Division Ratios
1. **Problem 6:** Divide 5,264 by 52 and write the quotient and remainder.
2. **Problem 7:** Divide 8,630 by 65 and write the quotient and remainder.
3. **Problem 8:** Determine if a bat flying at 85 miles per hour can fly 29,401 miles around Earth in less than 2 weeks.
4. **Problem 9:** Analyze the ratio relationship between circles and boxes in the diagram.
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### Step 1: Divide 5,264 by 52
- Use division: $$5264 \div 52$$
- Calculate quotient: $$52 \times 101 = 5252$$
- Remainder: $$5264 - 5252 = 12$$
**Answer:** Quotient = 101, Remainder = 12
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### Step 2: Divide 8,630 by 65
- Use division: $$8630 \div 65$$
- Calculate quotient: $$65 \times 132 = 8580$$
- Remainder: $$8630 - 8580 = 50$$
**Answer:** Quotient = 132, Remainder = 50
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### Step 3: Bat flying problem
- Speed = 85 miles/hour
- Distance = 29,401 miles
- Time to fly: $$\text{time} = \frac{\text{distance}}{\text{speed}} = \frac{29401}{85} \approx 345.9 \text{ hours}$$
- Convert hours to days: $$\frac{345.9}{24} \approx 14.4 \text{ days}$$
- Two weeks = 14 days
Since 14.4 days is slightly more than 14 days, the bat would take just over 2 weeks.
**Answer:** Disagree with Yuna; it would take slightly more than 2 weeks.
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### Step 4: Ratio relationship analysis
- Diagram shows 4 groups: 4 circles, 4 boxes, 4 circles, 4 boxes
- Total circles: $$4 + 4 = 8$$
- Total boxes: $$4 + 4 = 8$$
Check each statement:
A. For every 4 boxes, there are 12 circles.
- False, ratio is 8 circles to 8 boxes, or 1:1.
B. For every 4 boxes, there are 3 circles.
- False, ratio is 1:1.
C. For every 4 circles, there are 3 boxes.
- False, ratio is 1:1.
D. For every 3 circles, there is 1 box.
- False, ratio is 1:1.
E. For every 1 box, there are 3 circles.
- False, ratio is 1:1.
**Answer:** None of the statements accurately describe the ratio shown.