Let's evaluate the given expression [tex]\(\frac{5}{12} + \frac{1}{4} + \frac{1}{8}\)[/tex] step by step to determine if it equals [tex]\(\frac{1}{2}\)[/tex].
1. Identify the fractions: We have the fractions [tex]\(\frac{5}{12}\)[/tex], [tex]\(\frac{1}{4}\)[/tex], and [tex]\(\frac{1}{8}\)[/tex].
2. Find a common denominator: To add these fractions together, we need to have a common denominator. The denominators we are working with are 12, 4, and 8. The least common multiple (LCM) of these numbers is 24.
- For [tex]\(\frac{5}{12}\)[/tex], we convert it to have a denominator of 24:
[tex]\[
\frac{5}{12} = \frac{5 \times 2}{12 \times 2} = \frac{10}{24}
\][/tex]
- For [tex]\(\frac{1}{4}\)[/tex], we convert it to have a denominator of 24:
[tex]\[
\frac{1}{4} = \frac{1 \times 6}{4 \times 6} = \frac{6}{24}
\][/tex]
- For [tex]\(\frac{1}{8}\)[/tex], we convert it to have a denominator of 24:
[tex]\[
\frac{1}{8} = \frac{1 \times 3}{8 \times 3} = \frac{3}{24}
\][/tex]
3. Add the fractions: Now that all the fractions have the same denominator, we can add them directly:
[tex]\[
\frac{10}{24} + \frac{6}{24} + \frac{3}{24} = \frac{10 + 6 + 3}{24} = \frac{19}{24}
\][/tex]
4. Compare with the expected sum: The result of the sum of the fractions is [tex]\(\frac{19}{24}\)[/tex]. We need to compare this to [tex]\(\frac{1}{2}\)[/tex] to see if they are equal. Simplify [tex]\(\frac{1}{2}\)[/tex] to the same denominator of 24 to compare directly:
[tex]\[
\frac{1}{2} = \frac{1 \times 12}{2 \times 12} = \frac{12}{24}
\][/tex]
5. Check equality: Comparing [tex]\(\frac{19}{24}\)[/tex] and [tex]\(\frac{12}{24}\)[/tex]:
[tex]\[
\frac{19}{24} \neq \frac{12}{24}
\][/tex]
Therefore, [tex]\[\frac{5}{12} + \frac{1}{4} + \frac{1}{8} \neq \frac{1}{2}\][/tex].
The result of adding the fractions [tex]\(\frac{5}{12}\)[/tex], [tex]\(\frac{1}{4}\)[/tex], and [tex]\(\frac{1}{8}\)[/tex] is [tex]\(\frac{19}{24}\)[/tex], which is not equal to [tex]\(\frac{1}{2}\)[/tex].
