Question
3. For which quotient is 70 a reasonable estimate? Choose all that apply. ( 3 answers) A. \( 194 \div 5 \) (B. \( 1,398 \div 69 \) C. \( 5,612 \div 82 \) (D. \( 2,777 \div 41 \) (E.) \( 4,209 \div 58 \) F. \( 6,254 \div 73 \)
Ask by Boyd Savage. in the United States
Feb 27,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The reasonable estimates of 70 are for options C, D, and E.
Solution
To determine which quotients are reasonable estimates for 70, we can estimate each division by rounding the numbers to make the calculations simpler.
1. **Option A: \( 194 \div 5 \)**
- Estimate: \( 200 \div 5 = 40 \)
2. **Option B: \( 1,398 \div 69 \)**
- Estimate: \( 1,400 \div 70 = 20 \)
3. **Option C: \( 5,612 \div 82 \)**
- Estimate: \( 5,600 \div 80 = 70 \)
4. **Option D: \( 2,777 \div 41 \)**
- Estimate: \( 2,800 \div 40 = 70 \)
5. **Option E: \( 4,209 \div 58 \)**
- Estimate: \( 4,200 \div 60 = 70 \)
6. **Option F: \( 6,254 \div 73 \)**
- Estimate: \( 6,300 \div 70 = 90 \)
Now, let's summarize the estimates:
- A: 40
- B: 20
- C: 70
- D: 70
- E: 70
- F: 90
The options that yield a reasonable estimate of 70 are:
- C. \( 5,612 \div 82 \)
- D. \( 2,777 \div 41 \)
- E. \( 4,209 \div 58 \)
Thus, the correct answers are **C, D, and E**.
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Simplify this solution Extra Insights
When estimating quotients, a good strategy is to round the numbers to simplify the division. For example, in option A, \(194\) rounds to \(200\) and \(5\) remains \(5\), giving an estimate of \(200 \div 5 = 40\). Nonetheless, this is clearly below \(70\). Checking options B through F, only option D gives an approximate value of \(2,777 \div 41\), where rounding yields \(2,800 \div 40 = 70\). Similarly, option E with \(4,209 \div 58\) rounds nicely to \(4,200 \div 60\) which also leads close to \(70\). Lastly, option F proves to be close as well! Therefore, the reasonable estimates fall under options \(D\), \(E\), and \(F\).
