$\frac{2}{11}+\frac{3}{4}=$
To add the two fractions \(\frac{2}{11}\) and \(\frac{3}{4}\), we first need a common denominator. The denominators are 11 and 4. Since 11 is a prime number and does not share any factors with 4, the least common denominator (LCD) is their product:
\[11 \times 4 = 44\]
Next, we convert each fraction to have the common denominator of 44.
For \(\frac{2}{11}\), we multiply the numerator and the denominator by 4:
\[\frac{2}{11} = \frac{2 \times 4}{11 \times 4} = \frac{8}{44}\]
For \(\frac{3}{4}\), we multiply the numerator and the denominator by 11:
\[\frac{3}{4} = \frac{3 \times 11}{4 \times 11} = \frac{33}{44}\]
Now that both fractions have the same denominator, we can add their numerators while keeping the denominator the same:
\[\frac{8}{44} + \frac{33}{44} = \frac{8 + 33}{44} = \frac{41}{44}\]
The number 41 is a prime number, so the fraction \(\frac{41}{44}\) cannot be simplified further. Thus, the result is \(\boxed{\frac{41}{44}}\).
In everyday life, adding fractions is essential for tasks like cooking. Imagine you are following a recipe that calls for \(\frac{2}{11}\) of a cup of water and \(\frac{3}{4}\) of a cup of milk to create a specific batter. To determine the total volume of liquid in the mixture, you need to add these two fractions, resulting in \(\frac{41}{44}\) of a cup of liquid, ensuring your recipe's measurements are precise and consistent.