Sure, let's break down the given mathematical expression step by step.
1. Simplify the fractions:
The first fraction is [tex]\(\frac{3}{6}\)[/tex]. This can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 3:
[tex]\[
\frac{3}{6} = \frac{3 \div 3}{6 \div 3} = \frac{1}{2}
\][/tex]
The second fraction is already [tex]\(\frac{1}{2}\)[/tex], so there is no need to simplify it further.
2. Calculate the product of the two fractions:
Now we multiply the two fractions together:
[tex]\[
\frac{1}{2} \times \frac{1}{2} = \frac{1 \times 1}{2 \times 2} = \frac{1}{4}
\][/tex]
3. Add the product to the initial value:
The initial value given is 15. We need to add the product of the fractions, [tex]\(\frac{1}{4}\)[/tex], to this initial value:
[tex]\[
15 + \frac{1}{4} = 15 + 0.25 = 15.25
\][/tex]
So, putting it all together, the simplified expression is:
[tex]\[
15 + \left(\frac{3}{6} \times \frac{1}{2}\right) = 15.25
\][/tex]
To summarize:
- The product of [tex]\(\frac{3}{6}\)[/tex] and [tex]\(\frac{1}{2}\)[/tex] is [tex]\(\frac{1}{4}\)[/tex].
- Adding [tex]\(\frac{1}{4}\)[/tex] to the initial value of 15 gives the final result of 15.25.
Thus, the detailed step-by-step solution shows that:
[tex]\[ \boxed{15.25} \][/tex]
