Reciprocal values
Manipulate one algebraic fraction to solve another.
Age
14 to 16
Challenge level
Problem
What is the value of $\frac{1}{x+2}$, given that $\frac{1}{x} = 3.5$?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
As $\frac{1}{x} = 3.5 = \frac{7}{2}$, so $x = \frac{2}{7}$.
Then $x+2 = \frac{16}{7}$.
Hence $\frac{1}{x+2} = \frac{7}{16}$.
Then $x+2 = \frac{16}{7}$.
Hence $\frac{1}{x+2} = \frac{7}{16}$.