To find the sum of the fractions [tex]\( \frac{2}{5} \)[/tex] and [tex]\( \frac{2}{4} \)[/tex], follow these steps:
1. Find a common denominator:
The denominators of the fractions are 5 and 4. A common multiple of these denominators is 20.
2. Convert each fraction to an equivalent fraction with the common denominator:
- For [tex]\( \frac{2}{5} \)[/tex]:
[tex]\[
\frac{2}{5} = \frac{2 \times 4}{5 \times 4} = \frac{8}{20}
\][/tex]
- For [tex]\( \frac{2}{4} \)[/tex]:
[tex]\[
\frac{2}{4} = \frac{2 \times 5}{4 \times 5} = \frac{10}{20}
\][/tex]
3. Add the numerators of these equivalent fractions:
[tex]\[
\frac{8}{20} + \frac{10}{20} = \frac{8 + 10}{20} = \frac{18}{20}
\][/tex]
Therefore, the sum of [tex]\( \frac{2}{5} \)[/tex] and [tex]\( \frac{2}{4} \)[/tex] is [tex]\( \frac{18}{20}\)[/tex].
Simplifying [tex]\( \frac{18}{20} \)[/tex] by dividing numerator and denominator by their greatest common divisor, which is 2:
[tex]\[
\frac{18 \div 2}{20 \div 2} = \frac{9}{10}
\][/tex]
So, the best answer is:
D. [tex]\( \frac{9}{10} \)[/tex]
