To add the fractions [tex]\(\frac{2}{5}\)[/tex] and [tex]\(\frac{3}{10}\)[/tex], follow these steps:
1. Find a common denominator:
- The denominators of the fractions are 5 and 10. The least common multiple (LCM) of 5 and 10 is 10.
2. Convert each fraction to an equivalent fraction with the common denominator:
- For [tex]\(\frac{2}{5}\)[/tex], multiply both the numerator and the denominator by 2 to get [tex]\(\frac{4}{10}\)[/tex].
- The fraction [tex]\(\frac{3}{10}\)[/tex] already has the common denominator 10, so it remains [tex]\(\frac{3}{10}\)[/tex].
3. Add the fractions:
- Now that both fractions have the same denominator, you can add their numerators: [tex]\(4 + 3 = 7\)[/tex].
- The sum is [tex]\(\frac{7}{10}\)[/tex].
4. Simplify the fraction if possible:
- The fraction [tex]\(\frac{7}{10}\)[/tex] is already in its simplest form because 7 and 10 have no common factors other than 1.
So, the sum of [tex]\(\frac{2}{5}\)[/tex] and [tex]\(\frac{3}{10}\)[/tex] is [tex]\(\frac{7}{10}\)[/tex].
Thus, [tex]\(\frac{2}{5} + \frac{3}{10} = \frac{7}{10}\)[/tex].
