Calculate (1/2)² + (1/3)² + 1/4: Sum of Squared Fractions Problem

To solve the expression $(\frac{1}{2})^2+(\frac{1}{3})^2+\frac{1}{4}$, we will follow the order of operations and break it down step by step:

Step 1: Calculate the squares of the fractions:

- For$(\frac{1}{2})^2$:

$(\frac{1}{2})^2 = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4}$

- For $(\frac{1}{3})^2$:

$(\frac{1}{3})^2 = \frac{1}{3} \times \frac{1}{3} = \frac{1}{9}$

Step 2: Add the fractions together:

- Adding $\frac{1}{4}$, $\frac{1}{9}$, and $\frac{1}{4}$:

The least common denominator (LCD) of $4$ and $9$ is $36$.

Rewrite each fraction with the LCD:

• $\frac{1}{4} = \frac{9}{36}$

• $\frac{1}{9} = \frac{4}{36}$

• $\frac{1}{4} = \frac{9}{36}$

Now add them together:

$\frac{9}{36} + \frac{4}{36} + \frac{9}{36} = \frac{22}{36}$

Step 3: Simplify the result:

$\frac{22}{36}$ can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is $2$:

• $\frac{22 \div 2}{36 \div 2} = \frac{11}{18}$

Thus, the simplified result of the expression $(\frac{1}{2})^2+(\frac{1}{3})^2+\frac{1}{4}$ is $\frac{11}{18}$, which matches the provided correct answer.