Solve: 1/4 ÷ 1/2 + 1/4 - Mixed Fraction Operations

Complete the following exercise:

$\frac{1}{4}:\frac{1}{2}+\frac{1}{4}=\text{?}$

To solve the problem $\frac{1}{4} : \frac{1}{2} + \frac{1}{4}$, follow these steps:

Step 1: Perform the division $\frac{1}{4} : \frac{1}{2}$.

• When dividing by a fraction, multiply by the reciprocal. Hence, $\frac{1}{4} : \frac{1}{2}$ becomes $\frac{1}{4} \times \frac{2}{1}$.
• Multiply the numerators: $1 \times 2 = 2$.
• Multiply the denominators: $4 \times 1 = 4$.
• So, $\frac{1}{4} \times \frac{2}{1} = \frac{2}{4} = \frac{1}{2}$ after simplification.

Step 2: Now add the result from Step 1 to $\frac{1}{4}$.

• We need to add $\frac{1}{2} + \frac{1}{4}$.
• Convert $\frac{1}{2}$ to have a common denominator with $\frac{1}{4}$. $\frac{1}{2} = \frac{2}{4}$.
• Add the fractions: $\frac{2}{4} + \frac{1}{4} = \frac{3}{4}$.

Therefore, the solution to the problem is $\frac{3}{4}$.