1. The problem is to divide 13.2 by 66 using the division algorithm. 2. The division algorithm states that for two numbers $a$ and $b$ (with $b \neq 0$), dividing $a$ by $b$ gives a quotient $q$ and a remainder $r$ such that: $$a = bq + r$$ where $0 \leq r < |b|$. 3. Here, $a = 13.2$ and $b = 66$. Since 13.2 is less than 66, the quotient will be less than 1. 4. To perform the division, we can write it as: $$13.2 \div 66 = ?$$ 5. Convert 13.2 to 132 by multiplying numerator and denominator by 10 to avoid decimals: $$\frac{13.2}{66} = \frac{132}{660}$$ 6. Simplify the fraction $\frac{132}{660}$ by dividing numerator and denominator by their greatest common divisor (GCD). The GCD of 132 and 660 is 12. 7. Divide numerator and denominator by 12: $$\frac{132 \div 12}{660 \div 12} = \frac{11}{55}$$ 8. Simplify $\frac{11}{55}$ by dividing numerator and denominator by 11: $$\frac{11 \div 11}{55 \div 11} = \frac{1}{5}$$ 9. Therefore: $$13.2 \div 66 = \frac{1}{5} = 0.2$$ 10. So the quotient is $0.2$ and the remainder is $0$ because $66 \times 0.2 = 13.2$ exactly. Final answer: $$0.2$$