Question: Katy is trying to find $168 \div 42$. Since $160 \div 40 = 4$, she estimates the quotient is around $4$. Check Katy's estimate. How should she adjust her estimate? Adjust Katy's estimate as needed and find the quotient. $168 \div 42 =$
1. **State the problem:** We want to find the exact value of $168 \div 42$ and check if Katy's estimate of $4$ is accurate.
2. **Estimate given:** Katy used $160 \div 40 = 4$ as an estimate.
3. **Check the estimate:**
- The actual dividend is $168$, which is $8$ more than $160$.
- The actual divisor is $42$, which is $2$ more than $40$.
4. **Adjust the estimate:**
- Since the dividend increased by $8$ (from $160$ to $168$), the quotient should increase.
- Since the divisor increased by $2$ (from $40$ to $42$), the quotient should decrease.
5. **Calculate the exact quotient:**
$$168 \div 42 = \frac{168}{42}$$
6. **Simplify the fraction:**
- Both numerator and denominator are divisible by $6$:
$$\frac{168}{42} = \frac{\cancel{6}28}{\cancel{6}7} = \frac{28}{7}$$
7. **Divide $28$ by $7$:**
$$\frac{28}{7} = 4$$
8. **Conclusion:** Katy's estimate of $4$ is exactly correct.
**Final answer:**
$$168 \div 42 = 4$$