1. Stating the problem: Simplify the expression $9 - 3 \div \frac{1}{3} + 1$. 2. Recall the order of operations (PEMDAS/BODMAS): division and multiplication come before addition and subtraction. 3. First, perform the division $3 \div \frac{1}{3}$. 4. Dividing by a fraction is the same as multiplying by its reciprocal: $$3 \div \frac{1}{3} = 3 \times 3 = 9$$ 5. Substitute back into the expression: $$9 - 9 + 1$$ 6. Simplify step-by-step: $$9 - 9 = 0$$ 7. Then add 1: $$0 + 1 = 1$$ Final answer: $1$.