High School

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------------------------------------------------ Simplify the expression:

[tex]
\[
\begin{array}{l}
\frac{3 \times 6}{4 \times 6} + \frac{5 + 4}{6 + 4} = \frac{18}{24} + \frac{9}{10} \\
= \frac{3}{4} + \frac{9}{10} \\
= \frac{15}{20} + \frac{18}{20} \\
= \frac{33}{20} = 1\frac{13}{20}
\end{array}
\]
[/tex]

Note: Ensure all steps in calculations are shown and verified for accuracy.

Answer :

Sure, let's go through the steps to solve the problem and understand how the result was obtained.

1. Calculate Each Fraction Separately:
- The first term is calculated as [tex]\(\frac{3 \times 6}{4 \times 6}\)[/tex].
- Simplifying that, we have [tex]\(\frac{18}{24}\)[/tex], which is equal to 0.75.

2. Calculate the Second Term:
- The second term is [tex]\(\frac{5+4}{6+4}\)[/tex].
- Simplifying, we get [tex]\(\frac{9}{10}\)[/tex], which is equal to 0.9.

3. Add the Two Terms Together:
- The combined value of the two terms is 0.75 + 0.9, which equals 1.65.

4. Combine Fractions and Simplify:
- Combining the fractions [tex]\(\frac{18}{24} + \frac{20}{24}\)[/tex], we focus on a common denominator.
- This gives us [tex]\(\frac{38}{24}\)[/tex], which simplifies to approximately 1.58333.

5. Express the Result as a Mixed Number:
- The next step is to express the total as a mixed number.
- This results in [tex]\(1 + \frac{14}{24}\)[/tex].
- The fractional part, [tex]\(\frac{14}{24}\)[/tex], simplifies to approximately 0.58333.

6. Simplifying Further:
- Finally, when you divide [tex]\(\frac{14}{24}\)[/tex] by 2, you get approximately 0.29167.

That's how we reach the solution with the series of calculations we performed!