Recurring Mean
What is the mean of 1.2 recurring and 2.1 recurring?
Age
14 to 16
Challenge level
Problem
What is the mean of $1.\dot{2}$ and $2.\dot{1}$?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
Answer: $1.\dot{6}$ or $\frac53$ or $1\frac23$
Decimals
The mean is $(1.\dot{2}+2.\dot{1})\div2=3.\dot{3}\div2=1.\dot{6}$
Fractions
$1.\dot2 = 1\frac29$
$2.\dot1 = 2\frac19$
$1\frac29+2\frac19=3\frac39=3\frac13$
$3\frac13\div2=1\frac12+\frac16=1\frac23$