What is the largest multiple of $9$ which is smaller than $-70$?
Dividing $-70$ by $9$ gives $-8$ with a remainder of $2$, or $$-70 = -8 \cdot 9 + 2.$$Thus, $-8 \cdot 9 = \boxed{-72}$ is the largest multiple of $9$ which is smaller than $-70$.
-72
Level 2
Prealgebra
Problem: What is the largest multiple of $9$ which is smaller than $-70$?
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To find the largest multiple of $9$ that is smaller than $-70$, we first identify the multiples of $9$. The multiples of $9$ are generated by the formula $9n$, where $n$ is an integer. 

Next, we need to determine the integer values of $n$ that yield multiples of $9$ less than $-70$. We can start by calculating the multiple of $9$ that is closest to $-70$. 

Calculating $-70$ divided by $9$ gives us approximately $-7.777...$. The largest integer less than $-7.777...$ is $-8$. 

Now, we compute the multiple of $9$ for $n = -8$:
$9 \times -8 = -72$.

Next, we check the next integer, $-7$, to ensure it is greater than $-70$:
$9 \times -7 = -63$, which is indeed greater than $-70$.

Since $-72$ is less than $-70$ and $-63$ is greater than $-70$, we confirm that $-72$ is the largest multiple of $9$ that meets the condition of being smaller than $-70$. 

Thus, the final answer is $-72$.<|END_OF_LATENT|> The final answer is $-72$.