Let's determine the sum of the following:
[tex]\text{ }\frac{\text{ 1}}{\text{ 4}}\text{ + }\frac{\text{ 2}}{\text{ 7}}[/tex]Step 1: Make the two fractions into similar fractions.
The LCM of 4 and 7 is 28, thus, let's convert each fraction into one with a denominator of 28.
We get,
[tex]\text{ }\frac{\text{ 1}}{\text{ 4}}\text{ = }\frac{\text{ 1 x }7}{\text{ 28}}\text{ = }\frac{7}{28}[/tex][tex]\text{ }\frac{\text{ 2}}{\text{ 7}}\text{ = }\frac{\text{ 2 x 4}}{\text{ 28}}\text{ = }\frac{\text{ 8}}{\text{ 28}}[/tex]Step 2: Add the fractions.
[tex]\text{ }\frac{\text{ 1}}{\text{ 4}}\text{ + }\frac{\text{ 2}}{\text{ 7}}[/tex][tex]\text{ }\frac{7}{28}\text{ + }\frac{8}{28}\text{ = }\frac{15}{28}[/tex]Therefore, the answer is 15/28.