We need to add the fractions [tex]\(\frac{5}{12}\)[/tex] and [tex]\(\frac{3}{8}\)[/tex] by rewriting each fraction with the least common denominator (LCD).
Step-by-Step Solution:
1. Find the Least Common Denominator (LCD):
- The denominators of our fractions are 12 and 8.
- The least common denominator (LCD) of 12 and 8 is 24.
2. Rewrite each fraction with the LCD:
- To rewrite [tex]\(\frac{5}{12}\)[/tex] with a denominator of 24, we need to multiply both the numerator and the denominator by the same number. Since [tex]\(\frac{24}{12} = 2\)[/tex], we multiply by 2:
[tex]\[
\frac{5}{12} = \frac{5 \times 2}{12 \times 2} = \frac{10}{24}
\][/tex]
- To rewrite [tex]\(\frac{3}{8}\)[/tex] with a denominator of 24, we need to multiply both the numerator and the denominator by the same number. Since [tex]\(\frac{24}{8} = 3\)[/tex], we multiply by 3:
[tex]\[
\frac{3}{8} = \frac{3 \times 3}{8 \times 3} = \frac{9}{24}
\][/tex]
3. Add the fractions with the common denominator:
- Now we have [tex]\(\frac{10}{24}\)[/tex] and [tex]\(\frac{9}{24}\)[/tex].
- Adding these fractions gives:
[tex]\[
\frac{10}{24} + \frac{9}{24} = \frac{10 + 9}{24} = \frac{19}{24}
\][/tex]
Answers:
- The least common denominator (LCD) is [tex]\(24\)[/tex].
- The numerator 5 becomes [tex]\(10\)[/tex] when changing the denominator to 24.
- The numerator 3 becomes [tex]\(9\)[/tex] when changing the denominator to 24.
Thus, the sum of the fractions [tex]\(\frac{5}{12} + \frac{3}{8}\)[/tex] is [tex]\(\frac{19}{24}\)[/tex].
