Find the value of $12 \times 24 + 36 \times 12$.
By the associative property, $12 \times 24 + 36 \times 12$ equals $12 \times 24 + 12 \times 36$. Factoring 12 out, we obtain  \begin{align*}
12 \times 24 + 12 \times 36 &= 12 \times (24+36)\\
&= 12 \times 60\\
&= \boxed{720}.
\end{align*}
720
Level 1
Algebra
Problem: Find the value of $12 \times 24 + 36 \times 12$.
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To solve the problem, first, we need to break down the expression into manageable parts. The expression consists of two products: $12 \times 24$ and $36 \times 12$. 

We start with the first product:
1. Calculate $12 \times 24$. 
   - We can break this down further: $12 \times 24 = 12 \times (20 + 4) = 12 \times 20 + 12 \times 4$.
   - Calculate $12 \times 20 = 240$ and $12 \times 4 = 48$.
   - Therefore, $12 \times 24 = 240 + 48 = 288$.

Next, we calculate the second product:
2. Calculate $36 \times 12$.
   - This can be computed directly as $36 \times 12 = 432$.

Now, we combine the results of both products:
3. Add the two results together: $288 + 432$.
   - We can add these directly: $288 + 432 = 720$.

Thus, after performing the calculations step-by-step, we arrive at the final answer, which is $720$.<|END_OF_LATENT|> The final answer is $720$.