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Answer :
To find out which expression provides a better estimate for [tex]\(37.6 \div 11\)[/tex], we will evaluate the expressions [tex]\(30 \div 10\)[/tex] and [tex]\(40 \div 10\)[/tex] to see which is closer to the actual quotient.
1. First Expression: Evaluate [tex]\(30 \div 10\)[/tex].
- [tex]\(30 \div 10 = 3\)[/tex]
2. Second Expression: Evaluate [tex]\(40 \div 10\)[/tex].
- [tex]\(40 \div 10 = 4\)[/tex]
Now, we compare these estimates to the actual result of [tex]\(37.6 \div 11\)[/tex]:
3. Actual Division: Calculate [tex]\(37.6 \div 11\)[/tex].
- The actual result is approximately [tex]\(3.42\)[/tex].
4. Determine Which Estimate is Closer:
- Compare the distance between each estimate and the actual result.
- For [tex]\(30 \div 10 = 3\)[/tex], the difference is approximately [tex]\(0.42\)[/tex].
- For [tex]\(40 \div 10 = 4\)[/tex], the difference is approximately [tex]\(0.58\)[/tex].
Since the difference is smaller for [tex]\(30 \div 10 = 3\)[/tex], this estimate is closer to the actual quotient.
Therefore, the expression [tex]\(30 \div 10\)[/tex] gives a better estimate, so:
[tex]\[ 37.6 \div 11 \text{ is about } 3 \][/tex]
1. First Expression: Evaluate [tex]\(30 \div 10\)[/tex].
- [tex]\(30 \div 10 = 3\)[/tex]
2. Second Expression: Evaluate [tex]\(40 \div 10\)[/tex].
- [tex]\(40 \div 10 = 4\)[/tex]
Now, we compare these estimates to the actual result of [tex]\(37.6 \div 11\)[/tex]:
3. Actual Division: Calculate [tex]\(37.6 \div 11\)[/tex].
- The actual result is approximately [tex]\(3.42\)[/tex].
4. Determine Which Estimate is Closer:
- Compare the distance between each estimate and the actual result.
- For [tex]\(30 \div 10 = 3\)[/tex], the difference is approximately [tex]\(0.42\)[/tex].
- For [tex]\(40 \div 10 = 4\)[/tex], the difference is approximately [tex]\(0.58\)[/tex].
Since the difference is smaller for [tex]\(30 \div 10 = 3\)[/tex], this estimate is closer to the actual quotient.
Therefore, the expression [tex]\(30 \div 10\)[/tex] gives a better estimate, so:
[tex]\[ 37.6 \div 11 \text{ is about } 3 \][/tex]
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