To add the fractions [tex]\(\frac{5}{8}\)[/tex] and [tex]\(\frac{3}{4}\)[/tex], follow these steps:
1. Identify a common denominator: The denominators of the fractions are 8 and 4. The least common denominator (LCD) of 8 and 4 is 8.
2. Convert the fractions to have the same denominator:
- [tex]\(\frac{5}{8}\)[/tex]: This fraction already has the common denominator of 8, so it remains the same.
- [tex]\(\frac{3}{4}\)[/tex]: To convert [tex]\(\frac{3}{4}\)[/tex] to a fraction with a denominator of 8, multiply the numerator and the denominator by 2:
[tex]\[
\frac{3}{4} \times \frac{2}{2} = \frac{6}{8}
\][/tex]
3. Add the numerators: Now that both fractions have the same denominator, add the numerators together while keeping the denominator the same.
[tex]\[
\frac{5}{8} + \frac{6}{8} = \frac{5 + 6}{8} = \frac{11}{8}
\][/tex]
4. Simplify the result (if necessary): [tex]\(\frac{11}{8}\)[/tex] is an improper fraction, which can also be written as a mixed number. Divide 11 by 8:
- 11 divided by 8 is 1 with a remainder of 3.
- Therefore, [tex]\(\frac{11}{8} = 1 \frac{3}{8}\)[/tex].
In decimal form, [tex]\(\frac{11}{8}\)[/tex] is equivalent to approximately 1.375. So, in summary:
- The first fraction is [tex]\(\frac{5}{8}\)[/tex] or 0.625.
- The second fraction is [tex]\(\frac{6}{8}\)[/tex] or [tex]\(\frac{3}{4}\)[/tex] or 0.75.
- The result of the addition is [tex]\(\frac{11}{8}\)[/tex] or 1.375.
Thus, [tex]\(\frac{5}{8} + \frac{3}{4} = \frac{11}{8} = 1.375\)[/tex].
