To solve the given problem, we need to find the coefficient of [tex]\(e\)[/tex] in the expression [tex]\(11 \frac{3}{15}e - \frac{4}{5}e\)[/tex]. Here is the detailed step-by-step solution:
1. Convert the mixed number to an improper fraction:
- The mixed number [tex]\(11 \frac{3}{15}\)[/tex] can be converted into an improper fraction by adding the whole part to the fractional part.
- Convert the fractional part [tex]\( \frac{3}{15} \)[/tex] to its simplest form by dividing the numerator and the denominator by their greatest common divisor, which is 3, yielding [tex]\( \frac{1}{5} \)[/tex].
- So, [tex]\( 11 \frac{3}{15} \)[/tex] becomes [tex]\( 11 + \frac{1}{5} \)[/tex].
2. Simplify the mixed number:
- Convert [tex]\( \frac{1}{5} \)[/tex] to decimal form, which is 0.2.
- Thus, the mixed number [tex]\( 11 + \frac{1}{5} \)[/tex] equals [tex]\( 11 + 0.2 = 11.2 \)[/tex].
3. Combine like terms involving [tex]\( e \)[/tex]:
- We now know that [tex]\( 11 \frac{3}{15}e \)[/tex] simplifies to [tex]\( 11.2e \)[/tex].
- We need to subtract [tex]\( \frac{4}{5}e \)[/tex] from [tex]\( 11.2e \)[/tex].
- Convert [tex]\( \frac{4}{5} \)[/tex] to a decimal, which is 0.8.
- Thus, [tex]\( \frac{4}{5}e \)[/tex] becomes [tex]\( 0.8e \)[/tex].
4. Perform the subtraction:
- Subtract [tex]\( 0.8e \)[/tex] from [tex]\( 11.2e \)[/tex]:
[tex]\[
11.2e - 0.8e = (11.2 - 0.8)e = 10.4e
\][/tex]
5. Identify the coefficient:
- The coefficient of [tex]\( e \)[/tex] in the expression [tex]\( 11.2e - 0.8e \)[/tex] is [tex]\( 10.4 \)[/tex].
Thus, the coefficient of [tex]\( e \)[/tex] is [tex]\( \boxed{10.4} \)[/tex].
