To add the fractions [tex]\(\frac{3}{8}\)[/tex] and [tex]\(\frac{7}{4}\)[/tex], follow these steps:
1. Convert each fraction to a common denominator:
The denominators of [tex]\(\frac{3}{8}\)[/tex] and [tex]\(\frac{7}{4}\)[/tex] are 8 and 4, respectively. To add fractions, they must have the same denominator. Here, we can convert [tex]\(\frac{7}{4}\)[/tex] to a fraction with the denominator 8:
[tex]\[
\frac{7}{4} = \frac{7 \times 2}{4 \times 2} = \frac{14}{8}
\][/tex]
2. Rewrite the equation with the common denominator:
So the fractions become:
[tex]\[
\frac{3}{8} + \frac{14}{8}
\][/tex]
3. Add the numerators:
Now, add the numerators while keeping the denominator the same:
[tex]\[
\frac{3 + 14}{8} = \frac{17}{8}
\][/tex]
4. Convert the improper fraction to a mixed number (if desired):
[tex]\(\frac{17}{8}\)[/tex] can be written as a mixed number:
[tex]\[
17 \div 8 = 2 \text{ remainder } 1
\][/tex]
So, [tex]\(\frac{17}{8} = 2 \frac{1}{8}\)[/tex].
Thus, the final answer to adding [tex]\(\frac{3}{8}\)[/tex] and [tex]\(\frac{7}{4}\)[/tex] is:
[tex]\[
\frac{3}{8} + \frac{7}{4} = 2.125
\][/tex]
As a decimal, this sum is 2.125.
