~ \boxed{y = \dfrac5{21}}$