Let's go through each part of the image step by step and show the work for each question.

1. Solve: $\_\_\_ = \frac{342}{9}$

We need to find the result of $\frac{342}{9}$.

Solution:

$342 \div 9 = 38$ Thus, the missing number is 38.

2. Solve $\sqrt[3]{521}$ (cube root of 521)

We need to approximate the cube root of 521.

Solution:

To estimate the cube root of 521, we can find nearby perfect cubes:

• $8^3 = 512$
• $9^3 = 729$

Since $521$ is closer to $512$, we estimate: $\sqrt[3]{521} \approx 8$

Thus, $\sqrt[3]{521} \approx 8$.

3. Find the quotient of 88 divided by 7

We need to divide 88 by 7.

Solution:

$88 \div 7 = 12 \text{ remainder } 4 \quad \text{or} \quad 88 \div 7 = 12.5714 \ldots$

So, the quotient is 12 with a remainder of 4 or approximately 12.57.

Would you like further details or any clarifications? Here are five questions to expand your understanding:

1. How would you estimate cube roots for numbers that aren't perfect cubes?
2. What method can you use to quickly find the quotient and remainder in division?
3. What strategies are there for approximating values like cube roots more accurately?
4. Can you explain how you divide large numbers like 342 without a calculator?
5. How can you check your work when dividing numbers like 88 and 7?

Tip:

When dealing with cube roots, it's often helpful to remember cubes of small integers like 2³ = 8, 3³ = 27, up to around 10³ = 1000, so you can estimate quickly!