Question

leveled practice in 1–4, fill in the boxes.

1. \\( \overline{42\vert 9216} \\) \\( \square \\) r \\( \square \\)
2. \\( \overline{38\vert 15558} \\) \\( \square \\)
3. \\( \overline{77\vert 693} \\) \\( \square \\)
4. \\( \overline{21\vert 2567} \\) \\( \square \\) \\( \square \\) r \\( \square \\)

in 5–16, estimate, and then find the quotient. use your estimate to check reasonableness.

1. \\( 482 \div 77 \\)
2. \\( \overline{44\vert 817} \\)
3. \\( \overline{21\vert 777} \\)
4. \\( \overline{35\vert 280} \\)
5. \\( 2,465 \div 29 \\)
6. \\( 203 \div 29 \\)
7. \\( 8,114 \div 46 \\)
8. \\( \overline{13\vert 748} \\)
9. \\( 6,364 \div 81 \\)
10. \\( 5,578 \div 68 \\)
11. \\( 9,855 \div 45 \\)
12. \\( 7,308 \div 12 \\)

show your work!

Explanation:

Let's solve one of the division problems, for example, problem 1: \( 42 \enclose{longdiv}{9216} \) (assuming the notation is \( 9216 \div 42 \) with remainder). Wait, maybe it's \( 9216 \div 42 \). Let's do that.

Step 1: Divide 92 by 42

\( 42 \times 2 = 84 \), subtract from 92: \( 92 - 84 = 8 \)

Step 2: Bring down 1 (from 9216) to make 81

\( 42 \times 1 = 42 \), subtract: \( 81 - 42 = 39 \)

Step 3: Bring down 6 to make 396

\( 42 \times 9 = 378 \), subtract: \( 396 - 378 = 18 \)

Step 4: So the quotient is 219 and remainder 18. Wait, maybe the problem is \( 9216 \div 42 \). Let's check: \( 42 \times 219 = 42 \times (200 + 19) = 8400 + 798 = 9198 \), \( 9216 - 9198 = 18 \). So \( 9216 \div 42 = 219 \) with remainder 18.

Wait, maybe the first problem is \( 9216 \div 42 \). Let's confirm the notation: the box is for the quotient. Let's do long division properly.

Long division of 9216 by 42:

• 42 into 92: 2 times (42*2=84), remainder 8.
• Bring down 1: 81. 42 into 81: 1 time (42*1=42), remainder 39.
• Bring down 6: 396. 42 into 396: 9 times (42*9=378), remainder 18.

So the quotient is 219, remainder 18. So the box should have 219? Wait, maybe the problem is written as \( 42 \enclose{longdiv}{9216} \), so the quotient is 219, remainder 18.

Let's take another problem, say problem 5: \( 482 \div 77 \)

Step 1: Estimate 776=462, 777=539 (too big)

So estimate quotient is 6.

Step 2: Calculate 77*6=462, subtract from 482: 482-462=20

So \( 482 \div 77 = 6 \) with remainder 20.

Let's do problem 1 properly (assuming the first problem is \( 9216 \div 42 \)):

Step 1: Divide 92 (thousands and hundreds place) by 42. \( 42 \times 2 = 84 \), subtract: \( 92 - 84 = 8 \)

Step 2: Bring down 1 (tens place) to get 81. \( 42 \times 1 = 42 \), subtract: \( 81 - 42 = 39 \)

Step 3: Bring down 6 (ones place) to get 396. \( 42 \times 9 = 378 \), subtract: \( 396 - 378 = 18 \)

Step 4: The quotient is \( 219 \) (2 from first step, 1 from second, 9 from third) and remainder 18.

Answer:

For problem 1 (\( 9216 \div 42 \)), the quotient is \( 219 \) (remainder 18). So the box should have \( 219 \).

(Note: If the problem is different, please clarify the exact division problem. For example, if it's \( 9216 \div 42 \), the answer is 219 with remainder 18. If it's another problem, adjust accordingly.)