Certainly! Let's solve the problem step-by-step:
1. Identify the Given Fractions:
We have the fractions [tex]\(\frac{2}{5}\)[/tex], [tex]\(\frac{1}{4}\)[/tex], and [tex]\(\frac{7}{10}\)[/tex].
2. Find the Least Common Denominator (LCD):
We need to find the least common multiple (LCM) of the denominators 5, 4, and 10.
The LCM of 5, 4, and 10 is 20.
3. Convert Each Fraction to Have the Same Denominator (20):
- For [tex]\(\frac{2}{5}\)[/tex]:
[tex]\[
\frac{2}{5} = \frac{2 \times 4}{5 \times 4} = \frac{8}{20}
\][/tex]
- For [tex]\(\frac{1}{4}\)[/tex]:
[tex]\[
\frac{1}{4} = \frac{1 \times 5}{4 \times 5} = \frac{5}{20}
\][/tex]
- For [tex]\(\frac{7}{10}\)[/tex]:
[tex]\[
\frac{7}{10} = \frac{7 \times 2}{10 \times 2} = \frac{14}{20}
\][/tex]
So, the converted fractions are [tex]\(\frac{8}{20}\)[/tex], [tex]\(\frac{5}{20}\)[/tex], and [tex]\(\frac{14}{20}\)[/tex].
4. Add the Numerators of the Converted Fractions:
[tex]\[
\frac{8}{20} + \frac{5}{20} + \frac{14}{20} = \frac{8 + 5 + 14}{20} = \frac{27}{20}
\][/tex]
5. Simplify the Result (if possible):
In this case, [tex]\(\frac{27}{20}\)[/tex] is already in its simplest form as the greatest common divisor (GCD) of 27 and 20 is 1.
Therefore, the answer to the problem is:
[tex]\[
\frac{2}{5} + \frac{1}{4} + \frac{7}{10} = \frac{27}{20}
\][/tex]
