Halfway
Can you find a number that is halfway between two fractions?
Age
11 to 14
Challenge level
Problem
What number is halfway between $-\frac{2}{3}$ and $\frac{4}{5}$?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
Answer: $\frac1{15}$
Using a number line
Image
Distance $=\frac23 + \frac45 = \frac{10}{15}+\frac{12}{15} = \frac{22}{15}$
Half of distance $=\frac{11}{15}$
Midpoint $=-\frac{10}{15}+\frac{11}{15} = \frac{1}{15}$ (or $\frac{12}{15}-\frac{11}{15} = \frac{1}{15}$)
Using the mean as the midpoint
$\frac{4}{5} = \frac{12}{15}$ and $-\frac{2}{3} = -\frac{10}{15}$, so the number halfway between these is $\frac{1}{2} (-\frac{10}{15}+ \frac{12}{15})$ which is $\frac{1}{15}$.