1. ## Fractions problem

How can I show that $\displaystyle \frac {3}{10}$ is $\displaystyle \frac {1}{7}$ of the way from $\displaystyle \frac {1}{4}$ to $\displaystyle \frac {3}{5}$?

2. Originally Posted by sarahh
How can I show that $\displaystyle 3/10$ is $\displaystyle 1/7$ of the way from $\displaystyle 1/4$ to $\displaystyle 3/5$?
First you need to find out the length of "the whole way" from $\displaystyle \frac{1}{4}$ to $\displaystyle \frac{3}{5}$, which you do by subtraction:

$\displaystyle \frac{3}{5} - \frac{1}{4} = \frac{12}{20} - \frac{5}{20} = \frac{7}{20}$.

So what's 1/7 of 7/20? 1/20. So now the question becomes, is $\displaystyle \frac{3}{10}$ a distance of $\displaystyle \frac{1}{20}$ from $\displaystyle \frac{1}{4}$?

$\displaystyle \frac{3}{10} - \frac{1}{4} = \frac{6}{20} - \frac{5}{20} = \frac{1}{20}$

We figured out that $\displaystyle \frac{3}{5}$ and $\displaystyle \frac{1}{4}$ are $\displaystyle \frac{7}{20}$ apart. So a number which is $\displaystyle \frac{1}{7}$ of the way from $\displaystyle \frac{1}{4}$ to $\displaystyle \frac{3}{5}$ is going to be a distance of $\displaystyle \frac{1}{20}$ from $\displaystyle \frac{1}{4}$. Therefore, the desired answer is $\displaystyle \frac{1}{4} + \frac{1}{20} = \frac{5}{20} + \frac{1}{20} = \frac{6}{20} = \frac{3}{10}$.