To solve the problem of finding out how much of the school each student cleaned, we follow these steps:
1. Total Number of Students:
The total number of students who participated in the cleaning campaign is 1450.
2. Portion of the School Cleaned:
The students collectively cleaned [tex]\(\frac{5}{7}\)[/tex] of the school.
3. Portion Cleaned by Each Student:
Since the work was equally shared by all the students, we need to find out how much of the school was cleaned by each student individually.
To determine this, we divide the total portion of the school cleaned by the number of students:
[tex]\[
\text{Portion cleaned by each student} = \frac{\text{Total portion cleaned}}{\text{Total number of students}}
\][/tex]
Plugging in the values we have:
[tex]\[
\text{Portion cleaned by each student} = \frac{\frac{5}{7}}{1450}
\][/tex]
4. Simplifying the Expression:
To simplify the fraction:
[tex]\[
\frac{\frac{5}{7}}{1450} = \frac{5}{7 \times 1450}
\][/tex]
Multiplying the denominator:
[tex]\[
7 \times 1450 = 10150
\][/tex]
Thus, the fraction becomes:
[tex]\[
\frac{5}{10150}
\][/tex]
5. Final Answer:
Converting this fraction into a decimal for a clearer understanding, we get:
[tex]\[
\frac{5}{10150} \approx 0.0004926108374384236
\][/tex]
Therefore, the portion of the school cleaned by each student is approximately [tex]\( 0.0004926108374384236 \)[/tex].
