Simplify the Algebraic Expression: 3m⋅12n/(7m⋅4n)

Because we have one m in the numerator and one m in the denominator - they cancel completely! Same with n. When identical variables appear once on top and once on bottom, they cancel to 1.

Look for common factors in the remaining numbers. Here, both 12 and 4 are divisible by 4, so we can factor and cancel: $\frac{12}{4} = \frac{4 \times 3}{4}$

No! You can only cancel factors that are multiplied, not added. The two 3's in $3 \times 3$ multiply to give 9, so the final numerator is 9.

Divide the numerator by the denominator: $9 ÷ 7 = 1$ remainder $2$. So $\frac{9}{7} = 1\frac{2}{7}$

Subtract the exponents when canceling! For example: $\frac{m^3}{m^2} = m^{3-2} = m^1 = m$. But in this problem, all variables have exponent 1.