Question: Sarah is trying to find $414 \div 18$. Since $400 \div 20 = 20$, she estimates the quotient is around $20$. Adjust Sarah's estimate as needed and find the quotient. $414 \div 18 =$
1. **State the problem:** We need to find the exact value of $414 \div 18$.
2. **Initial estimate:** Sarah estimated $414 \div 18$ by comparing it to $400 \div 20 = 20$.
3. **Adjusting the estimate:** Since $18$ is less than $20$, dividing by $18$ will give a quotient slightly larger than dividing by $20$. Also, $414$ is slightly larger than $400$, so the quotient should be a bit more than $20$.
4. **Perform the exact division:**
$$414 \div 18 = \frac{414}{18}$$
5. **Simplify the fraction:**
Both numerator and denominator are divisible by $6$:
$$\frac{414}{18} = \frac{\cancel{6} \times 69}{\cancel{6} \times 3} = \frac{69}{3}$$
6. **Divide $69$ by $3$:**
$$69 \div 3 = 23$$
7. **Final answer:**
$$414 \div 18 = 23$$
So, Sarah's estimate of $20$ was a bit low; the exact quotient is $23$.