The task in the image is asking you to add two fractions: $\frac{1}{2}$ and $\frac{3}{4}$. The first instruction is to rewrite the expression using a common denominator.

Step 1: Finding a common denominator

The denominators of the two fractions are 2 and 4. The least common denominator (LCD) of 2 and 4 is 4.

Step 2: Rewriting fractions

• $\frac{1}{2}$ needs to be rewritten with a denominator of 4. Multiply both the numerator and denominator of $\frac{1}{2}$ by 2: $\frac{1}{2} = \frac{2}{4}$

• The fraction $\frac{3}{4}$ already has a denominator of 4, so it stays as $\frac{3}{4}$.

Step 3: Adding the fractions

Now, add the two fractions with a common denominator: $\frac{2}{4} + \frac{3}{4} = \frac{5}{4}$ The result is $\frac{5}{4}$, which is an improper fraction. You can leave it as $\frac{5}{4}$ or convert it to a mixed number: $\frac{5}{4} = 1 \frac{1}{4}$

Would you like more details on these steps or additional help with this problem?

Here are 5 related questions:

1. How do you subtract fractions with different denominators?
2. What is the least common denominator, and why is it important?
3. Can improper fractions always be written as mixed numbers?
4. How would you multiply or divide two fractions like these?
5. What is the best strategy for finding common denominators quickly?

Tip: When adding or subtracting fractions, always look for the least common denominator to simplify the calculations!