Divide and Conquer
Weekly Problem 23 - 2015
Can you simplify this algebraic expression with many divisions?
Can you simplify this algebraic expression with many divisions?
Age
11 to 16
Challenge level
Problem
Simplify
$(x \div (y \div z)) \div ((x \div y) \div z)$.
If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.
Student Solutions
$(x \div (y \div z)) \div ((x \div y) \div z) = (x \div \frac{y}{z}) \div ((\frac{x}{y}) \div z) = (x \times \frac{z}{y}) \div (\frac{x}{y} \times \frac{1}{z})$
$= \frac{xz}{y} \div \frac{x}{yz} = \frac{xz}{y} \times \frac{yz}{x} = z^2$.