# GMAT Arithmetic Shortcuts: Divide before you multiply

The GMAT loves to test complex proportions, cross multiplication, probability, and combinations. It’s a sure thing, therefore, that you will at some point encounter arithmetic like this:

This task probably won’t be given to you directly in the question stem—more likely, this would be an intermediate step after translating a word problem or plugging in numbers for variables. But it’s certain you’ll see something like this at some point on some GMAT problem.

In real life, you might plug these straight into a calculator. Doing so would give us this:

Ugly, huh? A five-digit number divided by a three-digit number. But the result is a nice even 30. There must be a better way to get there if the division is so neat! The shortcut is to divide. Any time you have numbers over numbers, you should always cancel, cancel, cancel. Dividing first keeps your numbers small and your arithmetic simple. Check out what happens if we cancel first in this problem:

Easy as pie! 7 goes evenly into 21, 9 goes evenly into 45, and 11 goes evenly into 22. Reducing fractions and ratios to their simplest form before multiplying will save you mountains of work on test day.