Solve the Algebraic Expression: (2a·3b)÷(3a·4b)

You can cancel variables when they appear exactly once in both the numerator and denominator. Since we have one 'a' on top and one 'a' on bottom, they divide to equal 1 and disappear!

If you had $a^2$ on top and $a$ on bottom, you'd subtract exponents: $a^{2-1} = a^1 = a$. Only cancel completely when exponents are the same.

It's easier to cancel variables first! This eliminates the letters early so you only work with numbers. You can multiply numbers in any order that feels comfortable.

You're done when: (1) All possible variables are canceled, (2) The fraction is in lowest terms, and (3) No more common factors exist between numerator and denominator.

The colon (:) means division, just like the ÷ symbol. So $2a \cdot 3b : 3a \cdot 4b$ is the same as $\frac{2a \cdot 3b}{3a \cdot 4b}$.