Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

1998 PMWC Problems/Problem I1

Revision as of 16:37, 8 August 2009 by Ihatepie (talk | contribs) (→‎Solution)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Problem I1

Calculate: $\frac{1*2*3+2*4*6+3*6*9+4*8*12+5*10*15}{1*3*5+2*6*10+3*9*15+4*12*20+5*15*25}$

Solution

If you factor the top, you get $(1*2*3)(1^{3}+2^{3}+3^{3}+4^{3}+5^{3})$


If you factor the bottom, you get $(1*3*5)(1^{3}+2^{3}+3^{3}+4^{3}+5^{3})$

Dividing out the common factor, you get $\frac {1*2*3}{1*3*5}=\frac {6}{15}= \frac {2}{5}$

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=1998_PMWC_Problems/Problem_I1&oldid=32612"