Fractions of fractions
If you know that a fraction of X is the same as a different fraction of Y, can you work out X/Y?
Age
14 to 16
Challenge level
Problem
Two thirds of five sixths of a number $X$ is the same as three quarters of four fifths of a number $Y$.
What is the value of $\frac{X}{Y}$ as a fraction in its lowest terms?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
Answer: $\frac{27}{25}$
$$ \frac{2}{3} \times \frac{5}{6} \times X = \frac{3}{4} \times \frac{4}{5} \times Y$$ $$ \frac{5X}{9} = \frac{3Y}{5}$$ $$ 25X = 27Y$$ $$ \frac{X}{Y} = \frac{27}{25}$$