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Answer :
To solve this problem and estimate the total length of the trench Eli dug, let's break it down into manageable steps:
1. Understanding the Problem:
- Eli dug a trench that is [tex]\(\frac{18}{20}\)[/tex] of a meter long on the first day.
- On the second day, he dug an additional [tex]\(\frac{17}{20}\)[/tex] of a meter.
2. Adding the Fractions:
- First, we need to add these two lengths together to find the total length he dug over the two days.
- [tex]\(\frac{18}{20} + \frac{17}{20}\)[/tex].
3. Calculate the Total Length:
- When you add the fractions [tex]\(\frac{18}{20}\)[/tex] and [tex]\(\frac{17}{20}\)[/tex], you combine the numerators while keeping the denominator the same:
[tex]\[
\frac{18 + 17}{20} = \frac{35}{20}.
\][/tex]
- Convert [tex]\(\frac{35}{20}\)[/tex] to a decimal, which equals 1.75 meters.
4. Estimating the Total Length:
- Given the options:
- [tex]\(\frac{1}{2}\)[/tex] meter
- 1 meter
- [tex]\(1 \frac{1}{2}\)[/tex] meters
- 2 meters
- We need to choose the closest estimation to 1.75 meters.
- The total length of 1.75 meters is closer to 2 meters than it is to any other option provided.
Therefore, the most reasonable estimate for the total length of the trench that Eli dug over the two days is 2 meters.
1. Understanding the Problem:
- Eli dug a trench that is [tex]\(\frac{18}{20}\)[/tex] of a meter long on the first day.
- On the second day, he dug an additional [tex]\(\frac{17}{20}\)[/tex] of a meter.
2. Adding the Fractions:
- First, we need to add these two lengths together to find the total length he dug over the two days.
- [tex]\(\frac{18}{20} + \frac{17}{20}\)[/tex].
3. Calculate the Total Length:
- When you add the fractions [tex]\(\frac{18}{20}\)[/tex] and [tex]\(\frac{17}{20}\)[/tex], you combine the numerators while keeping the denominator the same:
[tex]\[
\frac{18 + 17}{20} = \frac{35}{20}.
\][/tex]
- Convert [tex]\(\frac{35}{20}\)[/tex] to a decimal, which equals 1.75 meters.
4. Estimating the Total Length:
- Given the options:
- [tex]\(\frac{1}{2}\)[/tex] meter
- 1 meter
- [tex]\(1 \frac{1}{2}\)[/tex] meters
- 2 meters
- We need to choose the closest estimation to 1.75 meters.
- The total length of 1.75 meters is closer to 2 meters than it is to any other option provided.
Therefore, the most reasonable estimate for the total length of the trench that Eli dug over the two days is 2 meters.
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