Solve: (a+b+c)÷((3a+3b+3c)/2) - Expression Division Problem

The colon (:) is another way to write division, just like ÷. So $(a+b+c):(\frac{3a+3b+3c}{2})$ means the same as $(a+b+c) ÷ (\frac{3a+3b+3c}{2})$.

Same rule applies! Flip the fraction and multiply. So dividing by $\frac{3a+3b+3c}{2}$ becomes multiplying by $\frac{2}{3a+3b+3c}$.

Because $3a+3b+3c = 3(a+b+c)$ by the distributive property. This is the same as factoring out a common factor from addition!

Not in this problem! When the same expression $(a+b+c)$ appears in both numerator and denominator, they cancel out completely, leaving just the number $\frac{2}{3}$.

If $a+b+c = 0$, then both the numerator and denominator become zero, making the expression undefined. This is a special case where division cannot be performed.